Cavity-induced emergent topological spin textures in a Bose Einstein condensate

TL;DR

This paper explores how a three-component Bose-Einstein condensate in an optical cavity exhibits diverse topological spin textures and phase transitions driven by cavity-mediated interactions and pump parameters.

Contribution

It introduces a novel cavity QED setup that reveals emergent topological spin textures and phases in a multicomponent BEC, highlighting the role of unpumped modes and cavity-induced spin-orbit coupling.

Findings

Identification of three distinct steady-state phases with unique density and spin textures.

Discovery of topological spin-spiral states related to cavity-induced spin-orbit coupling.

Observation of phase transitions that are either topological and first order or second order.

Abstract

The coupled nonlinear dynamics of ultracold quantum matter and electromagnetic field modes in an optical resonator exhibits a wealth of intriguing collective phenomena. Here we study a $\Lambda$-type, three-component Bose-Einstein condensate coupled to four dynamical running-wave modes of a ring cavity, where only two of the modes are externally pumped. However, the unpumped modes play a crucial role in the dynamics of the system due to coherent back-scattering of photons. On a mean- field level we identify three fundamentally different steady-state phases with distinct characteristics in the density and spatial spin textures: a combined density and spin wave, a continuous spin spiral with a homogeneous density, and a spin spiral with a modulated density. The spin-spiral states, which are topological, are intimately related to cavity-induced spin-orbit coupling emerging beyond a critical pump power. The topologically trivial density-wave--spin-wave state has the characteristics of a supersolid with two broken continuous symmetries. The transitions between different phases are either simultaneously topological and first order, or second order. The proposed setup allows the simulation of intriguing many-body quantum phenomena by solely tuning the pump amplitudes and frequencies, with the cavity output fields serving as a built-in nondestructive observation tool.