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

TL;DR

This paper presents an analytical approach to study a non-Hermitian spin-orbit coupled ultracold atom in a double well with synchronous modulation, revealing conditions for PT-symmetry breaking and stable spin tunneling.

Contribution

It introduces a method for exact solutions in a non-Hermitian SO-coupled system under synchronous modulation, analyzing PT-symmetry and tunneling behaviors.

Findings

Analytical conditions for PT-symmetry breaking are derived.

Stable spin-conserving tunneling occurs with Zeeman field, but spin-flipping tunneling does not.

Parameter sets for system stabilization under unbalanced gain and loss are identified.

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 ($\mathcal{PT}$) 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 $\mathcal{PT}$-symmetry breaking is revealed analytically. Surprisingly, we find when the Zeeman field is present, the stable spin-flipping tunneling between two wells can not 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 $\mathcal{PT}$-symmetry breaking and quantum spin dynamics in a non-Hermitian SO-coupled system.