# Four-wave mixing in spin-orbit coupled Bose-Einstein condensates

## TL;DR

This paper explores four-wave mixing in spin-orbit coupled Bose-Einstein condensates, identifying conditions for different configurations, demonstrating unique dynamics through simulations, and highlighting potential experimental applications in quantum physics.

## Contribution

It derives phase matching conditions for FWM in spin-orbit coupled BECs and demonstrates possible configurations and dynamics through numerical simulations.

## Key findings

- Identified four distinct FWM configurations based on spinor states.
- Discovered a unique configuration with probe waves slower than the pump.
- Showed simultaneous occurrence of two FWM processes.

## Abstract

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin-orbit coupled Bose-Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play important role in the experiments of BEC with artificial gauge fields. Beams created by FWM processes are important source of correlated particles and can be used the experiments testing quantum properties of atomic ensembles.