Simulating cavity QED with spin-orbit coupled Bose-Einstein condensates revisited

Simulating cavity quantum electrodynamics in synthetic platforms offers a promising route to exploring light-matter interactions without real photons, while enabling the transfer of cavity-based techniques to other systems. Among such platforms, Bose-Einstein condensates with synthetic spin-orbit coupling provide a controllable setting where internal and motional degrees of freedom become coupled, mimicking aspects of cavity quantum electrodynamics. In this work, we critically assess the extent to which spin-orbit coupled Bose-Einstein condensates can emulate cavity quantum electrodynamics phenomena, with a focus on squeezing and entanglement generation. We show that spin-orbit coupled Bose-Einstein condensates can faithfully reproduce the physics of a single atom coupled to a quantized field, realizing an analogue of the quantum Rabi model but inherently fail to capture genuine collective effects characteristic of the Dicke model, such as cavity-mediated many-body entanglement. Our results clarify both the potential and the fundamental limitations of spin-orbit coupled Bose-Einstein condensates as analogue quantum simulators of cavity quantum electrodynamics, offering guidance for future strategies to generate and control non-classical states of matter in photon-free, highly tunable platforms.