# Nematic-orbit coupling and nematic density waves in spin-1 condensates

## TL;DR

This paper introduces a method to create artificial nematic-orbit coupling in spin-1 Bose-Einstein condensates using a microwave chip, revealing new quantum phases and density modulations without the need for Raman lasers.

## Contribution

It demonstrates a novel way to induce nematic-orbit coupling in spin-1 condensates via a designed microwave field, exploring resulting phases and excitations.

## Key findings

- Identification of three nematic quantum phases.
- Prediction of periodic nematic density modulations.
- Low energy excitation spectra for each phase.

## Abstract

We propose the creation of artificial nematic-orbit coupling in spin-1 Bose-Einstein condensates, in analogy to spin-orbit coupling. Using a suitably designed microwave chip, the quadratic Zeeman shift, normally uniform in space, can be made to be spatio-temporally varying, leading to a coupling between spatial and nematic degrees of freedom. A phase diagram is explored where three quantum phases with the nematic order emerge: easy-axis, easy-plane with single-well and easy-plane with double well structure in momentum space. By including spin-dependent and spin-independent interactions, we also obtain the low energy excitation spectra in these three phases. Lastly, we show that the nematic-orbit coupling leads to a periodic nematic density modulation in relation to the period $\lambda_T$ of the cosinusoidal quadratic Zeeman term. Our results point to the rich possibilities for manipulation of tensorial degrees of freedom in ultracold gases without requiring Raman lasers, and therefore, obviating light-scattering induced heating.