Optomechanically-Based Probing of Spin-Charge Separation in Ultracold Gases

We propose a new approach to investigate the spin-charge separation in 1D quantum liquids via the optomechanical coupled atom-cavity system. We show that, one can realize an effective two-modes optomechanical model with the spin/charge modes playing the role of mechanical resonators. By tuning the weak probe laser under a pump field, the signal of spin-charge separation could be probed explicitly in the sideband regime via cavity transmissions. Moreover, the spin/charge modes can be addressed separately by designing the probe field configurations, which may be beneficial for future studies of the atom-cavity systems and quantum many-body physics.