Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation

Cockburn, SP; Gallucci, Donatello; Proukakis, N. P.

doi:10.1103/physreva.84.023613

Cited by 29 publications

(48 citation statements)

References 92 publications

(162 reference statements)

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“…(Calculations of the position-space distribution based on a related formalism [18] were recently described in Ref. [19].) We find excellent agreement between the SPGPE results and the momentum-space measurements reported in Ref.…”

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confidence: 76%

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Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

et al. 2012

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We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide a quantitative description of the full momentum distribution measurements of Van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)]. We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry. Ultracold gases offer a unique opportunity to study fundamental problems in quantum many-body physics, allowing experimental observations to be compared directly with microscopic theories. An area of significant recent interest has been the measurement of thermodynamic relations [1][2][3]. The one-dimensional (1D) Bose gas with repulsive interactions has emerged as a paradigm system because exact solutions are available for both eigenstates [4] and thermodynamic quantities [5] (see Ref.[6] and references therein). Furthermore, this system exhibits a surprisingly rich variety of regimes [7,8] connected by broad crossovers. Most studies of the 1D Bose gas have focused on the position-space distributions [3,[8][9][10] and local correlations [7,8,[11][12][13][14], which can be directly obtained from the exact theories.A recent experiment by Van Amerongen et al.[10] measured the position and momentum distributions of a trapped 1D Bose gas throughout the crossover from an ideal gas to the quasicondensate regime. The position-space measurements were compared with the Yang-Yang (YY) thermodynamic solutions [5] within the local density approximation (LDA), and showed smooth behavior throughout the crossover. In contrast, the momentum distributions showed a pronounced temperature dependence, and, to the best of our knowledge, have been unexplained by theory to date. Previous work on the momentum properties of the 1D Bose gas has focused on limiting cases [12,13,15].Here we investigate the momentum properties of the 1D Bose gas and their application to thermometry through measurements of the system kinetic energy. Our methods provide a reliable foundation for accurate thermometry in all regimes of a 1D Bose gas with repulsive interactions, including the strongly correlated regime. This approach is reminiscent of molecular dynamics calculations, where the average kinetic energy per particle is a direct measure of the temperature [16].First, we use the exact YY thermodynamic formalism [5] to calculate the root-mean-square (rms) width of the momentum distribution, which is equivalent to determining the average kinetic energy per particle. In combination with * Current address: SRON, Netherlands Institute for Space Research, Utrecht, The Netherlands.the LDA for trapped (nonuniform) quasi-1D systems, we show how the YY kinetic energy results can be applied to accurate thermometry for a broad range of conditions that are re...

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confidence: 76%

“…[19]). As the SPGPE approach is suited to both equilibrium and dynamical simulations, this opens up an exciting avenue for exploring nonequilibrium phenomena in this system (e.g., quenches [30]), which cannot be explored using the YY solutions or equilibrium quantum Monte Carlo techniques.…”

Section: Fig 2 (Color Online) Examples Of the Experimental Momentummentioning

confidence: 99%

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

et al. 2012

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“…Such a coupled condensate-cloud description appears to be essential for accurately describing certain collective oscillations of the gas at high temperatures [65,86,87]. However, as it is based on the assumption that a well-defined condensate exists, the ZNG approach is not applicable to more general scenarios involving low-dimensional systems [34,48,88,89], regimes of turbulent matter-wave dynamics [23,45,90], or non-equilibrium passage through the transition to condensation [16,44,51].…”

Section: A Relevance To Other Theoriesmentioning

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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“…15 in the framework of the stochastic (projected) GrossPitaevskii equation (SPGPE) to model evaporative cooling of a pancake shaped thermal cloud and study the statistics of trapped vortices and found good agreement between experimental and numerical results. The SGPE and the SPGPE have been used before to model experimental results with success 15,35,36,[47][48][49] .…”

Section: Methodsmentioning

confidence: 99%

Winding up superfluid in a torus via Bose Einstein condensation

Das¹,

Sabbatini²,

Zurek³

2010

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Phase transitions are usually treated as equilibrium phenomena, which yields telltale universality classes with scaling behavior of relaxation time and healing length. However, in second-order phase transitions relaxation time diverges near the critical point (''critical slowing down''). Therefore, every such transition traversed at a finite rate is a non-equilibrium process. Kibble-Zurek mechanism (KZM) captures this basic physics, predicting sizes of domains -fragments of broken symmetry -and the density of topological defects, long-lived relics of symmetry breaking that can survive long after the transition. To test KZM we simulate Bose-Einstein condensation in a ring using stochastic Gross-Pitaevskii equation and show that BEC formation can spontaneously generate quantized circulation of the newborn condensate. The magnitude of the resulting winding numbers and the time-lag of BEC density growth -both experimentally measurable -follow scalings predicted by KZM. Our results may also facilitate measuring the dynamical critical exponent for the BEC transition. Second order phase transitions are always associated with divergence of both the relaxation time (''critical slowing down'') and healing length (''critical opalescence'') at the critical point. These divergences imply inevitable non-adiabaticity when a system is driven across the transition and result in a finite size of domains that can coordinate symmetry breaking. That size is set by the healing length at the time when the system can no longer keep up with the externally imposed change of parameters that drive it through the transition, and adiabatic following gives way to impulse ''freezeout'' of its state.This mosaic of domains with independent choices of broken symmetry may result in topological defects. Their densities at formation will bear universal signatures of the underlying phase transition. Kibble-Zurek mechanism (KZM) is the theoretical framework that describes the dynamics of symmetry breaking in second order phase transitions by taking into account finite speed of propagation of the relevant information [1][2][3][4][5] . KZM leads to a quantitative estimate for the density of defects [3][4][5][6] . In particular, it predicts that their density should scale with the quench rate. The scaling exponent predicted by KZM is a function of the critical exponents of the underlying equilibrium phase transition. The basic ingredients for this prediction are the critical exponents -i.e., the universality class of the transition. Therefore, applicability of KZM spans physical phenomena of enormous variety and scales, starting from microscopic phenomenon of vortex formation in superfluid, right up to phenomena of astronomical scales, like formation of structures (cosmic strings, monopoles, etc.) in the early Universe.Kibble-Zurek mechanism has been tested in a number of primarily numerical studies, see, e.g., Refs.7-14 . However, on the experimental side, while, as of now, data confirm key qualitative predictions of KZM (creation of topological excitat...

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Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation

Cited by 29 publications

References 92 publications

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

C-Field Methods for Non-Equilibrium Bose Gases

Winding up superfluid in a torus via Bose Einstein condensation

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