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

Abstract

We investigate the effects of spin-orbit coupling and Zeeman splitting on the coupled density-spin dynamics and collapse of the Bose-Einstein condensate driven by the quintic self-attraction in the same-and cross-spin channels. The characteristic feature of the collapse is the decrease in the width as given by the participation ratio of the density rather than by the expectation values of the coordinate. Qualitative arguments and numerical simulations reveal the existence of a critical spin-orbit coupling strength which either prohibits or leads to the collapse, and its dependence on other parameters, such as the condensate's norm, spin-dependent nonlinear coupling, and the Zeeman splitting. The entire nonlinear dynamics critically depends on the initial spin sate.

Evolution of Bose–Einstein condensate systems beyond the Gross–Pitaevskii equation

“…While we restricted our consideration of the relaxation of the BEC to two-body collision processes, three-body interactions can introduce many important effects. It was recently discussed, for example, that in addition to density losses, three-body interactions may result in internal pressure, resulting in repulsive potential [107]. A rigorous treatment of three-body interactions must account for both coherent effects, such as forces and spin precession, and fluctuation and relaxation effects via collision integral.…”

Stabilization of one-dimensional Townes solitons by spin-orbit coupling in a dual-core system

“…( 6) and ( 7), and comparing the results to Eqs. (41), it is easy to find an exact solution of the latter equations, which contains an arbitrary parameter representing an infinitesimal shift of the soliton's center of mass. Keeping the shift equal to zero, one obtains the following exact solution to Eqs.…”

“…The current work on BEC has suggested another possibility to stabilize 2D and 3D solitons, namely, the use of the (pseudo-) spin-orbit-coupling (SOC), which was implemented, as a linear effect, in binary condensates [36][37][38]. It was demonstrated that, if linear SOC terms, which mix two BEC components via the first spatial derivatives (which represent the anomalous velocity in the condensate superfluid [39][40][41]), are added to the usual cubic intraand inter-component attraction, they lift the above-mentioned conformal invariance, and thus allow the coupled NLS equations to create solitons with the norm falling below the fixed TS value. As a result, these solitons become stable (immune to the onset of the critical collapse).…”

“…It is relevant to mention that peculiarities of the collapse of 1D solitons in the SOC model with quintic attraction were recently addressed in Ref. [41], but a possibility of stabilization was not considered there.…”

Collapse of quasi-two-dimensional symmetrized Dresselhaus spin-orbit coupled Bose–Einstein condensate

“…Synthetic spin-orbit coupling (SOC) and optically produced pseudospin-1/2 [10] is one of the most interesting phenomena of the BEC physics with intriguing effects based on "anomalous" spin-dependent velocity. Effect of this "anomalous" velocity in the collapse of BEC was considered in various SOC and interatomic interaction regimes [9,11].…”