Critical properties of a trapped interacting Bose gas

Bezett, A.; Blakie, P. B.

doi:10.1103/physreva.79.033611

Cited by 40 publications

(67 citation statements)

References 53 publications

(87 reference statements)

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“…Because the PGPE neglects collisional processes that transfer population between the coherent and incoherent regions, it is likely to underestimate damping rates (for example), and the PGPE dynamics are potentially sensitive to the value of the cutoff [65]. However, dynamical calculations within a pure PGPE formalism are able to provide useful insights into the dynamics of degenerate Bose-gas systems in situations where a precise identification of the method with the full field theory is impractical [45,58,66].…”

Section: Projected Gross-pitaevskii Equation (Pgpe)mentioning

confidence: 99%

“…The main advantage that the ZNG method offers is a description of the coupled dynamics of the condensate and the full thermal cloud, in which the kinetics of the latter are modelled in a Boltzmann equation approach. 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%

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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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Section: Projected Gross-pitaevskii Equation (Pgpe)mentioning

confidence: 99%

Section: A Relevance To Other Theoriesmentioning

confidence: 99%

C-Field Methods for Non-Equilibrium Bose Gases

et al. 2013

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“…At low to moderate temperatures generalised mean field theories have been developed, and successfully modelled a number of experimental scenarios. The Zaremba-Nikuni-Griffin (ZNG) [28][29][30][31][32][33], projected Gross-Pitaevskii equation (PGPE) [34][35][36][37][38][39][40][41][42][43][44] (including applications to spinor condensates [45,46]), and number conserving [47][48][49] theories each have advantages for describing BEC evolution, namely, relative ease of handling thermal cloud dynamics, inclusion of many appreciably populated coherent modes, and inclusion of off-diagonal long range order, respectively. At temperatures well below the BEC transition (T c ), these effects are essential aspects of finite-temperature BEC physics.…”

Section: Introductionmentioning

confidence: 99%

Stochastic projected Gross-Pitaevskii equation for spinor and multicomponent condensates

Bradley

Blakie

2014

Phys. Rev. A

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A stochastic Gross-Pitaevskii equation is derived for partially condensed Bose gas systems subject to binary contact interactions. The theory we present provides a classical-field theory suitable for describing dissipative dynamics and phase transitions of spinor and multi-component Bose gas systems comprised of an arbitrary number of distinct interacting Bose fields. A new class of dissipative processes involving distinguishable particle interchange between coherent and incoherent regions of phase-space is identified. The formalism and its implications are illustrated for two-component mixtures and spin-1 Bose-Einstein condensates. For systems comprised of atoms of equal mass, with thermal reservoirs that are close to equilibrium, the dissipation rates of the theory are reduced to analytical expressions that may be readily evaluated. The unified treatment of binary contact interactions presented here provides a theory with broad relevance for quasi-equilibrium and far-from-equilibrium Bose-Einstein condensates.

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“…A key appeal is that they provide an approximation to the full distribution function of the ultracold gas and give access to physics beyond the mean field. They have been used, e.g., to probe the large critical fluctuations near the phase transition [61][62][63], to study dynamical effects of fluctuations on condensate growth [48,49,64] and macroscopic excitations [65][66][67][68][69]. Another quantity of interest is the counting statistics of the condensate mode [63,[70][71][72][73], which is analogous to the photon number distribution in quantum laser theory [74].…”

Section: Introductionmentioning

confidence: 99%

Comparison between microscopic methods for finite-temperature Bose gases

et al. 2011

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We analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a number-conserving Bogoliubov (ncB) approach and a stochastic GrossPitaevskii equation (sGPe) that have been extensively used in numerical simulations. Equilibrium properties like density profiles, correlation functions, and the condensate statistics are compared to predictions based upon a number of alternative theories. We find that due to thermal phase fluctuations, and the corresponding condensate depletion, the ncB approach loses its validity at relatively low temperatures. This can be attributed to the change in the Bogoliubov spectrum, as the condensate gets thermally depleted, and to large fluctuations beyond perturbation theory. Although the two stochastic theories are built on different thermodynamic ensembles (ncB: canonical, sGPe: grandcanonical), they yield the correct condensate statistics in a large BEC (strong enough particle interactions). For smaller systems, the sGPe results are prone to anomalously large number fluctuations, well-known for the grand-canonical, ideal Bose gas. Based on the comparison of the above theories to the modified Popov approach, we propose a simple procedure for approximately extracting the Penrose-Onsager condensate from first-and second-order correlation functions that is computationally convenient. This also clarifies the link between condensate and quasi-condensate in the Popov theory of low-dimensional systems.

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Critical properties of a trapped interacting Bose gas

Cited by 40 publications

References 53 publications

C-Field Methods for Non-Equilibrium Bose Gases

C-Field Methods for Non-Equilibrium Bose Gases

Stochastic projected Gross-Pitaevskii equation for spinor and multicomponent condensates

Comparison between microscopic methods for finite-temperature Bose gases

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