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

Physical Review A

Quasicondensation in a two-dimensional interacting Bose gas

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

Published Mar 16, 2000• 71 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.61.043608

Related papers

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

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

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.

arXiv:cond-mat/9811090•Nov 6, 1998•0 citations

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

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

Finite-temperature phase transitions in quasi-two-dimensional spin-1 Bose gases

Ville Pietilä, Tapio Simula, Mikko Möttönen

Recently, the Berezinskii-Kosterlitz-Thouless transition was found to be mediated by half-quantum vortices (HQVs) in two-dimensional (2D) antiferromagnetic Bose gases [S. Mukerjee, C. Xu, and J. E. Moore, Phys. Rev. Lett. 97, 120406 (2006)]. We study the thermal activation of HQVs in the experimentally relevant trapped quasi-2D system and find a crossover temperature at which free HQVs proliferate at the center of the trap. Above the crossover temperature, we observe transitions corresponding to the onset of a coherent condensate and a quasicondensate and discuss the absence of a fragmented condensate.

arXiv:0909.1898•Physical Review A•Mar 23, 2010•12 citations

The trapped two-dimensional Bose gas: from Bose–Einstein condensation to Berezinskii–Kosterlitz–Thouless physics

Zoran Hadzibabic, P. Krüger, Marc Cheneau +2 more

We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional (2D) geometry. In this experiment a well-defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent 2D clouds. We first show that this transition cannot be explained in terms of conventional Bose–Einstein condensation of the trapped ideal Bose gas. Using the local density approximation (LDA), we then combine the mean-field (MF) Hartree–Fock theory with the prediction for the Berezinskii–Kosterlitz–Thouless (BKT) transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent quantum Monte Carlo (QMC) analysis. However, when the residual thermal excitation of the strongly confined degree of freedom is taken into account, excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor ∼2). Quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.

arXiv:0712.1265•New Journal of Physics•Apr 30, 2008•111 citations

Two-dimensional weakly interacting Bose gas in the fluctuation region

Nikolay V. Prokof'ev, Boris V. Svistunov

We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii-Kosterlitz-Thouless phase transition point. We argue that this crossover is described by universal (for all weakly interacting $|\ensuremath{\psi}{|}^{4}$ models) relations between thermodynamic parameters of the system, including superfluid and quasicondensate densities. We establish these relations with high-precision Monte Carlo simulations of the classical $|\ensuremath{\psi}{|}^{4}$ model on a lattice, and check their asymptotic forms against analytic expressions derived on the basis of the mean-field theory.

arXiv:cond-mat/0206223•Physical Review A•Oct 11, 2002•191 citations
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 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 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 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.
Recently, the Berezinskii-Kosterlitz-Thouless transition was found to be mediated by half-quantum vortices (HQVs) in two-dimensional (2D) antiferromagnetic Bose gases [S. Mukerjee, C. Xu, and J. E. Moore, Phys. Rev. Lett. 97, 120406 (2006)]. We study the thermal activation of HQVs in the experimentally relevant trapped quasi-2D system and find a crossover temperature at which free HQVs proliferate at the center of the trap. Above the crossover temperature, we observe transitions corresponding to the onset of a coherent condensate and a quasicondensate and discuss the absence of a fragmented condensate.
We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional (2D) geometry. In this experiment a well-defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent 2D clouds. We first show that this transition cannot be explained in terms of conventional Bose–Einstein condensation of the trapped ideal Bose gas. Using the local density approximation (LDA), we then combine the mean-field (MF) Hartree–Fock theory with the prediction for the Berezinskii–Kosterlitz–Thouless (BKT) transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent quantum Monte Carlo (QMC) analysis. However, when the residual thermal excitation of the strongly confined degree of freedom is taken into account, excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor ∼2). Quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.
We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii-Kosterlitz-Thouless phase transition point. We argue that this crossover is described by universal (for all weakly interacting $|\ensuremath{\psi}{|}^{4}$ models) relations between thermodynamic parameters of the system, including superfluid and quasicondensate densities. We establish these relations with high-precision Monte Carlo simulations of the classical $|\ensuremath{\psi}{|}^{4}$ model on a lattice, and check their asymptotic forms against analytic expressions derived on the basis of the mean-field theory.