# Collective excitation of a trapped Bose-Einstein condensate with spin-orbit coupling

## TL;DR

This paper studies the collective excitations in a spin-orbit coupled Bose-Einstein condensate confined in a one-dimensional trap, revealing phase-dependent features and proposing experimental methods to identify phase boundaries.

## Contribution

It introduces a detailed analysis of collective modes across different quantum phases in a spin-orbit coupled BEC using Bogoliubov theory and numerical simulations.

## Key findings

- Distinct excitation features for each quantum phase
- Spin dipole and breathing modes map phase boundaries
- Numerical simulations confirm theoretical predictions

## Abstract

We investigate the collective excitations of a Raman-induced spin-orbit coupled Bose-Einstein condensate confined in a quasi one-dimension harmonic trap using the Bogoliubov method. By tuning the Raman coupling strength, three phases of the system can be identified. By calculating the transition strength, we are able to classify various excitation modes that are experimentally relevant. We show that the three quantum phases possess distinct features in their collective excitation properties. In particular, the spin dipole and the spin breathing modes can be used to clearly map out the phase boundaries. We confirm these predictions by direct numerical simulations of the quench dynamics that excites the relevant collective modes.