On the finite-size effects in two segregated Bose-Einstein condensates restricted by a hard wall

Quyet Quyet,Thu Thu,Phat Phat,Tam Tam

doi:10.5488/cmp.22.13001

Abstract

The finite-size effects in two segregated Bose-Einstein condensates (BECs) restricted by a hard wall is studied by means of the Gross-Pitaevskii equations in the double-parabola approximation (DPA). Starting from the consistency between the boundary conditions (BCs) imposed on condensates in confined geometry and in the full space, we find all possible BCs together with the corresponding condensate profiles and interface tensions. We discover two finite-size effects: a) The ground state derived from the Neumann BC is stable whereas the ground states derived from the Robin and Dirichlet BCs are unstable. b) Thereby, there equally manifest two possible wetting phase transitions originating from two unstable states. However, the one associated with the Robin BC is more favourable because it corresponds to a smaller interface tension.

Highlights

The physics of binary Bose-Einstein condensate mixture in infinite space has explored many interesting instabilities
Based on the GP equations in the double-parabola approximation (DPA), we investigated the system of two segregated Bose-Einstein condensates restricted by a hard wall
Our main results are in order: a) Making use of the consistency between the the boundary conditions (BCs) imposed on the condensates in confined geometry and in infinite space, we determined the BCs for both condensates at a hard wall, namely, the Neumann BC for the second condensate and Dirichlet BC for the first condensate

Summary

Introduction

The physics of binary Bose-Einstein condensate mixture in infinite space has explored many interesting instabilities. In [12, 13], with the Dirichlet BCs imposed for both condensates, the authors indicated impeccably that the system of interest can undergo a wetting phase transition. In the present paper we explore the unstable states associated with the BCs at a hard wall, and we proceed to the study of wetting phase transitions. We prove that the wetting phase transition associated with the Robin BC at hard wall is more favourable. To this end, we make use of the double-parabola approximation (DPA) method which was proposed in [14, 15] and was developed in [16,17,18].

Ground state in DPA

Interface tension in grand canonical ensemble

Conclusion and outlook