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:1112.4457 · Physical Review Letters

Condensation Dynamics in a Quantum-Quenched Bose Gas

Robert P. Smith, Scott Beattie, Stuart Moulder, Robert L. D. Campbell, Zoran Hadzibabic

Published Sep 6, 2012• 20 citations
arXivHTMLPDF

Abstract

By quenching the strength of interactions in a partially condensed Bose gas, we create a "supersaturated" vapor which has more thermal atoms than it can contain in equilibrium. Subsequently, the number of condensed atoms (N(0)) grows even though the temperature (T) rises and the total atom number decays. We show that the nonequilibrium evolution of the system is isoenergetic and, for small initial N(0), observe a clear separation between T and N(0) dynamics, thus explicitly demonstrating the theoretically expected "two-step" picture of condensate growth. For increasing initial N(0) values, we observe a crossover to classical relaxation dynamics. The size of the observed quench-induced effects can be explained using a simple equation of state for an interacting harmonically trapped atomic gas.

DOI
10.1103/physrevlett.109.105301

Related papers

Dynamical Equilibration Across a Quenched Phase Transition in a Trapped Quantum Gas

I-Kang Liu, S Donadello, G Lamporesi +4 more

The formation of an equilibrium state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of quantum many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously generated defects, whose emergence obeys a universal scaling law with quench duration. The ensuing re-equilibrating or “coarse-graining” stage is governed by the evolution and interactions of such defects under system-specific and external constraints. We perform a detailed numerical characterisation of the entire non-equilibrium process associated with the Bose–Einstein condensation phase transition in a three-dimensional gas of ultracold atoms, addressing subtle issues and demonstrating the quench-induced decoupling of condensate atom number and coherence growth during the re-equilibration process. Our findings agree, in a statistical sense, with experimental observations made at the later stages of the quench, and provide valuable information and useful dynamical visualisations in currently experimentally inaccessible regimes.

•Jun 11, 2018•0 citations

Dynamical equilibration across a quenched phase transition in a trapped quantum gas

I.-K. Liu, Simone Donadello, G. Lamporesi +4 more

Abstract The formation of an equilibrium state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of quantum many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously generated defects, whose emergence obeys a universal scaling law with quench duration. The ensuing re-equilibrating or “coarse-graining” stage is governed by the evolution and interactions of such defects under system-specific and external constraints. We perform a detailed numerical characterisation of the entire non-equilibrium process associated with the Bose–Einstein condensation phase transition in a three-dimensional gas of ultracold atoms, addressing subtle issues and demonstrating the quench-induced decoupling of condensate atom number and coherence growth during the re-equilibration process. Our findings agree, in a statistical sense, with experimental observations made at the later stages of the quench, and provide valuable information and useful dynamical visualisations in currently experimentally inaccessible regimes.

arXiv:1712.08074•Communications Physics•Jun 5, 2018•58 citations

Quench dynamics and emergence of phase separation in two-component atomic Bose gases at zero temperature and above the Bose-Einstein-condensation critical temperature

Chih-Chun Chien, Fred Cooper

We study the dynamics of two-component atomic Bose gases initially in a mixture encountering a sudden quench of the interspecies interactions. The dynamics above the critical temperature ${T}_{c}$ is studied using a leading-order large-$N$ approximation that predicted a phase transition from mixing to phase separation as a function of the interspecies coupling. Here, we explore the dynamics of this phase transition following a quench and compare our results to those found at zero temperature using the time-dependent Gross-Pitaevskii equations which ignore quantum and thermal fluctuations. In the regime above ${T}_{c}$ where no condensate is present, however, the time evolution of the densities following the quench exhibits features similar to those found at zero temperature where only the condensates contribute to the densities. When the interspecies interaction jumps above the critical value, we observe dynamical transitions from a homogeneous mixture to a phase-separated structure for both cases. Our simulations suggest that at temperatures above ${T}_{c}$ where no condensate is present this dynamical transition should still be observable in experiments.

arXiv:1212.4517•Physical Review A•Apr 10, 2013•7 citations

Formation of Bose-Einstein Condensates

Matthew J. Davis, Tod M. Wright, Thomas Gasenzer +2 more

The problem of understanding how a coherent, macroscopic Bose- Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently, there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases. Introduction The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature T c and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley). In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.

arXiv:1601.06197•Cambridge University Press eBooks•Oct 4, 2018•5 citations

Quench dynamics of an ultracold two-dimensional Bose gas

P. Comaron, F. Larcher, F. Dalfovo +1 more

We study the dynamics of a two-dimensional Bose gas after an instantaneous quench of an initially ultracold thermal atomic gas across the Berezinskii-Kosterlitz-Thouless phase transition, confirming via stochastic simulations that the system undergoes phase-ordering kinetics and fulfills the dynamical scaling hypothesis at late-time dynamics. Specifically, we find in that regime the vortex number decaying in time as $\ensuremath{\langle}{N}_{\mathrm{v}}\ensuremath{\rangle}\ensuremath{\propto}{t}^{\ensuremath{-}1}$, consistent with a dynamical critical exponent $z\ensuremath{\approx}2$ for both temperature and interaction quenches. Focusing on finite-size boxlike geometries, we demonstrate that such an observation is within current experimental reach.

arXiv:1905.05263•Physical Review A•Sep 27, 2019•27 citations

Equilibration time scales in homogeneous Bose–Einstein condensate dynamics

Daniel Gustavo Barci, Eduardo Souza Fraga, Marcelo Gleiser +1 more

We study the nonequilibrium growth of a weakly interacting homogeneous Bose gas after a quench from a high-temperature state to a temperature below the Bose–Einstein critical condensation temperature. We quantitatively characterize the departure from thermal equilibrium and observe the presence of two equilibration time scales. The equilibration times are shown to be inversely proportional to the density.

•Jan 1, 2003•5 citations
By quenching the strength of interactions in a partially condensed Bose gas, we create a "supersaturated" vapor which has more thermal atoms than it can contain in equilibrium. Subsequently, the number of condensed atoms (N(0)) grows even though the temperature (T) rises and the total atom number decays. We show that the nonequilibrium evolution of the system is isoenergetic and, for small initial N(0), observe a clear separation between T and N(0) dynamics, thus explicitly demonstrating the theoretically expected "two-step" picture of condensate growth. For increasing initial N(0) values, we observe a crossover to classical relaxation dynamics. The size of the observed quench-induced effects can be explained using a simple equation of state for an interacting harmonically trapped atomic gas.
The formation of an equilibrium state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of quantum many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously generated defects, whose emergence obeys a universal scaling law with quench duration. The ensuing re-equilibrating or “coarse-graining” stage is governed by the evolution and interactions of such defects under system-specific and external constraints. We perform a detailed numerical characterisation of the entire non-equilibrium process associated with the Bose–Einstein condensation phase transition in a three-dimensional gas of ultracold atoms, addressing subtle issues and demonstrating the quench-induced decoupling of condensate atom number and coherence growth during the re-equilibration process. Our findings agree, in a statistical sense, with experimental observations made at the later stages of the quench, and provide valuable information and useful dynamical visualisations in currently experimentally inaccessible regimes.
Abstract The formation of an equilibrium state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of quantum many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously generated defects, whose emergence obeys a universal scaling law with quench duration. The ensuing re-equilibrating or “coarse-graining” stage is governed by the evolution and interactions of such defects under system-specific and external constraints. We perform a detailed numerical characterisation of the entire non-equilibrium process associated with the Bose–Einstein condensation phase transition in a three-dimensional gas of ultracold atoms, addressing subtle issues and demonstrating the quench-induced decoupling of condensate atom number and coherence growth during the re-equilibration process. Our findings agree, in a statistical sense, with experimental observations made at the later stages of the quench, and provide valuable information and useful dynamical visualisations in currently experimentally inaccessible regimes.
We study the dynamics of two-component atomic Bose gases initially in a mixture encountering a sudden quench of the interspecies interactions. The dynamics above the critical temperature Tc{T}_{c}Tc​ is studied using a leading-order large-NNN approximation that predicted a phase transition from mixing to phase separation as a function of the interspecies coupling. Here, we explore the dynamics of this phase transition following a quench and compare our results to those found at zero temperature using the time-dependent Gross-Pitaevskii equations which ignore quantum and thermal fluctuations. In the regime above Tc{T}_{c}Tc​ where no condensate is present, however, the time evolution of the densities following the quench exhibits features similar to those found at zero temperature where only the condensates contribute to the densities. When the interspecies interaction jumps above the critical value, we observe dynamical transitions from a homogeneous mixture to a phase-separated structure for both cases. Our simulations suggest that at temperatures above Tc{T}_{c}Tc​ where no condensate is present this dynamical transition should still be observable in experiments.
The problem of understanding how a coherent, macroscopic Bose- Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently, there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases. Introduction The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature T c and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley). In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.
We study the dynamics of a two-dimensional Bose gas after an instantaneous quench of an initially ultracold thermal atomic gas across the Berezinskii-Kosterlitz-Thouless phase transition, confirming via stochastic simulations that the system undergoes phase-ordering kinetics and fulfills the dynamical scaling hypothesis at late-time dynamics. Specifically, we find in that regime the vortex number decaying in time as $\ensuremath{\langle}{N}_{\mathrm{v}}\ensuremath{\rangle}\ensuremath{\propto}{t}^{\ensuremath{-}1}$, consistent with a dynamical critical exponent $z\ensuremath{\approx}2$ for both temperature and interaction quenches. Focusing on finite-size boxlike geometries, we demonstrate that such an observation is within current experimental reach.