Quantum-classical correspondence of non-Hermitian spin-orbit coupled bosonic junction

TL;DR

This paper explores the classical-quantum correspondence in non-Hermitian spin-orbit coupled bosonic systems, revealing conditions for symmetry-breaking, atomic self-trapping, and synchronized oscillations, with implications for understanding non-Hermitian quantum dynamics.

Contribution

It analytically establishes the classical Hamiltonian structure of non-Hermitian spin-orbit coupled bosonic junctions and uncovers unique dynamical behaviors related to symmetry and coupling strength.

Findings

Classical-quantum correspondence breaks near symmetry-breaking points.

Atomic self-trapping occurs at half-integer SOC strength, independent of particle number.

SOC enhances synchronized oscillations between spin components.

Abstract

We investigate the classical-quantum correspondence of non-Hermitian Spin-orbit (SO)-coupled bosonic junctions, where an effective decay term is introduced in one of the two wells. Starting from the normalized two-point functions, we analytically demonstrate that the mean-field system has a classical Hamiltonian structure, and we successfully derive a non-Hermitian discrete nonlinear Schr\"odinger (Gross-Pitaevskii) equation. We discover that near the symmetry-breaking phase transition point, the correspondence between classical (mean-field) and quantum dynamics is more likely to break down. When the effective spin-orbit coupling (SOC) strength assumes half-integer values, atomic self-trapping in the non-lossy well definitely occurs, regardless of the system parameters, and the quantum dynamics is insensitive to the number of particles. Additionally, we reveal that in both the mean-field and many-particle models, the SOC effects can greatly promote the synchronous periodic oscillations between the spin-up and spin-down components, and this synchronization dynamics is protected by a symmetry mechanism.