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:1701.03133 · Journal of Physics B Atomic Molecular and Optical Physics

Cross-over to quasi-condensation: mean-field theories and beyond

Carsten Henkel, Tim-O Sauer, Nick P. Proukakis

Published May 15, 2017• 17 citations
arXivHTMLPDF

Abstract

We analyze the cross-over of a homogeneous, weakly interacting Bose gas in one dimension from the ideal gas into the dense quasi-condensate phase. We review a number of mean-field theories, perturbative or self-consistent, and provide accurate evaluations of equation of state, density fluctuations, and correlation functions. A smooth crossover is reproduced by classical-field simulations based on the stochastic Gross–Pitaevskii equation and the Yang–Yang solution to the one-dimensional Bose gas.

DOI
10.1088/1361-6455/aa6888

Related papers

Density fluctuations in a very elongated Bose gas : transition towards quasi-bec and 1D-3D crossover

Isabelle Bouchoule, Julien Armijo, T. Jacqmin +1 more

By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas. We also perform measurements of the third moment of atom number fluctuations. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasi-condensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three body correlations in the system.

•Aug 23, 2010•0 citations

Mapping out the quasi-condensate transition through the 1D-3D dimensional crossover

Julien Armijo, T. Jacqmin, Karen V. Kheruntsyan +1 more

By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.

arXiv:1011.3631•Nov 16, 2010•0 citations

Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation

S. P. Cockburn, Donatello Gallucci, Nick P. Proukakis

The stochastic Gross-Pitaevskii equation is shown to be an excellent model for quasi-one-dimensional Bose gas experiments, accurately reproducing the in situ density profiles recently obtained in the experiments of Trebbia et al. [Phys. Rev. Lett. 97, 250403 (2006)] and van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)] and the density fluctuation data reported by Armijo et al. [Phys. Rev. Lett. 105, 230402 (2010)]. To facilitate such agreement, we propose and implement a quasi-one-dimensional extension to the one-dimensional stochastic Gross-Pitaevskii equation for the low-energy, axial modes, while atoms in excited transverse modes are treated as independent ideal Bose gases.

arXiv:1103.2740•Physical Review A•Aug 8, 2011•26 citations

Dimensional and Temperature Crossover in Trapped Bose Gases

UAl Khawaja, Nick P. Proukakis, JO Andersen +2 more

We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.

•Dec 31, 2003•0 citations

Dimensional and temperature crossover in trapped Bose gases

Usama Al Khawaja, Nick P. Proukakis, Jens O. Andersen +2 more

We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.

arXiv:cond-mat/0303483•Physical Review A•Oct 6, 2003•35 citations

Interacting bosons in an optical lattice

Ch. Moseley, Oleksandr Fialko, K. Ziegler

Several models of a strongly interacting Bose gas in an optical lattice are studied within the functionalintegral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-

•Nov 27, 2012•17 citations
We analyze the cross-over of a homogeneous, weakly interacting Bose gas in one dimension from the ideal gas into the dense quasi-condensate phase. We review a number of mean-field theories, perturbative or self-consistent, and provide accurate evaluations of equation of state, density fluctuations, and correlation functions. A smooth crossover is reproduced by classical-field simulations based on the stochastic Gross–Pitaevskii equation and the Yang–Yang solution to the one-dimensional Bose gas.
By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas. We also perform measurements of the third moment of atom number fluctuations. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasi-condensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three body correlations in the system.
By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.
The stochastic Gross-Pitaevskii equation is shown to be an excellent model for quasi-one-dimensional Bose gas experiments, accurately reproducing the in situ density profiles recently obtained in the experiments of Trebbia et al. [Phys. Rev. Lett. 97, 250403 (2006)] and van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)] and the density fluctuation data reported by Armijo et al. [Phys. Rev. Lett. 105, 230402 (2010)]. To facilitate such agreement, we propose and implement a quasi-one-dimensional extension to the one-dimensional stochastic Gross-Pitaevskii equation for the low-energy, axial modes, while atoms in excited transverse modes are treated as independent ideal Bose gases.
We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.
We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.
Several models of a strongly interacting Bose gas in an optical lattice are studied within the functionalintegral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-