Controlling Normal‐Mode Splitting and Entanglement in an Optomechanical Cavity With Resonant Atomic Gain and Absorption

ABSTRACT

Hybrid optomechanical systems that combine a cavity field, mechanical motion, and intracavity atomic media offer a versatile platform for engineering normal‐mode structure and macroscopic quantum correlations. Most atom‐assisted systems rely on passive absorbing media, leaving the role of an inverted ensemble acting as a resonant intracavity gain element largely unexplored. Here, we investigate a driven optomechanical cavity containing a movable mirror and two resonant atomic ensembles, one prepared in its ground state and the other inverted, thereby realizing a combined absorptive–amplifying intracavity response. We find that the inverted ensemble acts as an active control resource: tuning the gain coupling reshapes the hybrid‐mode structure and produces resolved normal‐mode peaks in both the mechanical and optical spectra, while the absorbing ensemble independently sets the mode linewidths and relative peak amplitudes. The coupling parameters control and redistribute the bipartite and tripartite Gaussian entanglement shared among the optical, mechanical, and atomic modes, with the mechanical thermal occupation setting the robustness of the correlations. Formulated with experimentally feasible parameters of existing strong‐coupling optomechanics, the scheme provides a tunable route to controlling normal‐mode splitting and quantum correlations in hybrid quantum systems.