Sequential Landau-Zener transitions in spin-orbit coupled systems

TL;DR

This paper explores how spin-orbit coupling influences Landau-Zener transitions in single and multiple two-level systems, revealing sequential transitions, Franck-Condon effects, and the interplay with interactions, supported by analytical and numerical results.

Contribution

It provides a detailed analysis of sequential Landau-Zener transitions in spin-orbit coupled systems, including analytical formulas and the effects of interactions in many-body scenarios.

Findings

Sequential LZ transitions occur at low sweeping rates with strong SOC.

Franck-Condon blockade affects energy-level crossings.

Interaction effects modify transition dynamics in many-particle systems.

Abstract

We investigate the Landau-Zener (LZ) process in spin-orbit coupled systems of single or multiple two-level (spin-$\frac{1}{2}$) particles. The coupling between internal spin states and external vibrational states, a simple spin-orbit coupling (SOC), is induced by applying a spin-dependent harmonic trap. Because of the SOC, the single-particle energy-level structures are modified by the Franck-Condon (FC) effects, in which some avoided energy-level-crossings (ELCs) are almost closed and some ELCs are opened. The close of avoided ELCs and the open of ELCs result in the FC blockade and the vibrational transitions, respectively. For a given low sweeping rate, the sequential LZ transitions of ladder-like population transition can be induced by strong SOC. We derive an analytical formula for the final population which is well consistent with the numerical results. For a given strong SOC, the sequential LZ transitions are submerged in the non-adiabatic transitions if the sweeping rate is sufficiently high. Further, we study LZ transitions of multiple interacting two-level Bose particles in a spin-dependent harmonic trap. The interplay between the SOC effects and the interaction effects is explored.