Harmonically trapped attractive and repulsive spin–orbit and Rabi coupled Bose–Einstein condensates

Abstract

Abstract.Numerically we investigate the ground state of effective one-dimensional spin-orbit (SO) and Rabi coupled two pseudo-spinor Bose-Einstein condensates (BECs) under the effect of harmonic traps. For both signs of the interaction, density profiles of SO and Rabi coupled BECs in harmonic potentials, which simulate a real experimental situation are obtained. The harmonic trap causes a strong reduction of the multi-peak nature of the condensate and it increases its density. For repulsive interactions, the increase of SO coupling results in an uncompressed less dense condensate and with increased multi-peak nature of the density. The increase of Rabi coupling leads to a density increase with an almost constant number of multi-peaks. For both signs of the interaction and negative values of Rabi coupling, the condensate develops a notch in the central point and it seems to a dark-in-bright soliton. In the case of the attractive nonlinearity, an interesting result is the increase of the collapse threshold under the action of the SO and Rabi couplings.

Quasi-one-dimensional spin-orbit- and Rabi-coupled bright dipolar Bose-Einstein-condensate solitons

“…To find the values of the normalization constants d j , we introduce the constraint on the total pseudomagnetization as N −1 j=1,2 (−1) j−1 d 2 j N j = M . Solving the nonlinear system of equations given by these two conditions, we get explicitly the normalization constants as d j = [N [1 + (−1) j−1 M ]/(2N j )] 1/2 [23]. We investigate the stationary and symmetric solutions of Eq.…”

“…So, we construct stationary states setting φ j (z, t) → √ N φ j (z) exp (−iµt). The two resulting stationary equations to the fields φ 1 (z) and φ 2 (z) are tantamount to each other, and these satisfy the condition φ * 1 (z) = φ 2 (z) [22,23]. This condition does not apply to asymmetric solutions [24].…”

Coupled density-spin Bose–Einstein condensates dynamics and collapse in systems with quintic nonlinearity

“…Here we consider effects of SOC and Zeeman splitting (ZS) on the collapse in a 1D system with various forms of the quintic self-attraction [21][22][23]. In 1D settings these effects can be presented in simple and transparent form as a competition between the velocity caused by self-attraction, which is generated in the collapse process, and an anomalous SOC-induced spin-dependent velocity.…”

Nonlinear Management of Topological Solitons in a Spin-Orbit-Coupled System

“…(1) below, generate vorticity in one component if the other one is taken in the zero-vorticity form.The SOC effect, being linear by itself, may be naturally combined with the intrinsic nonlinearity of bosonic gases, represented by cubic terms in the respective GPEs [13] (and/or by nonlocal cubic terms accounting for long-range interactions in BEC built of dipole atoms [14]). The interplay of SOC and nonlinearity makes it possible to predict a great variety of stable modes, including 1D and 2D solitons [15][16][17][18] and various nonlinear topological states in 2D, such as vortices and vortex lattices [19]-[28] and skyrmions [29]. In fact, the 2D and 3D SOC systems is one of the most prolific sources of nonlinear states with intrinsic topological structures.A majority of works addressing nonlinear dynamics of SOC systems investigated the case of self-repulsion, which is relevant to the current experiments with 87 Rb [6].…”

“…On the other hand, it may be efficiently emulated by the similar 1D system, where a counterpart of the SV is a semi-dipole (SD), with a fundamental (spatially even) structure in one component, and a dipole structure (a spatially odd localized state with zero at the central point) in the other (see, e.g., Ref. [17]). MM states are possible in 1D as well, with the fundamental and dipole terms mixed in both components.…”