Ultracold Spin-Orbit Coupled Bose-Einstein Condensate in a Cavity: Route to Magnetic Phases Through Cavity Transmission

TL;DR

This paper explores how a spin-orbit coupled Bose-Einstein condensate in a cavity can realize various magnetic phases, controllable via cavity parameters, with phase detection possible through cavity transmission measurements.

Contribution

It introduces a cavity-controlled method to realize and detect quantum magnetic phases in spin-orbit coupled ultracold atoms, linking cavity transmission to magnetic order.

Findings

Atomic dispersion shows Dirac points and Hofstadter spectrum controlled by cavity parameters.

System realizes diverse quantum magnetic phases detectable via cavity transmission.

Cavity-induced optical bistability influences phase stability and experimental observables.

Abstract

We study the spin orbit coupled ultra cold Bose-Einstein condensate placed in a single mode Fabry-P\'erot cavity. The cavity introduces a quantum optical lattice potential which dynamically couples with the atomic degrees of freedom and realizes a generalized extended Bose Hubbard model whose zero temperature phase diagram can be controlled by tuning the cavity parameters. In the non-interacting limit, where the atom-atom interaction is set to zero, the resulting atomic dispersion shows interesting features such as bosonic analogue of Dirac points, cavity controlled Hofstadter spectrum which bears the hallmark of pseudo-spin-1/2 bosons in presence of Abelian and non-Abelian gauge field (the later due to spin-orbit coupling) in a cavity induced optical lattice potential. In the presence of atom-atom interaction, using a mapping to a generalized Bose Hubbard model of spin-orbit coupled bosons in classical optical lattice, we show that the system realizes a host of quantum magnetic phases whose magnetic order can be be detected from the cavity transmission. This provides an alternative approach for detecting quantum magnetism in ultra cold atoms. We discuss the effect of cavity induced optical bistability on this phases and their experimental consequences.