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

Bikash Padhi,Sankalpa Ghosh

doi:10.3390/atoms4010001

Bikash Padhi, Sankalpa Ghosh

Open Access

https://doi.org/10.3390/atoms4010001

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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.

Highlights

The fact that electromagnetic radiation can apply forces on mechanical objects through radiation pressure follows directly from Maxwell’s equations and was experimentally verified more than a century ago [1,2]
It is no wonder that cavity quantum optomechanics has emerged as an extremely fascinating branch in experimental or theoretical physics and it comes with a number of promising practical implementation
One may try to investigate what modification cavity does to quantum phases of ultracold atomic system in synthetic gauge field or what type of quantum phenomena can be simulated by placing synthetically gauged ultracold atoms in a cavity [33,34]. To facilitate this direction of investigation, in the first part of this review article we provide a general introduction on the two related sub-fields of ultracold atoms (a) cavity optomechanics with ultracold atoms and (b) ultracold atoms in synthetic gauge field

Summary

Introduction

The fact that electromagnetic radiation can apply forces on mechanical objects through radiation pressure follows directly from Maxwell’s equations and was experimentally verified more than a century ago [1,2]. Cavity optomechanics offers a route to determine and control the quantum states of microscopic as well as macroscopic object This is why using cavity optomechanical technique it is possible to do hypersensitive measurement down to the size limited only by quantum mechanics. It is conventional to consider the mechanical motion to be simple harmonic under the assumption that the typical damping rate of this mechanical motion is much slower than the damping rate κ of the inter-cavity field. This model is very generic in nature and can be realized in a large number of systems [6] with optomechanical coupling frequency. Using this harmonic approximation we can model the motion of the end-mirror as x (t) ≈ x0 sin(Ωm t)

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