# Spatiotemporal Bloch states of a spin-orbit coupled Bose-Einstein condensate in an optical lattice

## TL;DR

This paper investigates the properties of spatiotemporal Bloch states in a driven two-component Bose-Einstein condensate with spin-orbit coupling in an optical lattice, revealing how SOC influences entanglement, population imbalance, and quantum transport.

## Contribution

It introduces a novel method to tune spin-orbit coupling via external fields and analyzes exact solutions for the system's quasistationary states.

## Key findings

- SOC induces spin-motion entanglement in Bloch states
- SOC enhances population imbalance in the BEC
- SOC enables manipulation of atomic flow for quantum control

## Abstract

We study the spatiotemporal Bloch states of a high-frequency driven two-component Bose-Einstein condensate (BEC) with spin-orbit coupling (SOC) in an optical lattice. By adopting the rotating-wave approximation (RWA) and applying an exact trial-solution to the corresponding quasistationary system, we establish a different method for tuning SOC via external field such that the existence conditions of the exact particular solutions are fitted. Several novel features related to the exact states are demonstrated, such as SOC leads to spin-motion entanglement for the spatiotemporal Bloch states, SOC increases the population imbalance of the two-component BEC and SOC can be applied to manipulate the stable atomic flow which is conducive to control quantum transport of the BEC for different application purposes.