Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates

Abstract

We investigate the dynamics of a spin-orbit (SO) coupled BECs in a time dependent harmonic trap and show the dynamical system to be completely integrable by constructing the Lax pair. We then employ gauge transformation approach to witness the rapid oscillations of the condensates for a relatively smaller value of SO coupling in a time independent harmonic trap compared to their counterparts in a transient trap. Keeping track of the evolution of the condensates in a transient trap during its transition from confining to expulsive trap, we notice that they collapse in the expulsive trap. We further show that one can manipulate the scattering length through Feshbach resonance to stretch the lifetime of the confining trap and revive the condensate. Considering a SO coupled state as the initial state, the numerical simulation indicates that the reinforcement of Rabi coupling on SO coupled BECs generates the striped phase of the bright solitons and does not impact the stability of the condensates despite destroying the integrability of the dynamical system.

Exotic complexes in one-dimensional Bose-Einstein condensates with spin-orbit coupling

“…The nonlinear dynamics of BECs with SOC in quasi-one dimension is described by the coupled Gross-Pitaevskii equations in the mean-field limit 1,2,5,6 in which the linear cross coupling Rabi term of strength R has been set to zero ( R = 0) for simplicity 40 . Such a situation was recently suggested in ref.…”

“…Such a situation was recently suggested in ref. 40 since the presence of the cross coupling Rabi term does not impact the stability of the condensates and merely induces small stripes for small values of R . In Eq.…”

Dragging spin-orbit-coupled solitons by a moving optical lattice

“…( 15) and ( 16), in which the y derivatives are dropped (this limit case is opposite to one considered above in the form of Eqs. ( 20) and (21), where the x derivatives were omitted). The stationary version of these equations for real functions ũ± (x), defined as in Eq.…”

“…( 15) and ( 16) into its 1D version. In turn, the 1D system may be reduced, as mentioned above, to the single GPE ( 21), which has no limitation for the existence of solitons at any velocity.…”

“…Many theoretical works addressed the interplay of SOC with the intrinsic nonlinearity of BEC, which represents, in the mean-field approximation, effects of collisions between atoms in the dilute quantum gas. In the case of the self-attractive sign of the nonlinearity, the analysis has predicted the modulational instability [10] and various species of one-dimensional (1D) solitons [11]- [21] under the action of SOC. In the case of the repulsive nonlinearity, the use of spatially periodic optical-lattice (OL) potentials has made it possible to predict 1D gap solitons [22,23,25].…”