Softening of Roton and Phonon Modes in a Bose-Einstein Condensate with Spin-Orbit Coupling

TL;DR

This study investigates the excitation spectrum of a spin-orbit coupled Bose-Einstein condensate, revealing roton and phonon mode softening near phase transitions, supported by experimental Bragg spectroscopy and theoretical calculations.

Contribution

It demonstrates the emergence and softening of roton and phonon modes in a weakly interacting BEC with spin-orbit coupling, linking these phenomena to phase transitions.

Findings

Roton-mode softening observed as Raman coupling decreases.

Measured roton gaps match theoretical predictions.

Phonon-mode softening occurs near the phase transition.

Abstract

Roton-type excitations usually emerge from strong correlations or long-range interactions, as in superfluid helium or dipolar ultracold atoms. However, in weakly short-range interacting quantum gas, the recently synthesized spin-orbit (SO) coupling can lead to various unconventional phases of superfluidity, and give rise to an excitation spectrum of roton-maxon character. Using Bragg spectroscopy we study a SO coupled Bose-Einstein condensate of $^{87}$Rb atoms, and show that the excitation spectrum in a "magnetized" phase clearly possesses a two-branch and roton-maxon structure. As Raman coupling strength $\Omega$ is decreased, a roton-mode softening is observed, as a precursor of the phase transition to a stripe phase that spontaneously breaks spatially translational symmetry. The measured roton gaps agree well with theoretical calculations. Further, we determine sound velocities both in the magnetized and the non-magnetized phase, and a phonon-mode softening is observed around the phase transition in between. The validity of the $f$-sum rule is examined.