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/0603821 · Physical Review A

Finite-temperature properties of quasi-two-dimensional Bose-Einstein condensates

Kwangsik T. Nho, David Paul Landau

Published Mar 9, 2006• 13 citations
arXivHTMLPDF

Abstract

Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range, $s$-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.

DOI
10.1103/physreva.73.033606

Related papers

Finite-temperature properties of binary mixtures of two Bose-Einstein condensates

Kwangsik T. Nho, David Paul Landau

This work reports studies of a mixture of two interacting Bose condensates in a quasi-one-dimensional geometry using a finite-temperature path-integral Monte Carlo method. For weakly interacting dilute gases, the interactions between atoms are modeled by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interspecies interaction on the static properties, such as the density profile and the superfluid fraction, is discussed. Our results show that for repulsive intra- and interspecies interactions, the presence of the interspecies interactions dramatically changes the structure of both the density profile and the superfluid fraction, and two species are seen to partially separate in space, and there is a finite-size effect on the phase separation between two partially separating Bose-Einstein condensates. In general, our results agree with the theoretical predictions and experimental observations.

Physical Review A•Nov 13, 2007•6 citations

Kosterlitz-Thouless Transition of the Quasi-Two-Dimensional Trapped Bose Gas

Markus Holzmann, Werner Krauth

We use quantum Monte Carlo methods to compute the density profile, the nonclassical moment of inertia, and the condensate fraction of an interacting quasi-two-dimensional trapped Bose gas with up to N ~ 5 x 10(5) atoms and parameters closely related to recent experiments. We locate the Kosterlitz-Thouless temperature T(KT) and discuss intrinsic signatures of the onset of superfluidity in the density profile. Below T(KT), the condensate fraction is macroscopic even for our largest systems and decays only slowly with system size. We show that the thermal population of excited states in the transverse direction changes the two-dimensional density profile noticeably in both the normal and the superfluid phase.

arXiv:0710.5060•Physical Review Letters•May 12, 2008•87 citations

Properties of Bose-Einstein condensates in a quasi-one-dimensional box trap

Chongshan Zhang, Kwangsik T. Nho, David Paul Landau

We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the $s$-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas--like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.

Physical Review A•Feb 11, 2008•6 citations

Critical Temperature of Interacting Bose Gases in Two and Three Dimensions

Sebastiano Pilati, S. Giorgini, Nikolay V. Prokof'ev

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.

arXiv:0801.3424•Physical Review Letters•Apr 9, 2008•75 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

The free energy of a dilute two-dimensional Bose gas

Mayer, Simon

We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case. We motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks.

•Jan 1, 2020•0 citations
Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range, sss-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.
This work reports studies of a mixture of two interacting Bose condensates in a quasi-one-dimensional geometry using a finite-temperature path-integral Monte Carlo method. For weakly interacting dilute gases, the interactions between atoms are modeled by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interspecies interaction on the static properties, such as the density profile and the superfluid fraction, is discussed. Our results show that for repulsive intra- and interspecies interactions, the presence of the interspecies interactions dramatically changes the structure of both the density profile and the superfluid fraction, and two species are seen to partially separate in space, and there is a finite-size effect on the phase separation between two partially separating Bose-Einstein condensates. In general, our results agree with the theoretical predictions and experimental observations.
We use quantum Monte Carlo methods to compute the density profile, the nonclassical moment of inertia, and the condensate fraction of an interacting quasi-two-dimensional trapped Bose gas with up to N ~ 5 x 10(5) atoms and parameters closely related to recent experiments. We locate the Kosterlitz-Thouless temperature T(KT) and discuss intrinsic signatures of the onset of superfluidity in the density profile. Below T(KT), the condensate fraction is macroscopic even for our largest systems and decays only slowly with system size. We show that the thermal population of excited states in the transverse direction changes the two-dimensional density profile noticeably in both the normal and the superfluid phase.
We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the sss-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas--like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.
We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.
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 the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case. We motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks.