# Two-mode Dicke model from non-degenerate polarization modes

## TL;DR

This paper demonstrates a non-degenerate two-mode Dicke model using a Bose-Einstein condensate coupled to two orthogonal polarization modes of an optical cavity, revealing a crossover from single-mode to two-mode behavior.

## Contribution

It introduces a novel realization of a two-mode Dicke model with tunable interactions via scalar and vectorial atomic polarizability in a BEC-cavity system.

## Key findings

- Observation of a crossover from single-mode to two-mode Dicke model
- Independent control of scalar and vectorial couplings
- Characterization of the self-organization phase transition

## Abstract

We realize a non-degenerate two-mode Dicke model with competing interactions in a Bose-Einstein condensate (BEC) coupled to two orthogonal polarization modes of a single optical cavity. The BEC is coupled to the cavity modes via the scalar and vectorial part of the atomic polarizability. We can independently change these couplings and determine their effect on a self-organization phase transition. Measuring the phases of the system, we characterize a crossover from a single-mode to a two-mode Dicke model. This work provides perspectives for the realization of coupled phases of spin and density.