Continuous variable entanglement in a cold-atoms mirrorless optical parametric oscillator

In this work, we explore both the internal and external atomic degrees of freedom to observe quantum entanglement between the modes produced by a mirrorless optical parametric oscillator operating below the oscillation threshold in a sample of free-space cold cesium atoms. Using a new heterodyne technique, we recover the covariance matrix that reveals the quantum entanglement for two different pairs of modes, thus demonstrating the generation of four entangled modes in this system. Applications to quantum networks, and the possibilities of studying higher orders of entanglement are a direct consequence of the present study.

💡 Research Summary

In this paper the authors investigate continuous‑variable (CV) quantum entanglement generated by a mirrorless optical parametric oscillator (MOPO) based on four‑wave mixing (FWM) in a cold cloud of cesium atoms. Unlike traditional χ(2) OPOs that require phase‑matched crystals and external mirrors, the χ(3) nonlinearity of FWM allows self‑feedback and mirrorless operation, making the system intrinsically multimode. Two counter‑propagating pump beams (P1 and P2) with orthogonal linear polarizations intersect a magneto‑optical trap (MOT) containing ~2 mm diameter, optical density ≈5, and temperatures of a few hundred µK. The pumps are red‑detuned by ~25 MHz (≈5 Γ) from the closed Cs D2 transition and are switched on for 6.5 ms after the MOT fields are turned off. Under these conditions four spatially separated output modes (S1–S4) are generated via cascaded FWM processes involving Zeeman and recoil‑induced resonances.

Theoretical description starts from the interaction Hamiltonian
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