Bloch bound state of spin-orbit-coupled fermions in an optical lattice

TL;DR

This paper investigates how spin-orbit coupling and optical lattice depth influence two-body bound states of fermions, revealing non-monotonic stability behavior due to the interplay of these effects, with implications for experimental detection.

Contribution

It introduces a detailed analysis of two-body bound state stability in spin-orbit coupled optical lattices, highlighting the non-monotonic effects of lattice depth and SOC, including high-band effects.

Findings

Weak SOC and shallow lattices destabilize bound states.

Deep lattices stabilize bound states regardless of SOC strength.

High-band effects influence bound state stability and experimental detection.

Abstract

Understanding fundamentals of few-body physics provides an interesting bottom-up approach for the clarification of many-body properties. The remarkable experimental progress in realizing spin-orbit coupling (SOC) in optical Raman lattices offers a renewed thrust towards discovering novel few-body features induced by the interplay between SOC and optical lattices. Using the Wilson renormalization method to account for high-band effects, we study the low-energy two-body scattering processes of spin-$1/2$ fermions in spin-orbit coupled optical lattices. We demonstrate that, under weak SOC, adding a small lattice potential would destabilize shallow two-body bound states, contrary to conventional wisdom. On the other hand, when lattice is sufficiently deep, two-body bound states are always stabilized by increasing the lattice depth. This intriguing non-monotonic behavior of the bound-state stability derives from the competition between SOC and optical lattices, and can be explained by analyzing the low-energy density of states. We also discuss the impact of high-band effects on such a behavior, as well as potential experimental detections.