Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0904.2881 · Physical Review A

Supercritical superfluid and vortex unbinding following a quantum quench

Ludwig Mathey, Anatoli Polkovnikov

Published Oct 5, 2009• 17 citations
arXivHTMLPDF

Abstract

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled, using truncated Wigner approximation. On short time scales the relative phase shows ``light-cone''-like thermalization and creates a metastable superfluid state, which can be supercritical. On longer time scales this state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We observe dynamics of creation of vortex-antivortex pairs and their consequent motion. Our predictions can be directly measured in interference experiments [Z. Hadzibabic et al., Nature (London) 441, 1118 (2006)].

DOI
10.1103/physreva.80.041601

Related papers

Light cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench

Ludwig Mathey, Anatoli Polkovnikov

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled. We find that on short time scales the relative phase shows ``light cone''-like dynamics and creates a metastable superfluid state, which can be supercritical. We also demonstrate similar light cone dynamics for the transverse field Ising model. On longer time scales the supercritical state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We study this effect both numerically using truncated Wigner approximation and analytically within a newly suggested time dependent renormalization group approach (RG). In particular, within RG we show that there are two possible fixed points for the real-time evolution corresponding to the superfluid and normal steady states. So depending on the initial conditions and the microscopic parameters of the Hamiltonian the system undergoes a nonequilibrium phase transition of the Kosterlitz-Thouless type. The time scales for the vortex unbinding near the critical point are exponentially divergent, similar to the equilibrium case.

arXiv:1001.0098•Physical Review A•Mar 11, 2010•80 citations

Exact Solution for Vortex Dynamics in Temperature Quenches of Two-Dimensional Superfluids

Andrew Forrester, Han-Ching Chu, Gary A. Williams

An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature T(KT). An approximate solution for quenches at and above above T(KT) provides insights into the origin of logarithmic transients in the vortex decay, and is in general agreement with recent simulations of the quenched XY model. These results confirm that there is no "creation" of vortices whose density increases with the quench rate as predicted by the Kibble-Zurek theory but only monotonic decay of the thermal vortices already present at the initial temperature.

arXiv:1211.0661•Physical Review Letters•Apr 19, 2013•15 citations

Non-equilibrium dynamics in Mott-to-superfluid transition in Bose-Einstein condensation in optical lattices

Naoto Horiguchi, Takashi Oka, Hideo Aoki

Bose-Einstein condensates of cold atoms in optical lattices are interesting because the dynamics of the transition from a Mott insulator to a superfluid driven by a quench into the superfluid phase exemplifies non-equilibrium evolutions of gauge-symmetry broken quantum phases. Here we have actually visualised features in real space, which have domain structures that depend on the stage of the transition dynamics. Namely, the system after the quench relaxes in three processes: (i) an exponential growth of the superfluid density, (ii) collapse of the domain structure, and (iii) vortex-antivortex pair-annihilation as the long-range superfluid order is formed. Topological picture due to Kibble-Zurek mechanism and Zurek's freeze-out scenario for slow quenches are confirmed.

Journal of Physics Conference Series•Feb 1, 2009•2 citations

Non-equilibrium dynamics in Mott-to-superfluid transition in Bose-Einstein condensation in optical lattices

Naoto Horiguchi, Takashi Oka, Hideo Aoki

Bose-Einstein condensates of cold atoms in optical lattices are interesting because the dynamics of the transition from a Mott insulator to a superfluid driven by a quench into the superfluid phase exemplifies non-equilibrium evolutions of gauge-symmetry broken quantum phases. Here we have actually visualised features in real space, which have domain structures that depend on the stage of the transition dynamics. Namely, the system after the quench relaxes in three processes: (i) an exponential growth of the superfluid density, (ii) collapse of the domain structure, and (iii) vortex-antivortex pair-annihilation as the long-range superfluid order is formed. Topological picture due to Kibble-Zurek mechanism and Zurek's freeze-out scenario for slow quenches are confirmed.

Journal of Physics Conference Series•Feb 1, 2009•10 citations

Quench dynamics of a superfluid Fermi gas

Geoffrey Warner, A. J. Leggett

With an eye toward the interpretation of so-called ``cosmological'' experiments performed on the low-temperature phases of $^{3}\mathrm{He}$, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter $\ensuremath{\lambda}$. In $^{3}\mathrm{He}$, the quenches induced by the rapid cooling of the ``hot spots'' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap ${\ensuremath{\Delta}}_{\ensuremath{\infty}}={ϵ}_{C}{({e}^{2∕N(0)\ensuremath{\lambda}}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.

Physical Review B•Apr 21, 2005•50 citations

Critical dynamics of a two-dimensional superfluid near a nonthermal fixed point

Jan Schole, Boris Nowak, Thomas Gasenzer

Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately rethermalizing, the system approaches a meta-stable transient state, characterized as a nonthermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the nonthermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex unbinding process and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the nonthermal fixed point in a reduced phase space is developed.

arXiv:1204.2487•Physical Review A•Jul 17, 2012•91 citations
We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled, using truncated Wigner approximation. On short time scales the relative phase shows ``light-cone''-like thermalization and creates a metastable superfluid state, which can be supercritical. On longer time scales this state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We observe dynamics of creation of vortex-antivortex pairs and their consequent motion. Our predictions can be directly measured in interference experiments [Z. Hadzibabic et al., Nature (London) 441, 1118 (2006)].
We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled. We find that on short time scales the relative phase shows ``light cone''-like dynamics and creates a metastable superfluid state, which can be supercritical. We also demonstrate similar light cone dynamics for the transverse field Ising model. On longer time scales the supercritical state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We study this effect both numerically using truncated Wigner approximation and analytically within a newly suggested time dependent renormalization group approach (RG). In particular, within RG we show that there are two possible fixed points for the real-time evolution corresponding to the superfluid and normal steady states. So depending on the initial conditions and the microscopic parameters of the Hamiltonian the system undergoes a nonequilibrium phase transition of the Kosterlitz-Thouless type. The time scales for the vortex unbinding near the critical point are exponentially divergent, similar to the equilibrium case.
An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature T(KT). An approximate solution for quenches at and above above T(KT) provides insights into the origin of logarithmic transients in the vortex decay, and is in general agreement with recent simulations of the quenched XY model. These results confirm that there is no "creation" of vortices whose density increases with the quench rate as predicted by the Kibble-Zurek theory but only monotonic decay of the thermal vortices already present at the initial temperature.
Bose-Einstein condensates of cold atoms in optical lattices are interesting because the dynamics of the transition from a Mott insulator to a superfluid driven by a quench into the superfluid phase exemplifies non-equilibrium evolutions of gauge-symmetry broken quantum phases. Here we have actually visualised features in real space, which have domain structures that depend on the stage of the transition dynamics. Namely, the system after the quench relaxes in three processes: (i) an exponential growth of the superfluid density, (ii) collapse of the domain structure, and (iii) vortex-antivortex pair-annihilation as the long-range superfluid order is formed. Topological picture due to Kibble-Zurek mechanism and Zurek's freeze-out scenario for slow quenches are confirmed.
Bose-Einstein condensates of cold atoms in optical lattices are interesting because the dynamics of the transition from a Mott insulator to a superfluid driven by a quench into the superfluid phase exemplifies non-equilibrium evolutions of gauge-symmetry broken quantum phases. Here we have actually visualised features in real space, which have domain structures that depend on the stage of the transition dynamics. Namely, the system after the quench relaxes in three processes: (i) an exponential growth of the superfluid density, (ii) collapse of the domain structure, and (iii) vortex-antivortex pair-annihilation as the long-range superfluid order is formed. Topological picture due to Kibble-Zurek mechanism and Zurek's freeze-out scenario for slow quenches are confirmed.
With an eye toward the interpretation of so-called ``cosmological'' experiments performed on the low-temperature phases of 3He^{3}\mathrm{He}3He, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter $\ensuremath{\lambda}$. In 3He^{3}\mathrm{He}3He, the quenches induced by the rapid cooling of the ``hot spots'' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap ${\ensuremath{\Delta}}_{\ensuremath{\infty}}={ϵ}_{C}{({e}^{2∕N(0)\ensuremath{\lambda}}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.
Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately rethermalizing, the system approaches a meta-stable transient state, characterized as a nonthermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the nonthermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex unbinding process and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the nonthermal fixed point in a reduced phase space is developed.