Superheterodyne Rydberg atomic receivers (RARs) combine high sensitivity, a broad operational frequency range, and phase- and frequency-resolved detection capabilities, making them promising candidates for next-generation radio-frequency receivers. Currently, the widespread deployment of RARs is limited by narrow instantaneous bandwidth. We use time-dependent perturbation theory to derive the linear approximate solution to the master equation. Floquet theory is employed to evaluate the total harmonic distortion arising from a single-tone excitation, enabling the characterization of the signal amplitude range over which the linear approximation remains valid. Transforming this linear solution into the Laplace domain yields an expression for the frequency response of the Rydberg atomic electro-optical conversion system. Furthermore, by vectorizing the superoperators and the density operator, we recast the original superoperator differential equation as a linear system of equations, enabling efficient numerical calculation. We numerically simulate the amplitude-frequency and phase-frequency response spectra, where the amplitude-frequency response reflects the gain across different frequencies. This enables analysis of how laser and local-oscillator parameters affect gain and bandwidth. Indeed, the gain metric based on the slope of the steady-state response curve coincides exactly with the zero-intermediate-frequency gain in the amplitude-frequency response. We employ the particle-swarm optimization algorithm to optimize the channel capacity of RARs under the constraints of photon shot noise and thermal-electrical noise. This algorithm demonstrates rapid convergence, efficiently identifying optimal laser and local-oscillator parameters. This study is expected to provide valuable insights for improving the sensitivity and bandwidth of superheterodyne RARs.

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• Open quantum systems & decoherence