# Topological Nonlinear Optics with Spin-Orbit coupled Bose-Einstein Condensate in Cavity

## TL;DR

This paper demonstrates topological nonlinear optical phenomena in a spin-orbit coupled Bose-Einstein condensate within a cavity, revealing new optical transparencies, topological features, and potential for quantum computation.

## Contribution

It introduces a novel scheme combining spin-orbit coupling and cavity QED to realize topological nonlinear optics with unique optical and topological properties.

## Key findings

- Discovery of inverted optical transparencies with atom-induced gain.
- Emergence of gapless Dirac-like cones and topological edge states.
- Enhanced control of probe light speed via spin-orbit and Zeeman effects.

## Abstract

We report topological nonlinear optics with spin-orbit coupled Bose-Einstein condensate in a cavity. The cavity is driven by a pump laser and weak probe laser which excite Bose-Einstein condensate to an intermediate storage level, where the standard Raman process engineers spin-orbit coupling. We show that the nonlinear photonic interactions at the transitional pathways of dressed states result in new type of optical transparencies, which get completely inverted with atom induced gain. These nonlinear interactions also implant topological sort of features in probe transmission modes by inducing gapless Dirac-like cones, which become gaped in presence of Raman detuning. The topological features get interestingly enhanced in gain regime where the gapless topological edge-like states emerge among the probe modes, which can cause non-trivial phase transition. We show that spin-orbit coupling and Zeeman field effects also impressively revamp fast and slow probe light. The manipulation of dressed states for quantum nonlinear optics with topological characteristics in our findings could be a crucial step towards topological quantum computation.