A normal metal placed next to an s-wave superconductor develops superconducting correlations because of the "proximity effect" -- Cooper pairs penetrate some distance into the normal metal, for basically the same reason as the eigenstates in a finite square well leak some distance out of the well. (I think this is true; the point is that the Cooper pairs have a longish lifetime in the normal metal.) This shouldn't work for a ferromagnetic material, however, as the Cooper pairs -- being a spin-singlet -- ought to be broken and aligned with the ferromagnet if they stray into it. Efetov and coworkers made the rather surprising prediction (Bergeret et al, PRL 86, 4096 (2001)) that under certain conditions a singlet superconductor can induce a triplet proximity effect in the ferromagnet, with pair correlations (i.e., <>) that are odd in time (Bergeret et al, Rev. Mod. Phys. 77, 1321 (2005)). Norman Birge's group has a new preprint out claiming to have seen this proximity effect:
Observation of spin-triplet superconductivity in Co-based Josephson Junctions
arXiv:0912.0205
Authors: Trupti S. Khaire, Mazin A. Khasawneh, W. P. Pratt, Jr., Norman O. Birge
Abstract: We have measured a long-range supercurrent in Josephson junctions containing Co (a strong ferromagnetic material) when we insert thin layers of either PdNi or CuNi weakly-ferromagnetic alloys between the Co and the two superconducting Nb electrodes. The critical current in such junctions hardly decays for Co thicknesses in the range of 12-28 nm, whereas it decays very steeply in similar junctions without the alloy layers. The long-range supercurrent is controllable by the thickness of the alloy layer, reaching a maximum for a thickness of a few nm. These experimental observations provide strong evidence for induced spin-triplet pair correlations, which have been predicted to occur in superconducting/ferromagnetic hybrid systems in the presence of certain types of magnetic inhomogeneity.
Wednesday, December 2, 2009
Friday, November 20, 2009
The thermodynamic limit and the FQHE
I'm taking Tony Leggett's course on two-dimensional physics; it's the first time I've thought hard about the fractional quantum Hall effect, the quantum Hall and spin-Hall effects, fractional statistics, and related "topological" phenomena. I think I'm finally beginning to understand what's behind these effects, and it's essentially a rather subtle business with adiabaticity. Hopefully I'll straighten all of this out in due course; for now, here are two papers on the ground-state degeneracy of the FQHE:
---
http://prola.aps.org/abstract/PRB/v41/i13/p9377_1
Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
X.-G. Wen and Q. Niu
Phys. Rev. B 41, 9377 - 9396 (1990)
The fractional quantum Hall (FQH) states are shown to have q̃^g-fold ground-state degeneracy on a Riemann surface of genus g, where q̃ is the ground-state degeneracy in a torus topology. The ground-state degeneracies are directly related to the statistics of the quasiparticles given by θ=p̃π/q̃. The ground-state degeneracy is shown to be invariant against weak but otherwise arbitrary perturbations. Therefore the ground-state degeneracy provides a new quantum number, in addition to the Hall conductance, characterizing different phases of the FQH systems. The phases with different ground-state degeneracies are considered to have different topological orders. For a finite system of size L, the ground-state degeneracy is lifted. The energy splitting is shown to be at most of order e-L/ξ. We also show that the Ginzburg-Landau theory of the FQH states (in the low-energy limit) is a dual theory of the U(1) Chern-Simons topological theory.
http://prola.aps.org/abstract/PRL/v66/i6/p806_1
Fractional quantum Hall effect and multiple Aharonov-Bohm periods
D.J. Thouless and Y. Gefen
Phys. Rev. Lett. 66, 806 - 809 (1991)
An arrangement for obtaining Aharonov-Bohm oscillations of basic periodicity qh/e (q>1) is discussed. The relaxation towards h/e periodicity is characterized by a decay time exponential in the system size at zero temperature, and linear in this size at finite temperature.
---
The Thouless-Gefen paper is particularly good, see esp. Fig. 1. [I think the following text is unintelligible without the figure but should make sense once you look at it.] The idea is to consider the FQHE in a CD-shaped geometry (called, for obscure reasons, a Corbino disk) with a fixed field B through the "substance" of the disk -- which creates the FQHE -- and a variable flux F (sorry about the notation, I really ought to install the tex widget...) threading the hole. Quantum mechanics says that the ground state energy should be periodic in the flux threading the hole, with a period of one flux quantum; Cooper pairs give you half this period because they have charge 2e, whereas a system with "fractionally charged" excitations (say q = e/3, the classic Laughlin state) gives you three times this period, which appears to contradict a basic quantum mechanical result called the Byers-Yang theorem. Ultimately this turns out to be about level crossings (Fig. 1 of Thouless-Gefen): there are three ground states that have vanishingly small matrix elements mixing them; if one increased the flux F vanishingly slowly, one would track the ground state of the system, and have 1/e-periodic behavior; if one increased the flux rapidly, one would go straight up the original curve, not notice the level crossings, and get no periodicity at all ("physically" this corresponds to continually adding quasiparticles); in practice, one goes "rapidly" as far as the second level crossing and "adiabatically" with respect to that (b'se there's a much bigger avoided-level-crossing there) so one comes back to the ground state with 3/e periodicity.
A key corollary, I think, is that fractional charge (and therefore fractional statistics) are a consequence of non-avoided and avoided level crossings when you "slowly" move a particle around another -- i.e. a consequence of the order in which you take the limit of infinite system size and the limit of moving a particle around another (or ramping up a flux) infinitely slowly. This does not mean they aren't "real," of course, since phase transitions, which are evidently real, are also ultimately a consequence of the order in which one takes limits. It appears to be true that in all known cases of fractional statistics, at least of the abelian kind (another example is Kitaev's toric code model), one has this sort of ground-state degeneracy.
---
http://prola.aps.org/abstract/PRB/v41/i13/p9377_1
Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
X.-G. Wen and Q. Niu
Phys. Rev. B 41, 9377 - 9396 (1990)
The fractional quantum Hall (FQH) states are shown to have q̃^g-fold ground-state degeneracy on a Riemann surface of genus g, where q̃ is the ground-state degeneracy in a torus topology. The ground-state degeneracies are directly related to the statistics of the quasiparticles given by θ=p̃π/q̃. The ground-state degeneracy is shown to be invariant against weak but otherwise arbitrary perturbations. Therefore the ground-state degeneracy provides a new quantum number, in addition to the Hall conductance, characterizing different phases of the FQH systems. The phases with different ground-state degeneracies are considered to have different topological orders. For a finite system of size L, the ground-state degeneracy is lifted. The energy splitting is shown to be at most of order e-L/ξ. We also show that the Ginzburg-Landau theory of the FQH states (in the low-energy limit) is a dual theory of the U(1) Chern-Simons topological theory.
http://prola.aps.org/abstract/PRL/v66/i6/p806_1
Fractional quantum Hall effect and multiple Aharonov-Bohm periods
D.J. Thouless and Y. Gefen
Phys. Rev. Lett. 66, 806 - 809 (1991)
An arrangement for obtaining Aharonov-Bohm oscillations of basic periodicity qh/e (q>1) is discussed. The relaxation towards h/e periodicity is characterized by a decay time exponential in the system size at zero temperature, and linear in this size at finite temperature.
---
The Thouless-Gefen paper is particularly good, see esp. Fig. 1. [I think the following text is unintelligible without the figure but should make sense once you look at it.] The idea is to consider the FQHE in a CD-shaped geometry (called, for obscure reasons, a Corbino disk) with a fixed field B through the "substance" of the disk -- which creates the FQHE -- and a variable flux F (sorry about the notation, I really ought to install the tex widget...) threading the hole. Quantum mechanics says that the ground state energy should be periodic in the flux threading the hole, with a period of one flux quantum; Cooper pairs give you half this period because they have charge 2e, whereas a system with "fractionally charged" excitations (say q = e/3, the classic Laughlin state) gives you three times this period, which appears to contradict a basic quantum mechanical result called the Byers-Yang theorem. Ultimately this turns out to be about level crossings (Fig. 1 of Thouless-Gefen): there are three ground states that have vanishingly small matrix elements mixing them; if one increased the flux F vanishingly slowly, one would track the ground state of the system, and have 1/e-periodic behavior; if one increased the flux rapidly, one would go straight up the original curve, not notice the level crossings, and get no periodicity at all ("physically" this corresponds to continually adding quasiparticles); in practice, one goes "rapidly" as far as the second level crossing and "adiabatically" with respect to that (b'se there's a much bigger avoided-level-crossing there) so one comes back to the ground state with 3/e periodicity.
A key corollary, I think, is that fractional charge (and therefore fractional statistics) are a consequence of non-avoided and avoided level crossings when you "slowly" move a particle around another -- i.e. a consequence of the order in which you take the limit of infinite system size and the limit of moving a particle around another (or ramping up a flux) infinitely slowly. This does not mean they aren't "real," of course, since phase transitions, which are evidently real, are also ultimately a consequence of the order in which one takes limits. It appears to be true that in all known cases of fractional statistics, at least of the abelian kind (another example is Kitaev's toric code model), one has this sort of ground-state degeneracy.
Monday, October 26, 2009
Cond-mat journal club on AdS/CFT
Here's a cond-mat journal club thing on AdS/CFT and applications to cond-mat, e.g. explaining the strange metal phase. The commentary is written by cond-mat theorists incl. Abrahams who's most famous for being one of the Gang of Four.
Giant SPIDERs etc.
Some good recent stuff in PRL:
Giant Surface-Plasmon-Induced Drag Effect in Metal Nanowires
Maxim Durach,1 Anastasia Rusina,1 and Mark I. Stockman1,2,3
Phys. Rev. Lett. 103, 186801 (2009)
Here, for the first time we predict a giant surface-plasmon-induced drag-effect rectification (SPIDER), which exists under conditions of the extreme nanoplasmonic confinement. In nanowires, this giant SPIDER generates rectified THz potential differences up to 10 V and extremely strong electric fields up to ~105–106 V/cm. The giant SPIDER is an ultrafast effect whose bandwidth for nanometric wires is ~20 THz. It opens up a new field of ultraintense THz nanooptics with wide potential applications in nanotechnology and nanoscience, including microelectronics, nanoplasmonics, and biomedicine.
[sg] I haven't read this paper and I'm not sure I want to, I'm just awed by the brilliance of "giant SPIDER effect." This is obviously going to collect oodles of citations, mostly from me.
---
Holstein Polarons Near Surfaces
Glen L. Goodvin, Lucian Covaci, and Mona Berciu
Phys. Rev. Lett. 103, 176402 (2009)
We study the effects of a nearby surface on the spectral weight of a Holstein polaron, using the inhomogeneous momentum average approximation which is accurate over the entire range of electron-phonon (e-ph) coupling strengths. The broken translational symmetry is taken into account exactly. We find that the e-ph coupling gives rise to a large additional surface potential, with strong retardation effects, which may bind surface states even when they are not normally expected. The surface, therefore, has a significant effect and bulk properties are recovered only very far away from it. These results demonstrate that interpretation in terms of bulk quantities of spectroscopic data sensitive only to a few surface layers is not always appropriate.
[sg] The recent work on surface polarons is pretty interesting and it's something I'd like to get into at some point. It's primarily motivated by the recent glut of exptal work on heterostructures of strongly correlated materials; the interfaces often undergo substantial electronic and/or lattice reconstruction. Naturally these not-terribly-stable surfaces are morbidly sensitive to, e.g., the electrostatic force exerted by a moving electron.
I'm also curious about whether the authors are right about the interpretation of surface-based spectroscopic data.
---
Phys. Rev. Lett. 103, 177002 (2009)
Evidence for Two Time Scales in Long SNS Junctions
F. Chiodi, M. Aprili, and B. Reulet
We use microwave excitation to elucidate the dynamics of long superconductor–normal metal–superconductor Josephson junctions. By varying the excitation frequency in the range 10 MHz–40 GHz, we observe that the critical and retrapping currents, deduced from the dc voltage versus dc current characteristics of the junction, are set by two different time scales. The critical current increases when the ac frequency is larger than the inverse diffusion time in the normal metal, whereas the retrapping current is strongly modified when the excitation frequency is above the electron-phonon rate in the normal metal. Therefore the critical and retrapping currents are associated with elastic and inelastic scattering, respectively.
[sg] In the traditional Josephson junction model (i.e. tilted washboard + friction), switching happens when the washboard's wells cease to be metastable and retrapping happens when the terminal velocity of a particle going down the washboard goes to zero. Retrapping depends on friction and switching doesn't, so you have a clean separation of energy scales. In long junctions things are generally messier because switching depends on heat transfer from a locally normal area to the rest of the wire, etc.; however, this paper manages to retrieve a rather nice separation of scales.
Giant Surface-Plasmon-Induced Drag Effect in Metal Nanowires
Maxim Durach,1 Anastasia Rusina,1 and Mark I. Stockman1,2,3
Phys. Rev. Lett. 103, 186801 (2009)
Here, for the first time we predict a giant surface-plasmon-induced drag-effect rectification (SPIDER), which exists under conditions of the extreme nanoplasmonic confinement. In nanowires, this giant SPIDER generates rectified THz potential differences up to 10 V and extremely strong electric fields up to ~105–106 V/cm. The giant SPIDER is an ultrafast effect whose bandwidth for nanometric wires is ~20 THz. It opens up a new field of ultraintense THz nanooptics with wide potential applications in nanotechnology and nanoscience, including microelectronics, nanoplasmonics, and biomedicine.
[sg] I haven't read this paper and I'm not sure I want to, I'm just awed by the brilliance of "giant SPIDER effect." This is obviously going to collect oodles of citations, mostly from me.
---
Holstein Polarons Near Surfaces
Glen L. Goodvin, Lucian Covaci, and Mona Berciu
Phys. Rev. Lett. 103, 176402 (2009)
We study the effects of a nearby surface on the spectral weight of a Holstein polaron, using the inhomogeneous momentum average approximation which is accurate over the entire range of electron-phonon (e-ph) coupling strengths. The broken translational symmetry is taken into account exactly. We find that the e-ph coupling gives rise to a large additional surface potential, with strong retardation effects, which may bind surface states even when they are not normally expected. The surface, therefore, has a significant effect and bulk properties are recovered only very far away from it. These results demonstrate that interpretation in terms of bulk quantities of spectroscopic data sensitive only to a few surface layers is not always appropriate.
[sg] The recent work on surface polarons is pretty interesting and it's something I'd like to get into at some point. It's primarily motivated by the recent glut of exptal work on heterostructures of strongly correlated materials; the interfaces often undergo substantial electronic and/or lattice reconstruction. Naturally these not-terribly-stable surfaces are morbidly sensitive to, e.g., the electrostatic force exerted by a moving electron.
I'm also curious about whether the authors are right about the interpretation of surface-based spectroscopic data.
---
Phys. Rev. Lett. 103, 177002 (2009)
Evidence for Two Time Scales in Long SNS Junctions
F. Chiodi, M. Aprili, and B. Reulet
We use microwave excitation to elucidate the dynamics of long superconductor–normal metal–superconductor Josephson junctions. By varying the excitation frequency in the range 10 MHz–40 GHz, we observe that the critical and retrapping currents, deduced from the dc voltage versus dc current characteristics of the junction, are set by two different time scales. The critical current increases when the ac frequency is larger than the inverse diffusion time in the normal metal, whereas the retrapping current is strongly modified when the excitation frequency is above the electron-phonon rate in the normal metal. Therefore the critical and retrapping currents are associated with elastic and inelastic scattering, respectively.
[sg] In the traditional Josephson junction model (i.e. tilted washboard + friction), switching happens when the washboard's wells cease to be metastable and retrapping happens when the terminal velocity of a particle going down the washboard goes to zero. Retrapping depends on friction and switching doesn't, so you have a clean separation of energy scales. In long junctions things are generally messier because switching depends on heat transfer from a locally normal area to the rest of the wire, etc.; however, this paper manages to retrieve a rather nice separation of scales.
Friday, October 23, 2009
Title: Off-diagonal correlations in a one-dimensional gas of dipolar bosons
Authors: Tommaso Roscilde, Massimo Boninsegni
We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded, in favor of quasi-solidity. For all strengths of the dipolar interaction, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay; and the momentum distribution shows sharp kinks at the wavevectors of the oscillations, $Q = \pm 2\pi n$ (where $n$ is the atom density), beyond which it is strongly suppressed. This \emph{momentum filtering} effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that one-dimensional dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.
http://arxiv.org/abs/0910.4165
Authors: Tommaso Roscilde, Massimo Boninsegni
We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded, in favor of quasi-solidity. For all strengths of the dipolar interaction, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay; and the momentum distribution shows sharp kinks at the wavevectors of the oscillations, $Q = \pm 2\pi n$ (where $n$ is the atom density), beyond which it is strongly suppressed. This \emph{momentum filtering} effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that one-dimensional dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.
http://arxiv.org/abs/0910.4165
Thursday, October 22, 2009
Supersolid Helium and anamolous transport
Underlying Mechanism for the Giant Isochoric Compressibility of Solid 4he: Superclimb of Dislocations
authors:
S. G. Söyler,1 A. B. Kuklov,2 L. Pollet,3 N. V. Prokof'ev,1,4 and B. V. Svistunov1,4
In the experiment on superfluid transport in solid 4He [Phys. Rev. Lett. 100, 235301 (2008)], Ray and Hallock observed an anomalously large isochoric compressibility: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential, applied locally through Vycor “electrodes.” We propose that the effect is due to superclimb: edge dislocations can climb because of mass transport along superfluid cores. We corroborate the scenario by ab initio simulations of an edge dislocation in solid 4He at T=0.5 K. We argue that at low temperature the effect must be suppressed due to a crossover to the smooth dislocation.
http://link.aps.org/doi/10.1103/PhysRevLett.103.175301
authors:
S. G. Söyler,1 A. B. Kuklov,2 L. Pollet,3 N. V. Prokof'ev,1,4 and B. V. Svistunov1,4
In the experiment on superfluid transport in solid 4He [Phys. Rev. Lett. 100, 235301 (2008)], Ray and Hallock observed an anomalously large isochoric compressibility: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential, applied locally through Vycor “electrodes.” We propose that the effect is due to superclimb: edge dislocations can climb because of mass transport along superfluid cores. We corroborate the scenario by ab initio simulations of an edge dislocation in solid 4He at T=0.5 K. We argue that at low temperature the effect must be suppressed due to a crossover to the smooth dislocation.
http://link.aps.org/doi/10.1103/PhysRevLett.103.175301
Tuesday, October 20, 2009
QMC and Scaling
This letter addresses the case without a sign problem. I think eqn. 3 can be trivially applied to a DMC calculation. I should look at it further though.
Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions
Authors:
David Schwandt,1,2 Fabien Alet,1,2 and Sylvain Capponi1,2
1Laboratoire de Physique Théorique, Université de Toulouse, UPS, (IRSAMC), F-31062 Toulouse, France
2CNRS, LPT (IRSAMC), F-31062 Toulouse, France
Abstract:
When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.
http://link.aps.org/doi/10.1103/PhysRevLett.103.170501
Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions
Authors:
David Schwandt,1,2 Fabien Alet,1,2 and Sylvain Capponi1,2
1Laboratoire de Physique Théorique, Université de Toulouse, UPS, (IRSAMC), F-31062 Toulouse, France
2CNRS, LPT (IRSAMC), F-31062 Toulouse, France
Abstract:
When a system undergoes a quantum phase transition, the ground-state wave function shows a change of nature, which can be monitored using the fidelity concept. We introduce two quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behavior at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.
http://link.aps.org/doi/10.1103/PhysRevLett.103.170501
Sunday, October 11, 2009
Gowers on Complexity Bounds
Timothy Gowers has apparently been thinking about the P = NP problem. I've enjoyed his series of posts on this so far, even if the details are often a little over my head. Here's a link to the first post; the others can be accessed by conventional means.
Friday, October 9, 2009
New preprint
I have a new preprint on the arxiv with Siddhartha Lal and Paul Goldbart. It's about N-channel Kondo physics with interacting 1D bosons (e.g. cold atoms) as the leads.
Tuesday, October 6, 2009
Quenches as probes of quantum phase transitions
This numerical paper has some fascinating results, and the germ of a very clever idea (I heard about this work via Andy Millis):
Dynamical phase transition in correlated fermionic lattice systems
Martin Eckstein, Marcus Kollar, Philipp Werner
http://arxiv.org/abs/0904.0976
Abstract: We use non-equilibrium dynamical mean-field theory to demonstrate the existence of a critical interaction in the real-time dynamics of the Hubbard model after an interaction quench. The critical point is characterized by fast thermalization and separates weak-coupling and strong-coupling regimes in which the relaxation is delayed due to prethermalization on intermediate timescales. This dynamical phase transition should be observable in experiments on trapped fermionic atoms.
---
So what they do is quench the interaction strength and see how long it takes the system to thermalize. In general when you quench into a gapped state, thermalization can take a really long time because particles trapped on the wrong side of the gap don't have anything to decay into. (See here.) On the other hand, e.g. near a quantum phase transition, the gap is small and thermalization should be easy. So by looking at how long a system takes to approach equilibrium as you quench from a reference parameter value to some value U_f, you can essentially map out a quantum phase diagram and maybe get some information about the exponents. [I should note that this is all somewhat speculative.] What's particularly interesting about the Kollar/Eckstein case is that they didn't even know there was a phase transition there until they did their simulations.
There's some recent work on (possibly) similar ideas that I haven't read yet:
Quench dynamics as a probe of quantum criticality
Authors: R. A. Barankov
http://arxiv.org/abs/0910.0255
Abstract: Quantum critical points of many-body systems can be characterized by studying response of the ground-state wave function to the change of the external parameter, encoded in the ground-state fidelity susceptibility. This quantity characterizes the quench dynamics induced by sudden change of the parameter. In this framework, I analyze scaling relations concerning the probability of excitation and the excitation energy, with the quench amplitude of this parameter. These results are illustrated in the case of one-dimensional sine-Gordon model.
Dynamical phase transition in correlated fermionic lattice systems
Martin Eckstein, Marcus Kollar, Philipp Werner
http://arxiv.org/abs/0904.0976
Abstract: We use non-equilibrium dynamical mean-field theory to demonstrate the existence of a critical interaction in the real-time dynamics of the Hubbard model after an interaction quench. The critical point is characterized by fast thermalization and separates weak-coupling and strong-coupling regimes in which the relaxation is delayed due to prethermalization on intermediate timescales. This dynamical phase transition should be observable in experiments on trapped fermionic atoms.
---
So what they do is quench the interaction strength and see how long it takes the system to thermalize. In general when you quench into a gapped state, thermalization can take a really long time because particles trapped on the wrong side of the gap don't have anything to decay into. (See here.) On the other hand, e.g. near a quantum phase transition, the gap is small and thermalization should be easy. So by looking at how long a system takes to approach equilibrium as you quench from a reference parameter value to some value U_f, you can essentially map out a quantum phase diagram and maybe get some information about the exponents. [I should note that this is all somewhat speculative.] What's particularly interesting about the Kollar/Eckstein case is that they didn't even know there was a phase transition there until they did their simulations.
There's some recent work on (possibly) similar ideas that I haven't read yet:
Quench dynamics as a probe of quantum criticality
Authors: R. A. Barankov
http://arxiv.org/abs/0910.0255
Abstract: Quantum critical points of many-body systems can be characterized by studying response of the ground-state wave function to the change of the external parameter, encoded in the ground-state fidelity susceptibility. This quantity characterizes the quench dynamics induced by sudden change of the parameter. In this framework, I analyze scaling relations concerning the probability of excitation and the excitation energy, with the quench amplitude of this parameter. These results are illustrated in the case of one-dimensional sine-Gordon model.
My paper in Nature Phys.
I guess I should link to my paper with Benjamin Lev and Paul Goldbart on BECs in multimode cavities now that it's finally been published.
He-3B revisited
What happens to an anisotropic superconductor (e.g. helium-3) when you shrink the Cooper pairs? In the case of a normal (BCS) superconductor, nothing terribly interesting takes place: the system goes smoothly from a BCS-like condensate, in which the distance between an electron and its partner is larger than the spacing between them, to a regular condensate of diatomic molecules for which the reverse is true.
This result generalizes, e.g., to the case of p-wave pairing in a completely spin-polarized Fermi gas. (See Leggett, J. Phys. Colloques 41 (1980) C7-19-C7-26.) The situation of s-wave pairing in a spin-imbalanced Fermi gas is somewhat more interesting: at the BEC end the molecules don't really care about the presence of additional fermions and one therefore has a BEC with free fermions floating on top of it; at the BCS end, however, the spin-imbalance frustrates Cooper pairing -- which requires the spin-up and -down Fermi seas to be degenerate. For finite spin-imbalance, one therefore has a quantum phase transition (I believe this is also a thermal phase transition) instead of a crossover.
I was interested in generalizing these ideas to the case of equal-spin p-wave superconductors (or Fermi superfluids) like He-3A and He-3B. The basic reason one might expect something interesting to happen is that the superfluid states are extremely fancy: much fancier, in particular, than anything one expects from tightly bound diatomic molecules. (This is particularly true for the A phase, which is stable only because of a subtle feedback mechanism.) The question is whether there's a quantum phase transition between the BEC and BCS ends; the answer -- which, rather disappointingly, Volovik got to -- is that there is. Volovik constructs a topological invariant that's zero in the BEC limit and nonzero in the BCS limit; it follows, of course, that these limits cannot be adiabatically connected.
Topological invariant for superfluid 3He-B and quantum phase transitions
Authors: G.E. Volovik
http://arxiv.org/abs/0909.3084
Abstract: We consider topological invariant describing the vacuum states of superfluid 3He-B, which belongs to the special class of time-reversal invariant topological insulators and superfluids. Discrete symmetries important for classification of the topologically distinct vacuum states are discussed. One of them leads to the additional subclasses of 3He-B states and is responsible for the finite density of states of Majorana fermions living on the diffusive wall. Integer valued topological invariant is expressed in terms of the Green's function, which allows us to consider systems with interaction.
This result generalizes, e.g., to the case of p-wave pairing in a completely spin-polarized Fermi gas. (See Leggett, J. Phys. Colloques 41 (1980) C7-19-C7-26.) The situation of s-wave pairing in a spin-imbalanced Fermi gas is somewhat more interesting: at the BEC end the molecules don't really care about the presence of additional fermions and one therefore has a BEC with free fermions floating on top of it; at the BCS end, however, the spin-imbalance frustrates Cooper pairing -- which requires the spin-up and -down Fermi seas to be degenerate. For finite spin-imbalance, one therefore has a quantum phase transition (I believe this is also a thermal phase transition) instead of a crossover.
I was interested in generalizing these ideas to the case of equal-spin p-wave superconductors (or Fermi superfluids) like He-3A and He-3B. The basic reason one might expect something interesting to happen is that the superfluid states are extremely fancy: much fancier, in particular, than anything one expects from tightly bound diatomic molecules. (This is particularly true for the A phase, which is stable only because of a subtle feedback mechanism.) The question is whether there's a quantum phase transition between the BEC and BCS ends; the answer -- which, rather disappointingly, Volovik got to -- is that there is. Volovik constructs a topological invariant that's zero in the BEC limit and nonzero in the BCS limit; it follows, of course, that these limits cannot be adiabatically connected.
Topological invariant for superfluid 3He-B and quantum phase transitions
Authors: G.E. Volovik
http://arxiv.org/abs/0909.3084
Abstract: We consider topological invariant describing the vacuum states of superfluid 3He-B, which belongs to the special class of time-reversal invariant topological insulators and superfluids. Discrete symmetries important for classification of the topologically distinct vacuum states are discussed. One of them leads to the additional subclasses of 3He-B states and is responsible for the finite density of states of Majorana fermions living on the diffusive wall. Integer valued topological invariant is expressed in terms of the Green's function, which allows us to consider systems with interaction.
Polariton BEC
The cond-mat Journal Club has a thing on polariton BEC with a commentary by Peter Littlewood who's a relatively important figure in the field. I'm not super-familiar with the literature but there are two basic reasons to be interested in polariton BEC: (1) it's pretty high-temperature and might actually be useful, (2) it's intrinsically very non-equilibrium as the polaritons owe their existence to the pump laser -- this has some rather neat implications, at least if you like far-from-eqm physics, like the observation that the Goldstone mode goes diffusive at very long wavelengths, and therefore these condensates aren't unambiguously "superfluid."
Wednesday, September 30, 2009
Fourier-Legendre expansion of the one-electron density-matrix of ground-state two-electron atoms
Authors: Sebastien Ragot, Maria Belen Ruiz
Abstract: The density-matrix rho(r, r') of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials Pl(cos(theta) = r.r'/rr'). Application is here made to harmonically trapped electron pairs (i.e. Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r, r'). The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a two-term expansion accounts for most of the correlation effects, so that the correlated density-matrices of the atoms at issue are essentially a linear functions of P1(cos(theta)) = cos(theta). For example, in the case of the Hooke's atom: a two-term expansion takes in 99.9 % of the electrons and 99.6 % of the kinetic energy. The correlated density-matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density-matrix rho(r, r'), suggested by the Legendre expansion. Interestingly, two-particle correlation is shown to impact the angular delocalization of each electron, in the one-particle space spanned by the r and r' variables.
http://arxiv.org/abs/0909.3992
Authors: Sebastien Ragot, Maria Belen Ruiz
Abstract: The density-matrix rho(r, r') of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials Pl(cos(theta) = r.r'/rr'). Application is here made to harmonically trapped electron pairs (i.e. Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r, r'). The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a two-term expansion accounts for most of the correlation effects, so that the correlated density-matrices of the atoms at issue are essentially a linear functions of P1(cos(theta)) = cos(theta). For example, in the case of the Hooke's atom: a two-term expansion takes in 99.9 % of the electrons and 99.6 % of the kinetic energy. The correlated density-matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density-matrix rho(r, r'), suggested by the Legendre expansion. Interestingly, two-particle correlation is shown to impact the angular delocalization of each electron, in the one-particle space spanned by the r and r' variables.
http://arxiv.org/abs/0909.3992
Why are nonlinear fits so challenging?
Authors: M. K. Transtrum, B. B. Machta, J. P. Sethna
Abstract: Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to changes in parameters, and one is left to make adjustments by hand. We explain this difficulty by interpreting the fitting process as a generalized interpretation procedure. By considering the manifold of all model predictions in data space, we find that cross sections have a hierarchy of widths and are typically very narrow. Algorithms become stuck as they move near the boundaries. We observe that the model manifold, in addition to being tightly bounded, has low extrinsic curvature, leading to the use of geodesics in the fitting process. We improve the convergence of the Levenberg-Marquardt algorithm by adding the geodesic acceleration to the usual Levenberg-Marquardt step.
http://arxiv.org/abs/0909.3884
Authors: M. K. Transtrum, B. B. Machta, J. P. Sethna
Abstract: Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to changes in parameters, and one is left to make adjustments by hand. We explain this difficulty by interpreting the fitting process as a generalized interpretation procedure. By considering the manifold of all model predictions in data space, we find that cross sections have a hierarchy of widths and are typically very narrow. Algorithms become stuck as they move near the boundaries. We observe that the model manifold, in addition to being tightly bounded, has low extrinsic curvature, leading to the use of geodesics in the fitting process. We improve the convergence of the Levenberg-Marquardt algorithm by adding the geodesic acceleration to the usual Levenberg-Marquardt step.
http://arxiv.org/abs/0909.3884
Quantum Statistical Physics of Glasses at Low Temperatures
Authors: J. van Baardewijk, R. Kuehn
We present a quantum statistical analysis of a microscopic mean-field model of structural glasses at low temperatures. The model can be thought of as arising from a random Born von Karman expansion of the full interaction potential. The problem is reduced to a single-site theory formulated in terms of an imaginary-time path integral using replicas to deal with the disorder. We study the physical properties of the system in thermodynamic equilibrium and develop both perturbative and non-perturbative methods to solve the model. The perturbation theory is formulated as a loop expansion in terms of two-particle irreducible diagrams, and is carried to three-loop order in the effective action. The non-perturbative description is investigated in two ways, (i) using a static approximation, and (ii) via Quantum Monte Carlo simulations. Results for the Matsubara correlations at two-loop order perturbation theory are in good agreement with those of the Quantum Monte Carlo simulations. Characteristic low-temperature anomalies of the specific heat are reproduced, both in the non-perturbative static approximation, and from a three-loop perturbative evaluation of the free energy. In the latter case the result so far relies on using Matsubara correlations at two-loop order in the three-loop expressions for the free energy, as self-consistent Matsubara correlations at three-loop order are still unavailable. We propose to justify this by the good agreement of two-loop Matsubara correlations with those obtained non-perturbatively via Quantum Monte Carlo simulations.
http://arxiv.org/abs/0909.3675
Authors: J. van Baardewijk, R. Kuehn
We present a quantum statistical analysis of a microscopic mean-field model of structural glasses at low temperatures. The model can be thought of as arising from a random Born von Karman expansion of the full interaction potential. The problem is reduced to a single-site theory formulated in terms of an imaginary-time path integral using replicas to deal with the disorder. We study the physical properties of the system in thermodynamic equilibrium and develop both perturbative and non-perturbative methods to solve the model. The perturbation theory is formulated as a loop expansion in terms of two-particle irreducible diagrams, and is carried to three-loop order in the effective action. The non-perturbative description is investigated in two ways, (i) using a static approximation, and (ii) via Quantum Monte Carlo simulations. Results for the Matsubara correlations at two-loop order perturbation theory are in good agreement with those of the Quantum Monte Carlo simulations. Characteristic low-temperature anomalies of the specific heat are reproduced, both in the non-perturbative static approximation, and from a three-loop perturbative evaluation of the free energy. In the latter case the result so far relies on using Matsubara correlations at two-loop order in the three-loop expressions for the free energy, as self-consistent Matsubara correlations at three-loop order are still unavailable. We propose to justify this by the good agreement of two-loop Matsubara correlations with those obtained non-perturbatively via Quantum Monte Carlo simulations.
http://arxiv.org/abs/0909.3675
Friday, August 21, 2009
Phase determination
This paper is not particularly interesting in itself. It outlines how to determine the phase of a XRD beam and determine the crystal structure of the crystal. It essentially removes the monochromatic approximation from the problem, assumes a finite spectral width, then uses the Young's double slit apparatus to observe the phase information deduced from the interference patterns.
There are three things about it I find interesting. First, this has been an outstanding "problem" for 100 years! The second is that it is one of the few examples I have seen where introducing "real world" complications (non-ideal eg. finite spectral width) actually simplifying the calculation. I should disclose the fact that I usually read papers with little experimental impact: ideal systems and first principles papers. It is also kind of cute that it is only 2 pages of work including some fairly basic equations. This paper shows that "standard" models can sometimes be altered slightly (albeit in usually less obvious ways) and solved.
Solution of the Phase Problem in the Theory of Structure Determination of Crystals
from X-Ray Diffraction Experiments
There are three things about it I find interesting. First, this has been an outstanding "problem" for 100 years! The second is that it is one of the few examples I have seen where introducing "real world" complications (non-ideal eg. finite spectral width) actually simplifying the calculation. I should disclose the fact that I usually read papers with little experimental impact: ideal systems and first principles papers. It is also kind of cute that it is only 2 pages of work including some fairly basic equations. This paper shows that "standard" models can sometimes be altered slightly (albeit in usually less obvious ways) and solved.
Monday, July 27, 2009
Quantum scars
Most classical many-body systems are chaotic in the sense that trajectories that start off nearby end up in completely different -- essentially independent -- places. (This is more or less intuitive, consider what happens when you fuck up a pool shot.) Since a quantum trajectory is, intuitively, just a smeared-out quantum trajectory, one might expect the quantum mechanical evolution of a chaotic system to spread out a narrowly focused initial wavefunction all over trajectory space: it would appear to follow from this logic that the steady-state wavefunctions, i.e. the eigenfunctions, should be a featureless average over trajectories.
In fact this isn't true, and it turns out that closed classical trajectories, even if they're unstable to small perturbations, leave "scars" of high density on the eigenfunctions, and therefore on the steady-state and equilibrium density profiles of various systems. The scarring effect was first really explained by Eric Heller in 1984:
Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits
Phys. Rev. Lett. 53, 1515 - 1518 (1984)
Eric J. Heller
In the latest PRL, Huang et al. extend this work to relativistic quantum systems described by the Dirac equation. Among other things, the new work offers a nice example of how the electron gas in graphene, which obeys the Dirac equation, can be used to study features of relativistic quantum mechanics that would otherwise be experimentally inaccessible.
Relativistic Quantum Scars
Phys. Rev. Lett. 103, 054101 (2009)
Liang Huang et al.
Abstract. The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.
In fact this isn't true, and it turns out that closed classical trajectories, even if they're unstable to small perturbations, leave "scars" of high density on the eigenfunctions, and therefore on the steady-state and equilibrium density profiles of various systems. The scarring effect was first really explained by Eric Heller in 1984:
Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits
Phys. Rev. Lett. 53, 1515 - 1518 (1984)
Eric J. Heller
In the latest PRL, Huang et al. extend this work to relativistic quantum systems described by the Dirac equation. Among other things, the new work offers a nice example of how the electron gas in graphene, which obeys the Dirac equation, can be used to study features of relativistic quantum mechanics that would otherwise be experimentally inaccessible.
Relativistic Quantum Scars
Phys. Rev. Lett. 103, 054101 (2009)
Liang Huang et al.
Abstract. The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.
Tuesday, July 21, 2009
Topologically interesting superconductors
Cooper pairs with orbital angular momentum -- p-wave or d-wave -- have order parameters that are potentially more interesting than the U(1) order parameter of a BCS superconductor. The basic idea is that there are three p orbitals, five d orbitals, etc. instead of a single s orbital; therefore, e.g., p_x + i p_y and p_x - i p_y are equally good orbitals to Cooper pair in. In superconductors, the underlying crystal lattice picks out the axes and reduces the orbital symmetry group to a discrete one: e.g., in strontium ruthenate, one has domains of p_x + ip_y and of p_x - ip_y, separated by what appear to be domain walls. However, if one could make p- or d-wave pairs with cold fermions, one would presumably have Cooper pairs spontaneously breaking a large continuous symmetry, and this, in principle, could give rise to interesting sorts of topological defects. (e.g. triplet superfluids have half-quantum vortices, in which the orbital and spin parts each rotate by pi when you go around a loop, so that the total wavefunction returns to itself but the spatial part doesn't. These vortices turn out to be interesting for quantum computation.)
There are two new arxiv papers on this topic; the first is from Nigel Cooper and Gora Shlyapnikov, both quite well-known:
---
Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
N. R. Cooper, G. V. Shlyapnikov
http://arxiv.org/abs/0907.3080
Abstract: We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$.
---
The idea here is something like this. You trap a bunch of dipolar molecules in a 2D trap and impose an external magnetic field to line up the dipoles. Next, you use microwaves to have the make the dipole moments precess (a la NMR); if you do this right, the time-averaged dipole-dipole interaction is attractive and you get Cooper pairing. The authors don't offer an intuitive explanation of why p-wave pairing is preferred; I assume it has to do with the fact that dipolar-molecule systems are naturally ferromagnetic because of the external fields keeping the dipoles lined up, so the natural ground state tends to have all spins lined up pointing along the field, which favors spin-triplet pairing and therefore p-wave pairing.
The other paper is about d-wave pairing:
---
Textures and non-Abelian vortices in atomic d-wave paired Fermi condensates
Authors: H. M. Adachi, Y. Tsutsumi, J. A. M. Huhtamäki, K. Machida
http://arxiv.org/abs/0907.2972
Abstract: We report on fundamental properties of superfluids with d-wave pairing symmetry. We consider neutral atomic Fermi gases in a harmonic trap, the pairing being produced by a Feshbach resonance via a d-wave interaction channel. A Ginzburg-Landau (GL) functional is constructed which is symmetry constrained for five component order parameters (OP). We find OP textures in the cyclic phase and stability conditions for a non-Abelian fractional 1/3-vortex under rotation. It is proposed how to create the intriguing 1/3-vortex experimentally in atomic gases via optical means.
---
The 1/3-quantum vortex is interesting even if it isn't realizable. What seems to me most interesting about this paper is that it carefully accounts for the influence of the harmonic trap on vortex energetics -- that defects which would be energetically unstable in bulk might be stable in a trap is an interesting possibility.
There are two new arxiv papers on this topic; the first is from Nigel Cooper and Gora Shlyapnikov, both quite well-known:
---
Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
N. R. Cooper, G. V. Shlyapnikov
http://arxiv.org/abs/0907.3080
Abstract: We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$.
---
The idea here is something like this. You trap a bunch of dipolar molecules in a 2D trap and impose an external magnetic field to line up the dipoles. Next, you use microwaves to have the make the dipole moments precess (a la NMR); if you do this right, the time-averaged dipole-dipole interaction is attractive and you get Cooper pairing. The authors don't offer an intuitive explanation of why p-wave pairing is preferred; I assume it has to do with the fact that dipolar-molecule systems are naturally ferromagnetic because of the external fields keeping the dipoles lined up, so the natural ground state tends to have all spins lined up pointing along the field, which favors spin-triplet pairing and therefore p-wave pairing.
The other paper is about d-wave pairing:
---
Textures and non-Abelian vortices in atomic d-wave paired Fermi condensates
Authors: H. M. Adachi, Y. Tsutsumi, J. A. M. Huhtamäki, K. Machida
http://arxiv.org/abs/0907.2972
Abstract: We report on fundamental properties of superfluids with d-wave pairing symmetry. We consider neutral atomic Fermi gases in a harmonic trap, the pairing being produced by a Feshbach resonance via a d-wave interaction channel. A Ginzburg-Landau (GL) functional is constructed which is symmetry constrained for five component order parameters (OP). We find OP textures in the cyclic phase and stability conditions for a non-Abelian fractional 1/3-vortex under rotation. It is proposed how to create the intriguing 1/3-vortex experimentally in atomic gases via optical means.
---
The 1/3-quantum vortex is interesting even if it isn't realizable. What seems to me most interesting about this paper is that it carefully accounts for the influence of the harmonic trap on vortex energetics -- that defects which would be energetically unstable in bulk might be stable in a trap is an interesting possibility.
Saturday, July 18, 2009
Kondo polarons
A few days ago I had what I thought was a good idea: to look at the behavior of moving magnetic impurities, and see if they interpolate somehow between the Kondo effect and the polaron as you tune the mass of the impurity down from infinity. (There are some obvious ways to realize the interpolation experimentally using cold Fermi gases.) I was disappointed to find that someone else got there first, and tantalizingly recently (May 2008); Lamacraft's result is, however, really interesting, and would've been beyond my powers to derive:
Kondo Polarons in a One-Dimensional Fermi Gas
Austen Lamacraft
PRL 101, 225301 (2008)
Abstract: We consider the motion of a spin-1/2 impurity in a one-dimensional gas of spin-1/2 fermions. For antiferromagnetic interaction between the impurity and the fermions, the low temperature behavior of the system is governed by the two-channel Kondo effect, leading to the impurity becoming completely opaque to the spin excitations of the gas. As well as the known spectral signatures of the two-channel Kondo effect, we find that the low temperature mobility of the resulting `Kondo polaron' takes the universal form $\mu\to \frac{3\hbar v_F^2}{2\pi k_B^2T^2}$, in sharp contrast to the spinless case where $\mu\propto T^{-4}$.
The really interesting thing here is that the case of the mobile impurity differs drastically from that of the fixed (infinite-mass) impurity because certain processes that are permitted with an infinite-mass impurity are forbidden, because of the impossibility of simultaneously conserving energy and momentum, in a finite-mass impurity. One consequence of this is that, whereas the infinite-mass impurity couples to a single scattering channel (even combinations of left- and right-moving traveling waves) the finite-mass impurity couples independently to the left- and right-moving channels. This means that the 1D Kondo problem with recoil is not the one-channel Kondo problem but the far more exotic two-channel Kondo problem.
Kondo Polarons in a One-Dimensional Fermi Gas
Austen Lamacraft
PRL 101, 225301 (2008)
Abstract: We consider the motion of a spin-1/2 impurity in a one-dimensional gas of spin-1/2 fermions. For antiferromagnetic interaction between the impurity and the fermions, the low temperature behavior of the system is governed by the two-channel Kondo effect, leading to the impurity becoming completely opaque to the spin excitations of the gas. As well as the known spectral signatures of the two-channel Kondo effect, we find that the low temperature mobility of the resulting `Kondo polaron' takes the universal form $\mu\to \frac{3\hbar v_F^2}{2\pi k_B^2T^2}$, in sharp contrast to the spinless case where $\mu\propto T^{-4}$.
The really interesting thing here is that the case of the mobile impurity differs drastically from that of the fixed (infinite-mass) impurity because certain processes that are permitted with an infinite-mass impurity are forbidden, because of the impossibility of simultaneously conserving energy and momentum, in a finite-mass impurity. One consequence of this is that, whereas the infinite-mass impurity couples to a single scattering channel (even combinations of left- and right-moving traveling waves) the finite-mass impurity couples independently to the left- and right-moving channels. This means that the 1D Kondo problem with recoil is not the one-channel Kondo problem but the far more exotic two-channel Kondo problem.
Friday, July 17, 2009
Exciton-polariton-BEC-excitation-mediated superconductivity
New on the arxiv:
Exciton-polariton mediated superconductivity
Authors: Fabrice P. Laussy, Alexey Kavokin, Ivan Shelykh
http://arxiv.org/abs/0907.2374
Abstract: We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of a real exciton-polariton Bose-Einstein condensate. We consider a model microcavity where quantum wells with a two dimensional electron gas sandwich an undoped quantum well, where an exciton-polariton condensate is formed. We show that the critical temperature for superconductivity increases with the condensate population--opening a new route towards high temperature superconductivity.
---
The usual binding mechanism for a Cooper pair is some kind of attractive electron-boson-electron interaction. In the BCS theory the bosons are taken to be phonons, but in principle they could be anything. In particular, they could be excitations of a Bose condensate. There was some old work on this by Bardeen, Baym, and Pines when they were trying to make Cooper pairs of helium-3 through interactions mediated by helium-4:
Effective Interaction of He3 Atoms in Dilute Solutions of He3 in He4 at Low Temperatures
J. Bardeen, G. Baym, and D. Pines
Phys. Rev. 156, 207 - 221 (1967)
The new work suggests using exciton-polaritons, which are electron-hole pairs hybridized with laser photons, to serve a similar purpose. The basic appeal of exciton-polariton BECs is that they have a high transition temperature compared with other BECs so in principle an exciton polariton BEC could stabilize a relatively high-temperature superconductor via the electron--exciton-BEC-excitation--electron interaction.
Exciton-polariton mediated superconductivity
Authors: Fabrice P. Laussy, Alexey Kavokin, Ivan Shelykh
http://arxiv.org/abs/0907.2374
Abstract: We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of a real exciton-polariton Bose-Einstein condensate. We consider a model microcavity where quantum wells with a two dimensional electron gas sandwich an undoped quantum well, where an exciton-polariton condensate is formed. We show that the critical temperature for superconductivity increases with the condensate population--opening a new route towards high temperature superconductivity.
---
The usual binding mechanism for a Cooper pair is some kind of attractive electron-boson-electron interaction. In the BCS theory the bosons are taken to be phonons, but in principle they could be anything. In particular, they could be excitations of a Bose condensate. There was some old work on this by Bardeen, Baym, and Pines when they were trying to make Cooper pairs of helium-3 through interactions mediated by helium-4:
Effective Interaction of He3 Atoms in Dilute Solutions of He3 in He4 at Low Temperatures
J. Bardeen, G. Baym, and D. Pines
Phys. Rev. 156, 207 - 221 (1967)
The new work suggests using exciton-polaritons, which are electron-hole pairs hybridized with laser photons, to serve a similar purpose. The basic appeal of exciton-polariton BECs is that they have a high transition temperature compared with other BECs so in principle an exciton polariton BEC could stabilize a relatively high-temperature superconductor via the electron--exciton-BEC-excitation--electron interaction.
Thursday, July 16, 2009
Non-abelian FQHE with cold atoms
New in PRL:
Non-Abelian Optical Lattices: Anomalous Quantum Hall Effect and Dirac Fermions
Phys. Rev. Lett. 103, 035301 (2009)
N. Goldman,1 A. Kubasiak,2,3 A. Bermudez,4 P. Gaspard,1 M. Lewenstein,2,5 and M. A. Martin-Delgado4
Abstract: We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
---
This is an interesting proposal but I'm a little skeptical about its _actual_ realizability. The basic idea behind imposing the gauge fields is to drive rather involved sequences of transitions in multilevel atoms, as outlined, e.g., here:
Non-Abelian Gauge Potentials for Ultracold Atoms with Degenerate Dark States
Phys. Rev. Lett. 95, 010404 (2005)
J. Ruseckas1,2, G. Juzeliūnas1, P. Öhberg3, and M. Fleischhauer2
Abstract: We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.
It feels like it'd be pretty hard to separate out the cond-mat effect one is looking for, i.e. the FQHE, from all the atomic physics details.
Non-Abelian Optical Lattices: Anomalous Quantum Hall Effect and Dirac Fermions
Phys. Rev. Lett. 103, 035301 (2009)
N. Goldman,1 A. Kubasiak,2,3 A. Bermudez,4 P. Gaspard,1 M. Lewenstein,2,5 and M. A. Martin-Delgado4
Abstract: We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
---
This is an interesting proposal but I'm a little skeptical about its _actual_ realizability. The basic idea behind imposing the gauge fields is to drive rather involved sequences of transitions in multilevel atoms, as outlined, e.g., here:
Non-Abelian Gauge Potentials for Ultracold Atoms with Degenerate Dark States
Phys. Rev. Lett. 95, 010404 (2005)
J. Ruseckas1,2, G. Juzeliūnas1, P. Öhberg3, and M. Fleischhauer2
Abstract: We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.
It feels like it'd be pretty hard to separate out the cond-mat effect one is looking for, i.e. the FQHE, from all the atomic physics details.
Wednesday, July 15, 2009
Friedel sum rule and Levinson's Theorem
Having had a somewhat haphazard education, I hadn't heard of the Friedel sum rule until I needed it for my research. As usual, Google yielded nothing remotely pedagogical, just research articles, and neither Ashcroft nor AGD had anything to say about the rule. It turns out, however, that Ziman's book Principles of Solid-State Physics has a nice discussion. It also turns out that, if I'm not being a complete idiot, this rule is a case of a general scattering theory result -- again underrepresented in textbooks -- known as Levinson's theorem.
Levinson's theorem relates the zero-energy scattering phase shift of a short-range potential to the number of bound states in the potential. The Friedel sum rule relates the number of states below the Fermi energy to the scattering phase shift at the Fermi energy. The relation in both cases is that the zero-energy (Fermi-energy) phase shift is pi times the number of states. The idea behind Levinson's theorem goes something like this -- as you tune the energy of your incoming scatterer down from infinity (where there's no phase shift), the scattering phase shift goes through pi iff you hit a scattering resonance associated with a bound state in your potential. Add up all the pi's and you get the number of bound states.
The usual argument for the Friedel sum rule goes like this -- put the system in a box, the scattering phase shift feeds into the quantization condition at the edges of the box, and depending on what the phase shifts are you can change the number of states that are below the Fermi energy. I would assume, though, that you could alternatively prove it by putting the system in a box that extends up to the Fermi energy, then using Levinson's theorem to count the bound states.
I should mention that the Friedel sum rule is true for Fermi liquids as well as for the free Fermi gas, which is not terribly surprising as the states of the two are in 1-to-1 correspondence. The equivalence is proved in the following paper:
Friedel Sum Rule for a System of Interacting Electrons
J.S. Langer and V. Ambegaokar
Phys. Rev. 121, 1090 (1961)
Levinson's theorem relates the zero-energy scattering phase shift of a short-range potential to the number of bound states in the potential. The Friedel sum rule relates the number of states below the Fermi energy to the scattering phase shift at the Fermi energy. The relation in both cases is that the zero-energy (Fermi-energy) phase shift is pi times the number of states. The idea behind Levinson's theorem goes something like this -- as you tune the energy of your incoming scatterer down from infinity (where there's no phase shift), the scattering phase shift goes through pi iff you hit a scattering resonance associated with a bound state in your potential. Add up all the pi's and you get the number of bound states.
The usual argument for the Friedel sum rule goes like this -- put the system in a box, the scattering phase shift feeds into the quantization condition at the edges of the box, and depending on what the phase shifts are you can change the number of states that are below the Fermi energy. I would assume, though, that you could alternatively prove it by putting the system in a box that extends up to the Fermi energy, then using Levinson's theorem to count the bound states.
I should mention that the Friedel sum rule is true for Fermi liquids as well as for the free Fermi gas, which is not terribly surprising as the states of the two are in 1-to-1 correspondence. The equivalence is proved in the following paper:
Friedel Sum Rule for a System of Interacting Electrons
J.S. Langer and V. Ambegaokar
Phys. Rev. 121, 1090 (1961)
Tuesday, July 14, 2009
Integrability in disconnecting air bubbles
This is a rather neat bit of theory. It's motivated by the following paradox: integrable systems remember everything about their initial conditions, whereas the behavior of systems at "finite-time singularities" (the dynamical-systems equivalent of phase transitions; cf. Chapter 10 of Nigel Goldenfeld's book) exhibits "universality," which implies insensitivity to initial conditions. What happens to integrable systems with finite-time singularities, e.g. a disconnecting air bubble? It turns out that, while some properties of the bubble exhibit universal behavior, others are sensitive to the initial conditions.
Memory-encoding vibrations in a disconnecting air bubble
Laura E. Schmidt, Nathan C. Keim, Wendy W. Zhang & Sidney R. Nagel
Nature Phys. 5, 343 - 346 (2009)
Many nonlinear processes, such as the propagation of waves over an ocean or the transmission of light pulses down an optical fibre1, are integrable in the sense that the dynamics has as many conserved quantities as there are independent variables. The result is a time evolution that retains a complete memory of the initial state. In contrast, the nonlinear dynamics near a finite-time singularity, in which physical quantities such as pressure or velocity diverge at a point in time, is believed to evolve towards a universal form, one independent of the initial state2. The break-up of a water drop in air3 or a viscous liquid inside an immiscible oil4, 5 are processes that conform to this second scenario. These opposing scenarios collide in the nonlinearity produced by the formation of a finite-time singularity that is also integrable. We demonstrate here that the result is a novel dynamics with a dual character.
Memory-encoding vibrations in a disconnecting air bubble
Laura E. Schmidt, Nathan C. Keim, Wendy W. Zhang & Sidney R. Nagel
Nature Phys. 5, 343 - 346 (2009)
Many nonlinear processes, such as the propagation of waves over an ocean or the transmission of light pulses down an optical fibre1, are integrable in the sense that the dynamics has as many conserved quantities as there are independent variables. The result is a time evolution that retains a complete memory of the initial state. In contrast, the nonlinear dynamics near a finite-time singularity, in which physical quantities such as pressure or velocity diverge at a point in time, is believed to evolve towards a universal form, one independent of the initial state2. The break-up of a water drop in air3 or a viscous liquid inside an immiscible oil4, 5 are processes that conform to this second scenario. These opposing scenarios collide in the nonlinearity produced by the formation of a finite-time singularity that is also integrable. We demonstrate here that the result is a novel dynamics with a dual character.
Old(-ish) stuff: quenches and coarsening
Quenches are a generic term for when you take an initial density matrix (say the thermal density matrix of Hamiltonian H) and time-evolve it with a Hamiltonian H' that's very different from H. A classical quench is typically a thermal quench -- you cool a system rapidly across a phase transition, and watch the domain walls grow. A good review of the old stuff is:
Theory of Phase-Ordering Kinetics
A.J. Bray
cond-mat/9501089 (no figures)
Adv. Phys. 43, 357 (1994)
There are three basic take-away messages -- (1) the dynamic scaling hypothesis, which states that all the time-dependence of correlation functions, response functions, etc. depends on a single scale, which is set (in some models, at least) by the average bubble size. (2) The bubble growth laws depend on whether the order parameter is locally conserved (e.g., binary fluid at separation/mixing) or not (e.g., magnets), as well as on the dimensionality of the order parameter (so, e.g., domain walls grow differently from vortices and hedgehogs). (3) Within any bubble, the system behaves like an ordered state with the equilibrium order parameter at the final temperature: therefore, response functions tend to have a two-time/two-length behavior, depending on whether they're probing the short-time respones, which is basically equilibrium, or the long-time response, which depends on the motion of the domain walls.
There are variants on this problem that involve, e.g., quenching from/to a critical point (so that the initial state has long-range correlations), or quenching across a Kosterlitz-Thouless transition, or quenching in the presence of disorder.
Zero-temperature quenches (microcanonical)
Here the initial state is a wavefunction that is very far from being an eigenfunction of the Hamiltonian it evolves under. (Usually it's the ground state of a totally different Hamiltonian but that's unnecessary.) Most of the experimental work in this field has involved quenching across the superfluid-to-Mott transition in optical lattices; it is at present unclear whether the systems ever approach a locally equilibrium state.
Here are some papers that don't necessarily agree with each other about thermalization:
Oscillating superfluidity of bosons in optical lattices
E. Altman and A. Auerbach
PRL 89, 250404 (2002)
Altman and Auerbach argue that quenching from the Mott to the superfluid phase will lead to macroscopic oscillations of the order parameter (which eventually die out because of quasiparticle collisions), and that underdamped relaxation should be observable. I'm not sure that underdamped relaxation has been seen experimentally for this particular case, but it was observed experimentally for a quench from the SF to the Mott state.
Collapse and revival of the matter wave field of a Bose–Einstein condensate
Markus Greiner, Olaf Mandel, Theodor W. Hänsch & Immanuel Bloch
Nature 419, 51 (2002)
This famous experiment demonstrated the periodic collapse and revival of Bragg peaks (indicative, usually, of phase coherence) when a BEC was quenched into the Mott state. This is an instance of underdamped relaxation -- trap-induced anharmonicities, etc., eventually kill phase coherence. Interestingly, the deeper the quench, the slower the system is to relax.
A quantum Newton's cradle
T. Kinoshita, T. Wenger, and D. Weiss
Nature 440, 900 (2006)
In this experiment, a 1D Bose gas -- bosons confined in an array of very narrow tubes -- was started off in a far-from-equilibrium condition, with half the atoms flying off to the left and the other half flying off to the right, and allowed to time-evolve. The momentum distribution didn't seem to approach a thermal distribution on the experimental timescales; this was interpreted as a consequence of the integrability of the system. (Roughly, an integrable system has a huge number of conserved quantities, and therefore retains much more information about its initial conditions than a normal system does.) This is a stronger result than underdamped relaxation; the experiment showed no tendency towards relaxation at all.
Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model
C. Kollath, A. Lauchli, and E. Altman
PRL 98, 180601 (2007)
Kollath et al. found, rather surprisingly, that thermalization doesn't necessarily happen even in nonintegrable models. They simulated a quench from the SF to the Mott phase, using exact diagonalization techniques as well as a density-matrix renormalization group algorithm. The result is that if one quenches from the SF deep into the Mott, the system doesn't seem to thermalize. They explained their results with an argument that goes something like this -- thermalization occurs as a consequence of the decay of double occupancies; however, a double occupancy has energy U (on-site repulsion) and has to decay into quasi-particles that have energy of order J (roughly the bandwidth of the lower Mott band). If U >> J then this can only happen at very high orders in perturbation theory, so it takes forever.
One could interpret this result as being about the observation, rather than the occurrence, of thermalization -- from a practical point of view, a system that takes very long to thermalize looks like one that doesn't thermalize.
Thermalization and its mechanism for generic isolated quantum systems
M. Rigol, V. Dunjko, and M. Olshanii
Nature 452, 854-858 (arxiv version)
This paper presents the "eigenstate thermalization" hypothesis. The hypothesis, as I understand it (which is not very well), states that the expectation values of physically interesting observables are essentially constant for eigenstates that are near each other in energy. There is some numerical reason to believe that this is true, but as far as I know there hasn't been much analytic work. Rigol et al. also suggest a generalization of this hypothesis to integrable systems; the upshot is the idea of a generalized Gibbs ensemble, which introduces "chemical potentials" (i.e. Lagrange multipliers) corresponding to all the conserved quantities.
[... to be continued]
Theory of Phase-Ordering Kinetics
A.J. Bray
cond-mat/9501089 (no figures)
Adv. Phys. 43, 357 (1994)
There are three basic take-away messages -- (1) the dynamic scaling hypothesis, which states that all the time-dependence of correlation functions, response functions, etc. depends on a single scale, which is set (in some models, at least) by the average bubble size. (2) The bubble growth laws depend on whether the order parameter is locally conserved (e.g., binary fluid at separation/mixing) or not (e.g., magnets), as well as on the dimensionality of the order parameter (so, e.g., domain walls grow differently from vortices and hedgehogs). (3) Within any bubble, the system behaves like an ordered state with the equilibrium order parameter at the final temperature: therefore, response functions tend to have a two-time/two-length behavior, depending on whether they're probing the short-time respones, which is basically equilibrium, or the long-time response, which depends on the motion of the domain walls.
There are variants on this problem that involve, e.g., quenching from/to a critical point (so that the initial state has long-range correlations), or quenching across a Kosterlitz-Thouless transition, or quenching in the presence of disorder.
Zero-temperature quenches (microcanonical)
Here the initial state is a wavefunction that is very far from being an eigenfunction of the Hamiltonian it evolves under. (Usually it's the ground state of a totally different Hamiltonian but that's unnecessary.) Most of the experimental work in this field has involved quenching across the superfluid-to-Mott transition in optical lattices; it is at present unclear whether the systems ever approach a locally equilibrium state.
Here are some papers that don't necessarily agree with each other about thermalization:
Oscillating superfluidity of bosons in optical lattices
E. Altman and A. Auerbach
PRL 89, 250404 (2002)
Altman and Auerbach argue that quenching from the Mott to the superfluid phase will lead to macroscopic oscillations of the order parameter (which eventually die out because of quasiparticle collisions), and that underdamped relaxation should be observable. I'm not sure that underdamped relaxation has been seen experimentally for this particular case, but it was observed experimentally for a quench from the SF to the Mott state.
Collapse and revival of the matter wave field of a Bose–Einstein condensate
Markus Greiner, Olaf Mandel, Theodor W. Hänsch & Immanuel Bloch
Nature 419, 51 (2002)
This famous experiment demonstrated the periodic collapse and revival of Bragg peaks (indicative, usually, of phase coherence) when a BEC was quenched into the Mott state. This is an instance of underdamped relaxation -- trap-induced anharmonicities, etc., eventually kill phase coherence. Interestingly, the deeper the quench, the slower the system is to relax.
A quantum Newton's cradle
T. Kinoshita, T. Wenger, and D. Weiss
Nature 440, 900 (2006)
In this experiment, a 1D Bose gas -- bosons confined in an array of very narrow tubes -- was started off in a far-from-equilibrium condition, with half the atoms flying off to the left and the other half flying off to the right, and allowed to time-evolve. The momentum distribution didn't seem to approach a thermal distribution on the experimental timescales; this was interpreted as a consequence of the integrability of the system. (Roughly, an integrable system has a huge number of conserved quantities, and therefore retains much more information about its initial conditions than a normal system does.) This is a stronger result than underdamped relaxation; the experiment showed no tendency towards relaxation at all.
Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model
C. Kollath, A. Lauchli, and E. Altman
PRL 98, 180601 (2007)
Kollath et al. found, rather surprisingly, that thermalization doesn't necessarily happen even in nonintegrable models. They simulated a quench from the SF to the Mott phase, using exact diagonalization techniques as well as a density-matrix renormalization group algorithm. The result is that if one quenches from the SF deep into the Mott, the system doesn't seem to thermalize. They explained their results with an argument that goes something like this -- thermalization occurs as a consequence of the decay of double occupancies; however, a double occupancy has energy U (on-site repulsion) and has to decay into quasi-particles that have energy of order J (roughly the bandwidth of the lower Mott band). If U >> J then this can only happen at very high orders in perturbation theory, so it takes forever.
One could interpret this result as being about the observation, rather than the occurrence, of thermalization -- from a practical point of view, a system that takes very long to thermalize looks like one that doesn't thermalize.
Thermalization and its mechanism for generic isolated quantum systems
M. Rigol, V. Dunjko, and M. Olshanii
Nature 452, 854-858 (arxiv version)
This paper presents the "eigenstate thermalization" hypothesis. The hypothesis, as I understand it (which is not very well), states that the expectation values of physically interesting observables are essentially constant for eigenstates that are near each other in energy. There is some numerical reason to believe that this is true, but as far as I know there hasn't been much analytic work. Rigol et al. also suggest a generalization of this hypothesis to integrable systems; the upshot is the idea of a generalized Gibbs ensemble, which introduces "chemical potentials" (i.e. Lagrange multipliers) corresponding to all the conserved quantities.
[... to be continued]
Monday, July 13, 2009
Old stuff: Mott Insulators, Disorder, 1D gases
(Many of these links are cribbed from Brian DeMarco's now-defunct blog.)
Phase Coherence and Superfluid-Insulator Transition in a Disordered Bose-Einstein Condensate
by: Yong P. Chen, J. Hitchcock, D. Dries, M. Junker, C. Welford, R. G. Hulet
Abstract: We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate (BEC) of 7Li atoms. At moderate disorder strengths (V_D), we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. The interference reflects phase coherence in the disordered BEC and is interpreted as speckle for matter waves. At higher V_D, the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence.
arXiv:0710.5187v1 [cond-mat.other]
Non-equilibrium coherence dynamics in one-dimensional Bose gases
Authors: S. Hofferberth1,2, I. Lesanovsky3, B. Fischer1, T. Schumm2 & J. Schmiedmayer1,2
Abstract: Low-dimensional systems provide beautiful examples of many-body quantum physics1. For one-dimensional (1D) systems2, the Luttinger liquid approach3 provides insight into universal properties. Much is known of the equilibrium state, both in the weakly4, 5, 6, 7 and strongly8, 9 interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached10. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state11. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions12. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach13. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems14, 15, 16. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.
http://www.nature.com/nature/journal/v449/n7160/full/nature06149.html
Nature 449, 324-327 (20 September 2007)
Tonks–Girardeau gas of ultracold atoms in an optical lattice
Authors: Belén Paredes, Artur Widera, Valentin Murg, Olaf Mandel, Simon Fölling, Ignacio Cirac, Gora V. Shlyapnikov, Theodor W. Hänsch and Immanuel Bloch
Abstract: Strongly correlated quantum systems are among the most intriguing and fundamental systems in physics. One such example is the Tonks–Girardeau gas1, 2, proposed about 40 years ago, but until now lacking experimental realization; in such a gas, the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to minimize their mutual repulsion, the bosons are prevented from occupying the same position in space. This mimics the Pauli exclusion principle for fermions, causing the bosonic particles to exhibit fermionic properties1, 2. However, such bosons do not exhibit completely ideal fermionic (or bosonic) quantum behaviour; for example, this is reflected in their characteristic momentum distribution3. Here we report the preparation of a Tonks–Girardeau gas of ultracold rubidium atoms held in a two-dimensional optical lattice formed by two orthogonal standing waves. The addition of a third, shallower lattice potential along the long axis of the quantum gases allows us to enter the Tonks–Girardeau regime by increasing the atoms’ effective mass and thereby enhancing the role of interactions. We make a theoretical prediction of the momentum distribution based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.
Nature 429, 277-281 (20 May 2004)
http://www.nature.com/nature/journal/v429/n6989/abs/nature02530.html
Formation of Spatial Shell Structure in the Superfluid to Mott Insulator Transition
Authors: Simon Fölling, Artur Widera, Torben Müller, Fabrice Gerbier, and Immanuel Bloch
Abstract: We report on the direct observation of the transition from a compressible superfluid to an incompressible Mott insulator by recording the in-trap density distribution of a Bosonic quantum gas in an optical lattice. Using spatially selective microwave transitions and spin-changing collisions, we are able to locally modify the spin state of the trapped quantum gas and record the spatial distribution of lattice sites with different filling factors. As the system evolves from a superfluid to a Mott insulator, we observe the formation of a distinct shell structure, in good agreement with theory.
http://link.aps.org/abstract/PRL/v97/e060403
Phys. Rev. Lett. 97, 060403 (2006)
Phase Coherence and Superfluid-Insulator Transition in a Disordered Bose-Einstein Condensate
by: Yong P. Chen, J. Hitchcock, D. Dries, M. Junker, C. Welford, R. G. Hulet
Abstract: We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate (BEC) of 7Li atoms. At moderate disorder strengths (V_D), we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. The interference reflects phase coherence in the disordered BEC and is interpreted as speckle for matter waves. At higher V_D, the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence.
arXiv:0710.5187v1 [cond-mat.other]
Non-equilibrium coherence dynamics in one-dimensional Bose gases
Authors: S. Hofferberth1,2, I. Lesanovsky3, B. Fischer1, T. Schumm2 & J. Schmiedmayer1,2
Abstract: Low-dimensional systems provide beautiful examples of many-body quantum physics1. For one-dimensional (1D) systems2, the Luttinger liquid approach3 provides insight into universal properties. Much is known of the equilibrium state, both in the weakly4, 5, 6, 7 and strongly8, 9 interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached10. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state11. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions12. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach13. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems14, 15, 16. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.
http://www.nature.com/nature/journal/v449/n7160/full/nature06149.html
Nature 449, 324-327 (20 September 2007)
Tonks–Girardeau gas of ultracold atoms in an optical lattice
Authors: Belén Paredes, Artur Widera, Valentin Murg, Olaf Mandel, Simon Fölling, Ignacio Cirac, Gora V. Shlyapnikov, Theodor W. Hänsch and Immanuel Bloch
Abstract: Strongly correlated quantum systems are among the most intriguing and fundamental systems in physics. One such example is the Tonks–Girardeau gas1, 2, proposed about 40 years ago, but until now lacking experimental realization; in such a gas, the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to minimize their mutual repulsion, the bosons are prevented from occupying the same position in space. This mimics the Pauli exclusion principle for fermions, causing the bosonic particles to exhibit fermionic properties1, 2. However, such bosons do not exhibit completely ideal fermionic (or bosonic) quantum behaviour; for example, this is reflected in their characteristic momentum distribution3. Here we report the preparation of a Tonks–Girardeau gas of ultracold rubidium atoms held in a two-dimensional optical lattice formed by two orthogonal standing waves. The addition of a third, shallower lattice potential along the long axis of the quantum gases allows us to enter the Tonks–Girardeau regime by increasing the atoms’ effective mass and thereby enhancing the role of interactions. We make a theoretical prediction of the momentum distribution based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.
Nature 429, 277-281 (20 May 2004)
http://www.nature.com/nature/journal/v429/n6989/abs/nature02530.html
Phase Coherence of an Atomic Mott Insulator
Authors: Fabrice Gerbier, Artur Widera, Simon Fölling, Olaf Mandel, Tatjana Gericke, and Immanuel Bloch
Abstract: We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.
Phys. Rev. Lett. 95, 050404 (2005)
http://link.aps.org/abstract/PRL/v95/e050404
Formation of Spatial Shell Structure in the Superfluid to Mott Insulator Transition
Authors: Simon Fölling, Artur Widera, Torben Müller, Fabrice Gerbier, and Immanuel Bloch
Abstract: We report on the direct observation of the transition from a compressible superfluid to an incompressible Mott insulator by recording the in-trap density distribution of a Bosonic quantum gas in an optical lattice. Using spatially selective microwave transitions and spin-changing collisions, we are able to locally modify the spin state of the trapped quantum gas and record the spatial distribution of lattice sites with different filling factors. As the system evolves from a superfluid to a Mott insulator, we observe the formation of a distinct shell structure, in good agreement with theory.
http://link.aps.org/abstract/PRL/v97/e060403
Phys. Rev. Lett. 97, 060403 (2006)
What this blog is for
This blog is supposed to be a repository of recent (and not-so-recent) physics papers I find interesting. I'm a grad student in condensed matter theory; my current research is primarily on (1) applications of condensed matter ideas in cavity QED and (2) nonequilibrium condensed matter physics, but I've been known to be interested in other things. I don't know, at this stage, whether the plan is to blog papers before or after I've read them, but if the latter, I'll try to do summaries.
Subscribe to:
Posts (Atom)