Simulations of Bose Fields at Finite Temperature

Morgan, S. A.; Burnett, K.

doi:10.1103/physrevlett.87.160402

Cited by 226 publications

(369 citation statements)

References 18 publications

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“…Constructing and studying phase diagrams is an important goal in many areas of physics and our findings here serve as an example where equilibrium and dynamical phase diagrams are not identical. We confirm our predictions by comparing the hydrodynamic results to those obtained numerically using finite-temperature c-field simulations (for a review, see [20]) based on the projected Gross-Pitaevskii equation [19].…”

supporting

confidence: 76%

“…Here we develop a general finite-T hydrodynamic approach suitable for 1D Bose gases and specifically apply it to the breathing-mode oscillations of a harmonically trapped 1D quasicondensate. We find that the predictions agree with both experimental observations [18] and numerical simulations of a finitetemperature c-field methodology [19,20]. More remarkably, our hydrodynamic approach not only adequately describes the dynamics of the density distribution of the gas (the standard observable of the hydrodynamic theory), but it can also be used to describe the dynamics of the momentum distribution, which is a key observable for quantum gas experiments.…”

supporting

confidence: 69%

“…Although the applicability of the hydrodynamic theory in this system might be questionable, our analytic results have been benchmarked against finite-temperature c-field simulations (performed using the software package XMDS2 [36]), whose validity for degenerate weakly interacting Bose gases is well established [19,20,[37][38][39]. In this approach, the Bose gas is approximated as a classical field, whose evolution is governed by the time-dependent Gross-Pitaevskii equation, with the initial state being sampled from the classical Gibbs ensemble for the given temperature and density [31].…”

Section: Of Frequency ω(T)mentioning

confidence: 99%

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

et al. 2016

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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. DOI: 10.1103/PhysRevA.94.051602 Hydrodynamics is a powerful and broadly applicable approach for characterizing the collective nonequilibrium behavior of a wide range of classical and quantum fluids, including Fermi liquids, liquid helium, and ultracold atomic Bose and Fermi gases [1][2][3][4][5][6]. For ultracold gases, the hydrodynamic approach has been particularly successful in describing the breathing (monopole) and higher-order (multipole) collective oscillations of harmonically trapped three-dimensional (3D) Bose-Einstein condensates [2,6,7]. For condensates near zero temperature, the applicability of the approach stems from the fact that for long-wavelength (low-energy) excitations the hydrodynamic equations are essentially equivalent to those of superfluid hydrodynamics, which in turn can be derived from the Gross-Pitaevskii equation for the order parameter. For partially condensed samples at finite temperatures, the hydrodynamic equations should be generalized to the equations of two-fluid hydrodynamics, where the applicability of the approach to the normal (thermal) component of the gas is justified by fast thermalization times due to collisional relaxation [3,8].In contrast to 3D systems, the applicability of the hydrodynamic approach to 1D Bose gases is not well established. First, in the thermodynamic limit 1D Bose gases lack the long-range order required for superfluid hydrodynamics to be a priori applicable. Second, the very notion of local thermalization, required for the validity of collisional hydrodynamics of normal fluids, is questionable due to the underlying integrability of the uniform 1D Bose gas model [9]. Despite these reservations, the hydrodynamic approach has already been applied to zero-temperature (T = 0) dynamics of 1D Bose gases in various scenarios [10][11][12][13][14][15] (for related experiments, see [16][17][18]). The comparison of hydrodynamic predictions with exact theoretical results is challenging. In Ref.[13], timedependent density-matrix renorm...

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supporting

confidence: 76%

supporting

confidence: 69%

Section: Of Frequency ω(T)mentioning

confidence: 99%

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

et al. 2016

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“…This results in a closed system, and the resulting Hamiltonian evolution of the field Φ(r) conserves the energy, normalisation, and any other first integrals which may be present, such as the momentum [20,21], angular momentum [58], or spinor-gas magnetisation [59].…”

Section: Projected Gross-pitaevskii Equation (Pgpe)mentioning

confidence: 99%

C-Field Methods for Non-Equilibrium Bose Gases

et al. 2013

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We review c-field methods for simulating the non-equilibrium dynamics of degenerate Bose gases beyond the mean-field Gross-Pitaevskii approximation. We describe three separate approaches that utilise similar numerical methods, but have distinct regimes of validity. Systems at finite temperature can be treated with either the closed-system projected Gross-Pitaevskii equation (PGPE), or the open-system stochastic projected GrossPitaevskii equation (SPGPE). These are both applicable in quantum degenerate regimes in which thermal fluctuations are significant. At low or zero temperature, the truncated Wigner projected Gross-Pitaevskii equation (TWPGPE) allows for the simulation of systems in which spontaneous collision processes seeded by quantum fluctuations are important. We describe the regimes of validity of each of these methods, and discuss their relationships to one another, and to other simulation techniques for the dynamics of Bose gases. The utility of the SPGPE formalism in modelling non-equilibrium Bose gases is illustrated by its application to the dynamics of spontaneous vortex formation in the growth of a Bose-Einstein condensate.

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“…While in agreement, the theoretical results lie near the upper range of the experimental error bars. Previously one of us used the classical field projected Gross-Pitaevskii equation (PGPE) formalism [19][20][21] to give an estimate of the shift in T c of the homogeneous Bose gas [22], which was found to be in agreement with the Monte Carlo calculations [5,6]. The PGPE is a dynamical nonperturbative method, with the only approximation being that the highly occupied modes (hN k i 1) of the quantum Bose field are well approximated by a classical field evolved according to the GPE.…”

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confidence: 99%

Critical Temperature of a Trapped Bose Gas: Comparison of Theory and Experiment

2006

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We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature T c of a harmonically confined Bose gas as reported in Gerbier et al., Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment. The shift in critical temperature T c with interaction strength for the homogeneous Bose gas has been the subject of numerous studies spanning almost 50 years since the first calculations of Lee and Yang [1,2]. While there is a finite shift to the chemical potential in mean-field (MF) theory, the shift of the critical temperature is zero [3]. The leading order effect is due to long-wavelength critical fluctuations and is inherently nonperturbative. Using effective field theory it was determined that the shift is T c =T 0 c can 1=3 , where n is the particle number density, a is the s-wave scattering length, and c is a constant of order unity [4]. Until recently, results for the value of c disagreed by an order of magnitude and even sign, as summarized in Fig. 1

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Simulations of Bose Fields at Finite Temperature

Cited by 226 publications

References 18 publications

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

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

C-Field Methods for Non-Equilibrium Bose Gases

Critical Temperature of a Trapped Bose Gas: Comparison of Theory and Experiment

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