Geometric effects in the effective-mass theory and topological optical superlattices

TL;DR

This paper proposes a novel method to induce effective spin-orbit coupling in cold atom optical lattices by leveraging geometric effects in the effective-mass theory, enabling topological phases without internal state manipulation.

Contribution

It introduces a geometric approach to realize effective SOC in optical superlattices, bypassing the need for Raman coupling and internal atomic state control.

Findings

Effective SOC can be achieved through geometric effects in the effective-mass framework.

The approach induces nontrivial topological phases in 2D optical superlattices.

Relativistic-like effects such as an effective Darwin term are significant in this context.

Abstract

Cold atoms tailored by an optical lattice have become a fascinating arena for simulating quantum physics. In this area, one important and challenging problem is creating effective spin-orbit coupling (SOC), especially for fashioning a cold atomic gas into a topological phase, for which prevailing approaches mainly rely on the Raman coupling between the atomic internal states and a laser field. Herein, a strategy for realizing effective SOC is proposed by exploiting the geometric effects in the effective-mass theory, without resorting to internal atomic states. It is shown that the geometry of Bloch states can have nontrivial effects on the wave-mechanical states under external fields, leading to effective SOC and an effective Darwin term, which have been neglected in the standard effective-mass approximation. It is demonstrated that these relativisticlike effects can be employed to introduce effective SOC in a two-dimensional optical superlattice, and induce a nontrivial topological phase.