Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field

TL;DR

This paper explores the optomechanical properties of ultracold atoms in high finesse cavities under synthetic Abelian and non-Abelian gauge fields, revealing how cavity spectra can probe quantum phases and phenomena like Shubnikov de Haas oscillations.

Contribution

It provides a pedagogical analysis of how cavity optomechanics can be used to study ultracold atoms in synthetic gauge fields, linking atomic quantum phases with optical transmission spectra.

Findings

Detection of Shubnikov de Haas oscillations via cavity spectrum

Formation of quantum magnetic phases under non-Abelian gauge fields

Proposed methods to explore atomic phases through cavity transmission

Abstract

In this article we present a pedagogical discussion of some of the optomechanical properties of a high finesse cavity loaded with ultracold atoms in laser induced synthetic gauge fields of different types. Essentially, the subject matter of this article is an amalgam of two sub-fields of atomic molecular and optical (AMO) physics namely, the cavity optomechanics with ultracold atoms and ultracold atoms in synthetic gauge field. After providing a brief introduction to either of these fields we shall show how and what properties of these trapped ultracold atoms can be studied by looking at the cavity (optomechanical or transmission) spectrum. In presence of abelian synthetic gauge field we discuss the cold-atom analogue of Shubnikov de Haas oscillation and its detection through cavity spectrum. Then, in the presence of a non-abelian synthetic gauge field (spin-orbit coupling), we see when the electromagnetic field inside the cavity is quantized, it provides a quantum optical lattice for the atoms, leading to the formation of different quantum magnetic phases. We also discuss how these phases can be explored by studying the cavity transmission spectrum.