# Bright soliton dynamics in Spin Orbit-Rabi coupled Bose-Einstein condensates

## TL;DR

This paper explores the dynamics of spin-orbit coupled Bose-Einstein condensates, demonstrating integrability, oscillation behaviors, collapse phenomena, and the effects of Rabi coupling on soliton phases and stability.

## Contribution

It introduces a gauge transformation approach to analyze oscillations, shows how to manipulate condensate lifetime via Feshbach resonance, and examines the impact of Rabi coupling on soliton phases.

## Key findings

- Rapid oscillations occur at lower SO coupling in a time-independent trap.
- Condensates collapse when transitioning to an expulsive trap.
- Rabi coupling induces striped soliton phases without destabilizing the condensate.

## 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.