Two types of ground-state bright solitons in a coupled harmonically trapped pseudo-spin polarization Bose–Einstein condensate

Abstract

We study two types of bright solitons in an attractive Bose-Einstein condensate with a spin-orbit interaction. By solving the coupled nonlinear Schrödinger equations with the variational method and the imaginary time evolution method, fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength. The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate.

Two ground-state bright solitons in fractional-order spin–orbit-coupled Bose–Einstein condensates

“…Figure 1 shows that the density distribution of SOC-BECs is not bilateral symmetric, because the proposed wave function satisfies only the symmetry of σ x (we can also find the ground-state wave function satisfying σ z , but it is not given in this paper). This conclusion is consistent with the results shown for integer-order solitons [47].…”

“…In order to obtain the approximate solution of FSE, two kinds of general variational wave equations are considered based on the characteristics of stationary bright solitons suitable for zero detuning [47]:…”

“…In addition, the multi-component bosons with SOC can further enrich the study of solitons in matter-waves. It introduces more tunable parameters, the attracting (repulsive) interaction inside and outside, the detuning, the strength of the SOC, and the speed of the matter-wave, such as the linear and nonlinear interactions between BECs with spin-orbit and Rabi couplings [45], the interaction between spin-orbits coupled and BECs [46][47][48]. It also presents a new structure of nonlinear, for instance, dark-bright solitons [49], dark-dark solitons [50], and bright-bright solitons [51,52].…”

Gap solitons of spin–orbit-coupled Bose–Einstein condensates in PT periodic potential

“…The new door to the ultra-cold atom quantum system is thus opened, which creates many new possibilities for observing and analyzing quantum phenomena at the macro level. The SOC-BECs effect also shows many interesting localization phenomena, such as solitons, [5][6][7][8][9] band gap solitons [10][11][12] and vortex structures. [13,14] The concept of the 𝒫𝒯 periodic potential firstly appeared in the study of quantum operators and their spectra.…”