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arXiv:1305.5192 · Physical Review A

Coexistence of phase transitions and hysteresis near the onset of Bose-Einstein condensation

M. Männel, Klaus Morawetz, P. Lipavský

Published May 22, 2013• 5 citations
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Abstract

Multiple phases occurring in a Bose gas with finite-range interaction are investigated. In the vicinity of the onset of Bose-Einstein condensation (BEC), the chemical potential and the pressure show a van der Waals--like behavior indicating a first-order phase transition although there is no long-range attraction. Furthermore, the equation of state becomes multivalued near the BEC transition. For a Hartree-Fock or Popov (Hartree-Fock-Bogoliubov) approximation, such a multivalued region can be avoided by the Maxwell construction. For sufficiently weak interaction, the multivalued region can also be removed using a many-body $T$-matrix approximation. However, for strong interactions there remains a multivalued region even for the $T$-matrix approximation and after the Maxwell construction, which is interpreted as a density hysteresis. This unified treatment of normal and condensed phases becomes possible due to the recently found scheme to eliminate self-interaction in the $T$-matrix approximation, which allows one to calculate properties below and above the critical temperature.

DOI
10.1103/physreva.87.053617

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Multiple phases occurring in a Bose gas with finite-range interaction are investigated. In the vicinity of the onset of Bose-Einstein condensation (BEC), the chemical potential and the pressure show a van der Waals--like behavior indicating a first-order phase transition although there is no long-range attraction. Furthermore, the equation of state becomes multivalued near the BEC transition. For a Hartree-Fock or Popov (Hartree-Fock-Bogoliubov) approximation, such a multivalued region can be avoided by the Maxwell construction. For sufficiently weak interaction, the multivalued region can also be removed using a many-body TTT-matrix approximation. However, for strong interactions there remains a multivalued region even for the TTT-matrix approximation and after the Maxwell construction, which is interpreted as a density hysteresis. This unified treatment of normal and condensed phases becomes possible due to the recently found scheme to eliminate self-interaction in the TTT-matrix approximation, which allows one to calculate properties below and above the critical temperature.
We investigate a Bose gas with finite-range interaction using a scheme to eliminate unphysical processes in the T-matrix approximation. In this way the corrected T-matrix becomes suitable to calculate properties below the critical temperature. For attractive interaction, an Evans-Rashid transition occurs between a quasi-ideal Bose gas and a BCS-like phase with a gaped dispersion. The gap decreases with increasing density and vanishes at a critical density where the single-particle dispersion becomes linear for small momenta indicating Bose-Einstein condensation. The investigation of the pressure shows however, that the mentioned quantum phase transitions might be inaccessible due to a preceding first order transition.
Predictions from Hartree–Fock (HF), Popov (P), Yukalov–Yukalova (YY) and t -matrix approximations regarding the thermodynamics from the normal to the Bose–Einstein condensation (BEC) phase in weakly interacting Bose gases are considered. By analysing the dependence of the chemical potential μ on the temperature T and particle density ρ, we show that none of them predicts a second-order phase transition as required by symmetry-breaking general considerations. In this work, we find that the isothermal compressibility κ T predicted by these theories does not diverge at criticality as expected in a true second-order phase transition. Moreover, the isotherms μ = μ(ρ, T ) typically exhibit non-single-valued behaviour in the vicinity of the BEC transition, a feature forbidden by general thermodynamic principles. This behaviour can be avoided if a first-order phase transition is appealed. The facts described above show that although these mean field approximations give correct results near zero temperature, they are endowed with thermodynamic anomalies in the vicinity of the BEC transition. We address the implications of these results in the interpretation of current experiments with ultracold trapped alkali gases.
Abstract We consider a Bose gas with two-body Kac-like scaled interactions where is a given repulsive and integrable potential, while is a positive parameter which controls the range of the interactions and their amplitude at a distance r. Using the Hartree–Fock (HF) approximation we find that, at finite non-zero temperatures, the Bose–Einstein (BE) condensation is destroyed by the repulsive interactions when they are sufficiently long-range. More precisely, we show that for sufficiently small but finite the off-diagonal part of the one-body density matrix always vanishes at large distances. Our analysis sheds light on the coupling between critical correlations and long-range interactions, which might lead to the breakdown of the off-diagonal long-range order even beyond the HF approximation. Furthermore, our HF analysis shows the existence of a threshold value above which the BE condensation is restored. Since is an unbounded increasing function of the temperature this implies for a fixed , namely for a fixed scaled potential, that a condensate cannot form above some critical temperature whatever the value of the density.
The self-consistent equations for the order parameters of Bose–Einstein condensation (BEC) of molecules and Bardeen–Cooper–Schrieffer (BCS) condensation of atoms in a Fermi gas of atoms with an attractive two-body interaction between atoms have been derived within the Hartree–Fock–Bogoliubov approximation from the path integral representation of the grand partition function. We have found that the order parameters for BEC and BCS are proportional to each other, which implies that BEC and BCS onsets simultaneously. We have also found that the common critical temperature of BEC and BCS increases as the average number of molecules increases and that the atom-molecule coupling enhances the common critical temperature.
We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral Monte Carlo methods. Our focus is on the regime of interspecies interactions where the ground state is in a self-bound liquid phase, stabilized by beyond mean-field effects. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength and establish the extent of the coexistence region between liquid and vapor using the Maxwell construction. Notably, within the coexistence region, Bose-Einstein condensation occurs in a discontinuous way as the density jumps from the normal gas to the superfluid liquid phase. Furthermore, we determine the critical point where the line of first-order transition ends and investigate the behavior of the density discontinuity in its vicinity. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps.
Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.