Many-Body Phases of a Planar Bose-Einstein Condensate with Cavity-Induced Spin-Orbit Coupling

TL;DR

This paper investigates the complex many-body phases of a 2D Bose-Einstein condensate with cavity-induced dynamic spin-orbit coupling, revealing three distinct quantum phases with unique atomic and photonic properties.

Contribution

It introduces a novel setup with cavity-mediated spin-orbit coupling and identifies three new quantum phases, including a supersolid spin-density-wave phase with emergent lattice structure.

Findings

Identification of three quantum phases: homogeneous, spin-helix, and supersolid spin-density-wave.

Observation of a dynamically generated orthorhombic lattice structure in the supersolid phase.

Demonstration of cavity-mediated spin-orbit coupling inducing complex many-body phenomena.

Abstract

We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. By the help of two transverse non-interfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-$\Lambda$-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal ``homogeneous'' phase, the superradiant ``spin-helix'' phase, and the superradiant ``supersolid spin-density-wave'' phase. The latter exhibits an emergent periodic atomic density distribution with an orthorhombic centered rectangular-lattice structure due to the interplay between the coherent photon scattering into the resonator and the collision-induced momentum coupling. The transverse lattice spacing of the emergent crystal is set by the dynamic spin-orbit coupling.