Analytical results for a spin–orbit coupled atom held in a non-Hermitian double well under synchronous combined modulations

Abstract

We propose a simple method of synchronous combined modulations to generate the exact analytic solutions for a spin–orbit (SO) coupled ultracold atom held in a non-Hermitian double-well potential. Based on the obtained analytical solutions, we mainly study the parity-time () symmetry of this system and the system stability for both balanced and unbalanced gain–loss between two wells. Under balanced gain and loss, the effect of the proportional constants between synchronous combined modulations and the SO-coupling strength on the -symmetry breaking is revealed analytically. Surprisingly, we find when the Zeeman field is present, the stable spin-flipping tunneling between two wells cannot occur in the non-Hermitian SO-coupled ultracold atomic system, but the stable spin-conserving tunneling can be performed. Under unbalanced gain and loss, the unique set of parameter conditions that can cause the system to stabilize is found. The results may provide a possibility for the exact control of -symmetry breaking and quantum spin dynamics in a non-Hermitian SO-coupled system.