Synthetic spin-orbit coupling in ultracold $\Lambda$-type atoms

TL;DR

This paper demonstrates how to simulate non-abelian gauge potentials and spin-orbit coupling in ultracold $ ext{Lambda}$-type atoms, revealing that similar structures to tripod configurations can be achieved with proper parameterization.

Contribution

It introduces a method to realize spin-orbit coupling in $ ext{Lambda}$-type atoms, expanding the design possibilities for ultracold atom simulations of gauge fields.

Findings

Simulated gauge potentials match tripod configurations with proper Rabi frequency parameterization.

Spin-orbit coupling in $ ext{Lambda}$ configuration is limited to a form similar to $p_{x}\sigma_{y}$.

The scheme works even when Rabi frequencies are comparable to detuning.

Abstract

We consider the simulation of non-abelian gauge potentials in ultracold atom systems with atom-field interaction in the $\Lambda$ configuration where two internal states of an atom are coupled to a third common one with a detuning. We find the simulated non-abelian gauge potentials can have the same structures as those simulated in the tripod configuration if we parameterize Rabi frequencies properly, which means we can design spin-orbit coupling simulation schemes based on those proposed in the tripod configuration. We show the simulated spin-orbit coupling in the $\Lambda$ configuration can only be of a form similar to $p_{x}\sigma_{y}$ even when the Rabi frequencies are not much smaller than the detuning.