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Communications in Physics

Phase Transition in Binary Mixture of Bose Gases

Trân Hũu Phát, Le Viet Hoa, Nguyễn Tuấn Anh, Nguyen Van Long

Published Aug 15, 2012• 0 citations
Publisher

Abstract

Based on the Cornwall-Jackiw-Tomboulis (CJT) effective action approach a theoretical formalism is established for studying the Bose-Einstein condensation (BEC) in a binary mixture of Bose gases. The effective potential, which preserves the Goldstone theorem, is found in the Hartree-Fock (HF) approximation. This quantity is then used to consider the equation of state (EOS) and the phase transition of the system.

DOI
10.15625/0868-3166/20/3/2282

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Based on the Cornwall-Jackiw-Tomboulis (CJT) effective action approach a theoretical formalism is established for studying the Bose-Einstein condensation (BEC) in a binary mixture of Bose gases. The effective potential, which preserves the Goldstone theorem, is found in the Hartree-Fock (HF) approximation. This quantity is then used to consider the equation of state (EOS) and the phase transition of the system.
The quantum phase transition in binary Bose Gases is studied using the Cornwall-Jackiw-Tomboulis effective potential approach in the double-bubble approximation, which preserves the Goldstone theorem. Its main feature is that the transition is second order occurring at ultra-cold temperatures associated with the type of inverse symmetry-breaking transition occurring when the chemical potential reaches a critical value. However, it cannot simultaneously occur for the two components of a binary mixture of Bose gases.
By means of Cornwal–Jackiw–Tomboulis effective action approach we considered the finite-size effect on Bose–Einstein condensate mixtures confined between two parallel palates. Keeping upto double-bubble approximation and taking into account the conservation of Goldstone boson, our results are quite different from those in previous works within one-loop approximation. The order parameters strongly depend on the distance between palates and can be expressed via the correction terms. The Casimir force is also considered.
Beyond standard approaches in existing literature, we explore the relative shift in the transition temperature of a homogeneous dilute Bose gas using the Cornwall-Jackiw-Tomboulis effective action formalism within the improved Hartree-Fock approximation. The first correction to the enhancement of the transition temperature, as compared to that of the ideal Bose gas, is expressed in a universal form: it is linear with respect to the scattering length. The slope of this linear relationship shows excellent agreement with the exact numerical calculations presented in previous studies. Additionally, we identify non-universal terms contributing to the shift.
Experimental realizations of a variety of atomic binary Bose-Fermi mixtures have brought opportunities for studying composite quantum systems with different spin statistics. The binary atomic mixtures can exhibit a structural transition from a mixture into phase separation as the boson-fermion interaction increases. By using a path-integral formalism to evaluate the grand partition function and the thermodynamic grand potential, we obtain the effective potential of binary Bose-Fermi mixtures. Thermodynamic quantities in a broad range of temperatures and interactions are also derived. The structural transition can be identified as a loop of the effective potential curve, and the volume fraction of phase separation can be determined by the lever rule. For $^{6}\mathrm{Li}\ensuremath{-}^{7}\mathrm{Li}$ and $^{6}\mathrm{Li}\ensuremath{-}^{41}\mathrm{K}$ mixtures, we present the phase diagrams of the mixtures in a box potential at zero and finite temperatures. Due to the flexible densities of atomic gases, the construction of phase separation is more complicated when compared to conventional liquid or solid mixtures where the individual densities are fixed. For harmonically trapped mixtures, we use the local density approximation to map out the finite-temperature density profiles and present typical trap structures, including the mixture, partially separated phases, and fully separated phases.