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

Abstract

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.

Figures (4)

• Figure 1: (a) The standard Dicke model describes an ensemble of two-level atoms interacting with a single mode of an optical cavity. The cavity mode mediates transitions between the two atomic spin states. (b) A spin--orbit coupled Bose--Einstein condensate confined in an external trap. Here, two internal spin states are coupled via two counter-propagating Raman lasers. Although the physical realizations differ, the mathematical structure of the couplings is strikingly similar---particularly in the quadrature representation where $\hat{a} + \hat{a}^\dagger \sim \hat{x}$. The key distinction lies in the nature of the coupling: in the Dicke model, the interaction is collective, represented through the collective spin operator $\hat{S}_x$, as all atoms couple to a single harmonic oscillator mode associated with the cavity field.
• Figure 2: Spin squeezing with two spin-orbit coupled atoms. Solid blue line depicts the fluctuations of $\hat{S}_x$ and dotted orange line depicts fluctuations of $\hat{S}_y$. $(a)$ Shows the symmetric Dicke coupling which is known to generate squeezing, $(b)$ depicts the antisymmetric part of coupling which also generates squeezing but in an opposite direction to the squeezing generated by the Dicke coupling, $(c)$ represents a combined effect of the two coupling terms resulting in no squeezing at all. In the simulation we set $\omega/\Omega=10000$ to be deep in the dispersive regime.
• Figure 3: Spin squeezing with three spin-orbit coupled atoms. Solid blue line depicts the fluctuations of $\hat{S}_x$ and dotted orange line depicts fluctuations of $\hat{S}_y$. $(a)$ Shows the squeezing generated by the symmetric Dicke coupling, $(b)$ and $(c)$ depict squeezing generated by less symmetric couplings. Similarly as in the case of 2 atoms, there is no squeezing due to competition between all the coupling terms. In the simulation we set $\omega/\Omega=10000$ to be deep in the dispersive regime.
• Figure 4: Spin squeezing with four spin-orbit coupled atoms. Solid blue line depicts the fluctuations of $\hat{S}_x$ and dotted orange line depicts fluctuations of $\hat{S}_y$. $(a)$ Shows a combined effect of all the coupling terms resulting in no squeezing at all, $(b)$ shows the squeezing generated by the symmetric Dicke coupling, and $(c)$ depict squeezing generated by combined less symmetric couplings. In the simulation we set $\omega/\Omega=10000$ to be deep in the dispersive regime.