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:cond-mat/9811090

Quasicondensation in 2D Interacting Bose Gas: Quantum Monte Carlo Study

Yu. Kagan, V. А. Kashurnikov, Andrey V. Krasavin, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Nov 6, 1998• 0 citations
arXivHTMLPDF

Abstract

We present a detailed Monte Carlo study of correlations in an interacting two-dimensional Bose gas. The data for one-particle density matrix in coordinate representation are compared to the results for the local many-particle density correlators, which are responsible for the recombination rate in real experiments. We found that the appearance and growth of quasicondensate fluctuations changes local correlations between the particles well before the Kosterlitz-Thouless transition point. The amplitude of the $1/m!$-effect is very sensitive even to a rather moderate interaction, and is considerably smaller than its limiting value.

DOI
10.48550/arxiv.cond-mat/9811090

Related papers

Quasicondensation in a two-dimensional interacting Bose gas

Yu. Kagan, V. А. Kashurnikov, Andrey V. Krasavin +2 more

We present a detailed Monte Carlo study of the many-particle density correlations in an interacting two-dimensional (2D) Bose gas, which are responsible for the recombination and spin relaxation rates in real experiments. We confirm that a $1/m!$ effect for local correlators does exist in 2D and can be used for the study of phase transitions. In agreement with a recent experiment [A. I. Safonov et al., Phys. Rev. Lett. 81, 4545 (1998)], the appearance and growth of quasicondensate fluctuations changes local correlations well before the Kosterlitz-Thouless transition point. Even a moderate interaction considerably reduces the amplitude of the $1/m!$ effect. This conclusion indicates that the enhancement of the $1/m!$ effect observed in the experiment by Safonov et al. cannot be ascribed to finite-interaction effects in a purely 2D system.

Physical Review A•Mar 16, 2000•71 citations

Universal correlations and coherence in quasi-two-dimensional trapped Bose gases

Markus Holzmann, Maguelonne Chevallier, Werner Krauth

We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.

arXiv:0911.1704•Physical Review A•Apr 20, 2010•32 citations

Quasicondensation reexamined

Przemysław Bienias, Krzysztof Pawłowski, Mariusz Gajda +1 more

We study in detail the effect of quasicondensation. We show that this effect is strictly related to dimensionality of the system. It is present in one dimensional systems independently of interactions – exists in repulsive, attractive or in non-interacting Bose gas in some range of temperatures below characteristic temperature of the quantum degeneracy. Based on this observation we analyze the quasicondensation in terms of a ratio of the two largest eigenvalues of the single particle density matrix for the ideal gas. We show that in the thermodynamic limit in higher dimensions the second largest eigenvalue vanishes (as compared to the first one) with total number of particles as ≃ N −γ whereas goes to zero only logarithmically in one dimension. We also study the effect of quasicondensation for various geometries of the system: from quasi-1D elongated one, through spherically symmetric 3D case to quasi-2D pancake-like geometry.

arXiv:1203.1811•Journal of Physics Conference Series•Feb 8, 2013•1 citation

Quasicondensation and coherence in the quasi-two-dimensional trapped Bose gas

R. N. Bisset, Matthew J. Davis, Tapio Simula +1 more

We simulate a trapped quasi-two-dimensional Bose gas using a classical field method. To interpret our results we identify the uniform Berezinskii-Kosterlitz-Thouless (BKT) temperature ${T}_{\text{BKT}}$ as where the system phase-space density satisfies a critical value. We observe that density fluctuations are suppressed in the system well above ${T}_{\text{BKT}}$ when a quasicondensate forms as the first occurrence of degeneracy. At lower temperatures, but still above ${T}_{\text{BKT}}$, we observe the development of appreciable coherence as a prominent finite-size effect, which manifests as bimodality in the momentum distribution of the system. At ${T}_{\text{BKT}}$ algebraic decay of off-diagonal correlations occurs near the trap center with an exponent of 0.25, as expected for the uniform system. Our results characterize the low-temperature phase diagram for a trapped quasi-two-dimensional Bose gas and are consistent with observations made in recent experiments.

arXiv:0804.0286•Physical Review A•Mar 30, 2009•70 citations

Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

Nikolay V. Prokof'ev, Oliver Ruebenacker, Boris V. Svistunov

We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical $|\ensuremath{\psi}{|}^{4}$ model on a lattice. The critical density and chemical potential are given by relations ${n}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(mT/2\ensuremath{\pi}{\ensuremath{\Elzxh}}^{2})\mathrm{ln}(\ensuremath{\xi}{\ensuremath{\Elzxh}}^{2}/mU)$ and ${\ensuremath{\mu}}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(mTU/\ensuremath{\pi}{\ensuremath{\Elzxh}}^{2})\mathrm{ln}({\ensuremath{\xi}}_{\ensuremath{\mu}}{\ensuremath{\Elzxh}}^{2}/mU)$, where $T$ is the temperature, $m$ is the mass, and $U$ is the effective interaction. The dimensionless constant $\ensuremath{\xi}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}380\ifmmode\pm\else\textpm\fi{}3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ${\ensuremath{\xi}}_{\ensuremath{\mu}}$ our result is ${\ensuremath{\xi}}_{\ensuremath{\mu}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}13.2\ifmmode\pm\else\textpm\fi{}0.4$. We also report the study of the quasicondensate correlations at the critical point.

arXiv:cond-mat/0106075•Physical Review Letters•Dec 11, 2001•262 citations

Noise correlations of two-dimensional Bose gases

Vijay Pal Singh, Ludwig Mathey

We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in situ. We calculate the correlations of these fluctuations both in real space and in momentum space and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasicondensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasicondensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.

arXiv:1403.4233•Physical Review A•May 12, 2014•8 citations
We present a detailed Monte Carlo study of correlations in an interacting two-dimensional Bose gas. The data for one-particle density matrix in coordinate representation are compared to the results for the local many-particle density correlators, which are responsible for the recombination rate in real experiments. We found that the appearance and growth of quasicondensate fluctuations changes local correlations between the particles well before the Kosterlitz-Thouless transition point. The amplitude of the 1/m!1/m!1/m!-effect is very sensitive even to a rather moderate interaction, and is considerably smaller than its limiting value.
We present a detailed Monte Carlo study of the many-particle density correlations in an interacting two-dimensional (2D) Bose gas, which are responsible for the recombination and spin relaxation rates in real experiments. We confirm that a 1/m!1/m!1/m! effect for local correlators does exist in 2D and can be used for the study of phase transitions. In agreement with a recent experiment [A. I. Safonov et al., Phys. Rev. Lett. 81, 4545 (1998)], the appearance and growth of quasicondensate fluctuations changes local correlations well before the Kosterlitz-Thouless transition point. Even a moderate interaction considerably reduces the amplitude of the 1/m!1/m!1/m! effect. This conclusion indicates that the enhancement of the 1/m!1/m!1/m! effect observed in the experiment by Safonov et al. cannot be ascribed to finite-interaction effects in a purely 2D system.
We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.
We study in detail the effect of quasicondensation. We show that this effect is strictly related to dimensionality of the system. It is present in one dimensional systems independently of interactions – exists in repulsive, attractive or in non-interacting Bose gas in some range of temperatures below characteristic temperature of the quantum degeneracy. Based on this observation we analyze the quasicondensation in terms of a ratio of the two largest eigenvalues of the single particle density matrix for the ideal gas. We show that in the thermodynamic limit in higher dimensions the second largest eigenvalue vanishes (as compared to the first one) with total number of particles as ≃ N −γ whereas goes to zero only logarithmically in one dimension. We also study the effect of quasicondensation for various geometries of the system: from quasi-1D elongated one, through spherically symmetric 3D case to quasi-2D pancake-like geometry.
We simulate a trapped quasi-two-dimensional Bose gas using a classical field method. To interpret our results we identify the uniform Berezinskii-Kosterlitz-Thouless (BKT) temperature TBKT{T}_{\text{BKT}}TBKT​ as where the system phase-space density satisfies a critical value. We observe that density fluctuations are suppressed in the system well above TBKT{T}_{\text{BKT}}TBKT​ when a quasicondensate forms as the first occurrence of degeneracy. At lower temperatures, but still above TBKT{T}_{\text{BKT}}TBKT​, we observe the development of appreciable coherence as a prominent finite-size effect, which manifests as bimodality in the momentum distribution of the system. At TBKT{T}_{\text{BKT}}TBKT​ algebraic decay of off-diagonal correlations occurs near the trap center with an exponent of 0.25, as expected for the uniform system. Our results characterize the low-temperature phase diagram for a trapped quasi-two-dimensional Bose gas and are consistent with observations made in recent experiments.
We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical $|\ensuremath{\psi}{|}^{4}$ model on a lattice. The critical density and chemical potential are given by relations ${n}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(mT/2\ensuremath{\pi}{\ensuremath{\Elzxh}}^{2})\mathrm{ln}(\ensuremath{\xi}{\ensuremath{\Elzxh}}^{2}/mU)$ and ${\ensuremath{\mu}}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(mTU/\ensuremath{\pi}{\ensuremath{\Elzxh}}^{2})\mathrm{ln}({\ensuremath{\xi}}_{\ensuremath{\mu}}{\ensuremath{\Elzxh}}^{2}/mU)$, where TTT is the temperature, mmm is the mass, and UUU is the effective interaction. The dimensionless constant $\ensuremath{\xi}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}380\ifmmode\pm\else\textpm\fi{}3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ${\ensuremath{\xi}}_{\ensuremath{\mu}}$ our result is ${\ensuremath{\xi}}_{\ensuremath{\mu}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}13.2\ifmmode\pm\else\textpm\fi{}0.4$. We also report the study of the quasicondensate correlations at the critical point.
We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in situ. We calculate the correlations of these fluctuations both in real space and in momentum space and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasicondensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasicondensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.