# Quantum phases in spin-orbit-coupled Floquet spinor Bose gases

## TL;DR

This paper introduces a novel Floquet engineering approach to create spin-orbit-coupled spinor Bose-Einstein condensates with unique quantum phases, including new stripe phases influenced by magnetic interactions.

## Contribution

It proposes a Floquet method to realize spin-orbit coupling in spinor BECs, revealing new stripe phases and their dependence on magnetic interactions.

## Key findings

- Stripe phase exists over a wide quadratic Zeeman field range for antiferromagnetic interactions.
- A distinct stripe phase with higher contrast is found for ferromagnetic interactions.
- Floquet engineering modifies spin-exchange interactions and Rabi frequencies in the system.

## Abstract

We propose a spin-orbit-coupled Floquet spinor Bose-Einstein condensate (BEC) which can be implemented by Floquet engineering of a quadratic Zeeman field. The Floquet spinor BEC has a Bessel-function-modulated Rabi frequency and a Floquet-induced spin-exchange interaction. The quantum phase diagram of the spin-orbit-coupled Floquet spinor BEC is investigated by considering antiferromagnetic or ferromagnetic spin-spin interactions. In comparison with the usual spin-orbit-coupled spin-1 BEC, we find that a stripe phase for antiferromagnetic interactions can exist in a large quadratic Zeeman field regime, and a different stripe phase with an experimentally favorable contrast for ferromagnetic interactions is uncovered.