Bose−Einstein condensates with tunable spin−orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics

Abstract

We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose−Einstein condensates (BECs) with tunable spin−orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross−Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.

Graphical abstract

Keywords

spin−orbit coupled Bose−Einstein condensates / stability / collapse dynamics

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 12164042, 11764039, 11475027, 11865014, 12104374, 11964008, and 11847304; the Natural Science Foundation of Gansu Province under Grant Nos. 17JR5RA076, 20JR5RA194, and 20JR5RA526; the Scientific Research Project of Gansu Higher Education under Grant No. 2016A-005; the Innovation Capability Enhancement Project of Gansu Higher Education under Grant Nos. 2020A-146 and 2019A-014; the Creation of Science and Technology of Northwest Normal University under Grant No. NWNU-LKQN-18-33.

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