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:1711.00873 · SciPost Physics

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

Jean-Sébastien Caux, Benjamin Doyon, Jérôme Dubail, Robert Konik, Takato Yoshimura

Published Jun 20, 2019• 100 citations
arXivHTMLPDF

Abstract

Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900 (2006)], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the one-dimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges.

DOI
10.21468/scipostphys.6.6.070

Related papers

Thermalization of a quantum Newton's cradle in a one-dimensional quasicondensate

Kieran F. Thomas, Matthew J. Davis, Karen V. Kheruntsyan

We study the nonequilibrium dynamics of the quantum Newton's cradle in a one-dimensional (1D) Bose gas in the weakly interacting quasicondensate regime. This is the opposite regime to the original quantum Newton's cradle experiment of [Kinoshita et al., Nature 440, 900 (2006)], which was realized in the strongly interacting 1D Bose gas. Using finite temperature $c$-field methods, we calculate the characteristic relaxation rates to the final equilibrium state. Hence, we identify the different dynamical regimes of the system in the parameter space that characterizes the strength of interatomic interactions, the initial temperature, and the magnitude of the Bragg momentum used to initiate the collisional oscillations of the cradle. In all parameter regimes, we find that the system relaxes to a final equilibrium state for which the momentum distribution is consistent with a thermal distribution. For sufficiently large initial Bragg momentum, the system can undergo hundreds of repeated collisional oscillations before reaching the final thermal equilibrium. The corresponding thermalization timescales can reach tens of seconds, which is an order of magnitude smaller than in the strongly interacting regime.

arXiv:1811.01585•Physical Review A•Feb 15, 2021•30 citations

Benchmarks of Generalized Hydrodynamics for 1D Bose Gases

Raymon S. Watson, S. A. Simmons, Karen V. Kheruntsyan

Generalized hydrodynamics (GHD) is a recent theoretical approach that is becoming a go-to tool for characterizing out-of-equilibrium phenomena in integrable and near-integrable quantum many-body systems. Here, we benchmark its performance against an array of alternative theoretical methods, for an interacting one-dimensional Bose gas described by the Lieb-Liniger model. In particular, we study the evolution of both a localized density bump and dip, along with a quantum Newton's cradle setup, for various interaction strengths and initial equilibrium temperatures. We find that GHD generally performs very well at sufficiently high temperatures or strong interactions. For low temperatures and weak interactions, we highlight situations where GHD, while not capturing interference phenomena on short lengthscales, can describe a coarse-grained behaviour based on convolution averaging that mimics finite imaging resolution in ultracold atom experiments. In a quantum Newton's cradle setup based on a double-well to single-well trap quench, we find that GHD with diffusive corrections demonstrates excellent agreement with the predictions of a classical field approach.

arXiv:2208.06614•Aug 13, 2022•3 citations

Relaxation of bosons in one dimension and the onset of dimensional crossover

Chen Li, Tianwei Zhou, I. E. Mazets +8 more

We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.

arXiv:1804.01969•SciPost Physics•Oct 22, 2020•39 citations

Quantum shock waves and population inversion in collisions of ultracold atomic clouds

Sebastiano Peotta, Massimiliano Di Ventra

Using a time-dependent density matrix renormalization group (TDMRG) approach we study the collision of one-dimensional atomic clouds confined in a harmonic trap and evolving with the Lieb-Liniger Hamiltonian. It is observed that the motion is essentially periodic with the clouds bouncing elastically, at least on the time scale of the first few oscillations that can be resolved with high accuracy. This is in agreement with the results of the ``quantum Newton cradle'' experiment of Kinoshita et al. [Nature (London) 440, 900 (2006)]. We compare the results for the density profile against a hydrodynamic description, or generalized nonlinear Schr\"odinger equation, with the pressure term taken from the Bethe ansatz solution of the Lieb-Liniger model. We find that hydrodynamics can describe the breathing mode of a harmonically trapped cloud for arbitrary long times while it breaks down almost immediately for the collision of two clouds due to the formation of shock waves (gradient catastrophe). In the case of the clouds' collision TDMRG alone allows one to extract the oscillation period which is found to be measurably different from the breathing mode period. Concomitantly with the shock waves formation we observe a local energy distribution typical of population inversion, i.e., an effective negative temperature. Our results are an important step towards understanding the hydrodynamics of quantum many-body systems out of equilibrium and the role of integrability in their dynamics.

arXiv:1303.6916•Physical Review A•Jan 24, 2014•39 citations

Finite-temperature hydrodynamics for one-dimensional Bose gases: Breathing-mode oscillations as a case study

Isabelle Bouchoule, Stuart S. Szigeti, Matthew J. Davis +1 more

We develop a finite-temperature hydrodynamic approach for a harmonically trapped one-dimensional quasicondensate and apply it to describe the phenomenon of frequency doubling in the breathing-mode oscillations of the quasicondensate momentum distribution. The doubling here refers to the oscillation frequency relative to the oscillations of the real-space density distribution, invoked by a sudden confinement quench. By constructing a nonequilibrium phase diagram that characterizes the regime of frequency doubling and its gradual disappearance, we find that this crossover is governed by the quench strength and the initial temperature rather than by the equilibrium-state crossover from the quasicondensate to the ideal Bose gas regime. The hydrodynamic predictions are supported by the results of numerical simulations based on a finite-temperature $c$-field approach and extend the utility of the hydrodynamic theory for low-dimensional quantum gases to the description of finite-temperature systems and their dynamics in momentum space.

arXiv:1602.07889•Physical Review A•Nov 7, 2016•47 citations

Experiments on hydrodynamic transport in ultra-cold bose gasses

Sonja Koller

At temperatures near the absolut zero, a gas, here atomic sodium vapour, with high enough density cannot be described as tiny balls moving around as in classical physics. Since the temperature is low, the atoms are so slow that the matterwave of each atom starts to extend over the size of the atom and even over the interatomic distance. Therefore, they start to interfere like waves. Quantum mechanics start to dominate the physics in this regime. Further, depending on the sort of atoms (bosons or fermions) the atoms prefer to be in the same state or avoid to be in the same state. In the case of bosons as in the thesis, if the temperature is lowered to sub micro Kelvin temperature, a new state of matter appears after a phase transition - a macroscopic, standing wave, the Bose-Einstein condensate. This leads to a new phenomena: superfluidity - frictionless flow, second sound, vorticity and coherent scattering effects to name a few. The atoms are trapped in a elongated trap as in most of the experiments in ultra cold gasses. Usually experiments are done in a regime where the atoms seldomly collide with each other while travelling from one end to the other end of the cloud. In this experiment, however, the atoms collide many times with each other when they oscillate in the trap. This means that the cloud is hydrodynamic and leads to a very different behaviour. Two different sound waves (first and second sound), heat conduction, and collisional dominated transport can be observed in this case. The fact that the gas is weakly interacting allows comparison with current theory. At very low temperatures as in the experiments described in the thesis, the Bose character strongly alters the collisions of the atoms. The outcome of the collision does not only depend on the colliding atoms, but also on the atoms near by in phase space. The experiments outlined in this thesis cover some aspects of physics involved. Vortices have been created and observed in the Bose-Einstein condensate that rested in a weak trap. Both sound modes first and second sound have been observed with slight local heating. In the regime considered, first sound, that has not been observed in a dilute Bose-Einstein condensate before, is mainly a modulation in local temperature and not density. In another experiment a particular effect is observed when the cloud is only axially hydrodynamic. When the trap is suddenly axially relaxed, the cloud creats a strip pattern that is in the radial direction and moving outward. The analysis of this experiment suggests that this is only the case when the cloud is indeed only axially hydrodynamic. The last chapter describs a spin drag experiment. In this experiment two spin species of atoms are prepared and on one of them a force is applied. Through collisions, the other species is dragged along. This effect is Bose enhanced at temperatures approaching the transition temperature to a Bose-Einstein condensate which is observed and matches recent theory.

•Sep 10, 2012•3 citations
Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900 (2006)], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the one-dimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges.
We study the nonequilibrium dynamics of the quantum Newton's cradle in a one-dimensional (1D) Bose gas in the weakly interacting quasicondensate regime. This is the opposite regime to the original quantum Newton's cradle experiment of [Kinoshita et al., Nature 440, 900 (2006)], which was realized in the strongly interacting 1D Bose gas. Using finite temperature ccc-field methods, we calculate the characteristic relaxation rates to the final equilibrium state. Hence, we identify the different dynamical regimes of the system in the parameter space that characterizes the strength of interatomic interactions, the initial temperature, and the magnitude of the Bragg momentum used to initiate the collisional oscillations of the cradle. In all parameter regimes, we find that the system relaxes to a final equilibrium state for which the momentum distribution is consistent with a thermal distribution. For sufficiently large initial Bragg momentum, the system can undergo hundreds of repeated collisional oscillations before reaching the final thermal equilibrium. The corresponding thermalization timescales can reach tens of seconds, which is an order of magnitude smaller than in the strongly interacting regime.
Generalized hydrodynamics (GHD) is a recent theoretical approach that is becoming a go-to tool for characterizing out-of-equilibrium phenomena in integrable and near-integrable quantum many-body systems. Here, we benchmark its performance against an array of alternative theoretical methods, for an interacting one-dimensional Bose gas described by the Lieb-Liniger model. In particular, we study the evolution of both a localized density bump and dip, along with a quantum Newton's cradle setup, for various interaction strengths and initial equilibrium temperatures. We find that GHD generally performs very well at sufficiently high temperatures or strong interactions. For low temperatures and weak interactions, we highlight situations where GHD, while not capturing interference phenomena on short lengthscales, can describe a coarse-grained behaviour based on convolution averaging that mimics finite imaging resolution in ultracold atom experiments. In a quantum Newton's cradle setup based on a double-well to single-well trap quench, we find that GHD with diffusive corrections demonstrates excellent agreement with the predictions of a classical field approach.
We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.
Using a time-dependent density matrix renormalization group (TDMRG) approach we study the collision of one-dimensional atomic clouds confined in a harmonic trap and evolving with the Lieb-Liniger Hamiltonian. It is observed that the motion is essentially periodic with the clouds bouncing elastically, at least on the time scale of the first few oscillations that can be resolved with high accuracy. This is in agreement with the results of the ``quantum Newton cradle'' experiment of Kinoshita et al. [Nature (London) 440, 900 (2006)]. We compare the results for the density profile against a hydrodynamic description, or generalized nonlinear Schr\"odinger equation, with the pressure term taken from the Bethe ansatz solution of the Lieb-Liniger model. We find that hydrodynamics can describe the breathing mode of a harmonically trapped cloud for arbitrary long times while it breaks down almost immediately for the collision of two clouds due to the formation of shock waves (gradient catastrophe). In the case of the clouds' collision TDMRG alone allows one to extract the oscillation period which is found to be measurably different from the breathing mode period. Concomitantly with the shock waves formation we observe a local energy distribution typical of population inversion, i.e., an effective negative temperature. Our results are an important step towards understanding the hydrodynamics of quantum many-body systems out of equilibrium and the role of integrability in their dynamics.
We develop a finite-temperature hydrodynamic approach for a harmonically trapped one-dimensional quasicondensate and apply it to describe the phenomenon of frequency doubling in the breathing-mode oscillations of the quasicondensate momentum distribution. The doubling here refers to the oscillation frequency relative to the oscillations of the real-space density distribution, invoked by a sudden confinement quench. By constructing a nonequilibrium phase diagram that characterizes the regime of frequency doubling and its gradual disappearance, we find that this crossover is governed by the quench strength and the initial temperature rather than by the equilibrium-state crossover from the quasicondensate to the ideal Bose gas regime. The hydrodynamic predictions are supported by the results of numerical simulations based on a finite-temperature ccc-field approach and extend the utility of the hydrodynamic theory for low-dimensional quantum gases to the description of finite-temperature systems and their dynamics in momentum space.
At temperatures near the absolut zero, a gas, here atomic sodium vapour, with high enough density cannot be described as tiny balls moving around as in classical physics. Since the temperature is low, the atoms are so slow that the matterwave of each atom starts to extend over the size of the atom and even over the interatomic distance. Therefore, they start to interfere like waves. Quantum mechanics start to dominate the physics in this regime. Further, depending on the sort of atoms (bosons or fermions) the atoms prefer to be in the same state or avoid to be in the same state. In the case of bosons as in the thesis, if the temperature is lowered to sub micro Kelvin temperature, a new state of matter appears after a phase transition - a macroscopic, standing wave, the Bose-Einstein condensate. This leads to a new phenomena: superfluidity - frictionless flow, second sound, vorticity and coherent scattering effects to name a few. The atoms are trapped in a elongated trap as in most of the experiments in ultra cold gasses. Usually experiments are done in a regime where the atoms seldomly collide with each other while travelling from one end to the other end of the cloud. In this experiment, however, the atoms collide many times with each other when they oscillate in the trap. This means that the cloud is hydrodynamic and leads to a very different behaviour. Two different sound waves (first and second sound), heat conduction, and collisional dominated transport can be observed in this case. The fact that the gas is weakly interacting allows comparison with current theory. At very low temperatures as in the experiments described in the thesis, the Bose character strongly alters the collisions of the atoms. The outcome of the collision does not only depend on the colliding atoms, but also on the atoms near by in phase space. The experiments outlined in this thesis cover some aspects of physics involved. Vortices have been created and observed in the Bose-Einstein condensate that rested in a weak trap. Both sound modes first and second sound have been observed with slight local heating. In the regime considered, first sound, that has not been observed in a dilute Bose-Einstein condensate before, is mainly a modulation in local temperature and not density. In another experiment a particular effect is observed when the cloud is only axially hydrodynamic. When the trap is suddenly axially relaxed, the cloud creats a strip pattern that is in the radial direction and moving outward. The analysis of this experiment suggests that this is only the case when the cloud is indeed only axially hydrodynamic. The last chapter describs a spin drag experiment. In this experiment two spin species of atoms are prepared and on one of them a force is applied. Through collisions, the other species is dragged along. This effect is Bose enhanced at temperatures approaching the transition temperature to a Bose-Einstein condensate which is observed and matches recent theory.