Symmetry breaking of a matter-wave soliton in a double-well potential formed by spatially confined spin-orbit coupling

Abstract

We consider the symmetry breaking of a matter-wave soliton formed by spinor Bose-Einstein condensates (BECs) illuminated by a two-spot laser beam. This laser beam introduces spin-orbit (SO) coupling in the BECs such that the SO coupling produces an effect similar to a linear doublewell potential (DWP). It is well known that symmetry breaking in a DWP is an important effect and has been discussed in many kinds of systems. However, it has not yet been discussed in a DWP formed by SO coupling. The objective of this work is to study the symmetry breaking of spinor BECs trapped by a DWP formed by SO coupling. We find that two kinds of symmetry breaking, displacement symmetry breaking and bimodal symmetry breaking, can be obtained in this model. The influence of the symmetry transition is systematically discussed by controlling the interaction strength of the BECs and the distance between the center of the two spots. Moreover, because SO coupling violates Galilean invariance, the influence of symmetry breaking in the moving system is also addressed in this paper. PACS numbers: 03.75.Lm, 05.45.Yv I. INTRODUCTIONMatter-wave solitons have become an interesting subject of research due to their potential applications in various fields, such as atomic interferometry, quantum information processing, and atomic lasers [1]. Experimental research on a self-trapping soliton in Bose-Einstein condensates (BECs) began with the creation of a dark soliton, followed by bright soliton and bright soliton trains [2][3][4][5]. Many studies have shown that a cold-atom BEC is an excellent system for studying solitons [6][7][8][9][10]. In particular, a stable bright soliton has already been shown to improve the performance of a Mach-Zehnder interferometer compared to regular BECs [11]. Thus, the creation of stable soliton has become a fascinating area of research.Recently, the Gross-Pitaevskii equation (GPE) with the LHY correction term has been proven to be a good mechanism to generate stable quantum droplets , and the GP equation with long-range dipole-dipole interactions can also create stable matter-wave solitons in BECs [35][36][37][38][39]. With the help of spin-orbit (SO) coupling, absolutely stable (ground-state) and metastable matter-wave solitons in 2D and 3D free space have been reported [40][41][42][43][44][45][46][47][48][49]. Moreover, stable excited state solitons [50-54], gap solitons [55,56], and solitons with novel vortices [57][58][59][60][61][62] have been reported to be created by SO coupling [63,64], and similar configurations have also been realized in an optical system [65][66][67][68][69]. However, previous studies on 2D and 3D solitons in BECs with SO coupling tacitly assumed that the SO couplings were a homogeneous effect in the entire space. Recently, by using an external laser beam of a finite width, it was shown that one can implement spatially confined SO coupling, i.e., an SO coupling defect, in spinor BECs in 1D [70] and 2D [71] space. It is interesting to find that solitons are trapped and caught by the SO co...

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