Statistical properties of one-dimensional Bose gas

Bienias, Przemysław; Pawłowski, Krzysztof; Gajda, Mariusz; Rza̧żewski, Kazimierz

doi:10.1103/physreva.83.033610

Cited by 19 publications

(34 citation statements)

References 27 publications

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“…To determine its optimal value, we use similar approach to [18,23]. We turn to noninteracting gas of N bosons and calculate probability distribution P (N ex ) of having N ex atoms excited (8). We use the canonical ensemble and compare our results to similar distribution P cl (N ex ) which has the same physical meaning but is obtained using classical fields approximation (9).…”

Section: A Population Of the Condensate And Its Fluctuationsmentioning

confidence: 99%

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Statistical properties of cold bosons in a ring trap

2020

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A study of an interacting system of bosons in a ring trap at a finite temperature is presented. We consider a gas with contact and long-range dipolar interactions within a framework of the classical fields approximation. For a repulsive gas we have obtained coherence length, population of the ground state and its fluctuations as a function of temperature. In the case of an attractive gas we study local density fluctuations. Additionally, we exactly calculate the partition function for the ideal gas in the canonical ensemble and derive several other macroscopic state functions.

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Section: A Population Of the Condensate And Its Fluctuationsmentioning

confidence: 99%

“…Papers concerning canonical [5] and microcanonical [6] ensemble fluctuations in the experimentally relevant case of the harmonic trap appeared shortly after. These results were followed by studies of interacting gases in the later years [7][8][9][10]. It is worth stressing that there are still many open questions in this area, e.g.…”

Section: Introductionmentioning

confidence: 96%

Statistical properties of cold bosons in a ring trap

2020

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“…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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“…To avoid an ultraviolet catastrophe, we use an appropriate cutoff for the high energy modes [38]. Finally, we sample the phase space in thermal equilibrium by using the Metropolis algorithm [26,37]. Figure 4(b) shows our result in terms of the ratio between the maximal fluctuations of an interacting and a noninteracting BEC as a function of the interaction strength n(0) 1/3 a. Additionally, appropriately scaled results from all other available simulations for interacting harmonically trapped BECs are displayed.…”

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Observation of Atom Number Fluctuations in a Bose-Einstein Condensate

et al. 2019

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Fluctuations are a key property of both classical and quantum systems. While the fluctuations are well understood for many quantum systems at zero temperature, the case of an interacting quantum system at finite temperature still poses numerous challenges. Despite intense theoretical investigations of atom number fluctuations in Bose-Einstein condensates, their amplitude in experimentally relevant interacting systems is still not fully understood. Moreover, technical limitations have prevented their experimental investigation to date. Here we report the observation of these fluctuations. Our experiments are based on a stabilization technique, which allows for the preparation of ultracold thermal clouds at the shot noise level, thereby eliminating numerous technical noise sources. Furthermore, we make use of the correlations established by the evaporative cooling process to precisely determine the fluctuations and the sample temperature. This allows us to observe a telltale signature: the sudden increase in fluctuations of the condensate atom number close to the critical temperature. arXiv:1812.03064v2 [cond-mat.quant-gas]

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Statistical properties of one-dimensional Bose gas

Cited by 19 publications

References 27 publications

Statistical properties of cold bosons in a ring trap

Statistical properties of cold bosons in a ring trap

Comparison between microscopic methods for finite-temperature Bose gases

Observation of Atom Number Fluctuations in a Bose-Einstein Condensate

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