Axion polarimetry with parametric readout: photon-number conversion and sensitivity limits

We propose a bias-assisted active photon-number conversion scheme for axion-induced polarization rotation in a four-port optical ring cavity with parametric readout. A calibrated real polarization rotation applied \emph{before} the final optical parametric oscillator (OPO) converts the otherwise quadratic response of the summed output photon number into a linear signal. We derive the resulting photon moments and the extracted-field covariance, retaining the four-port optical transfer, finite axion coherence and linewidth. Our principal phenomenological result is a prospective low-mass sensitivity window at $m_a=10^{-18}$--$10^{-16}\,\mathrm{eV}$, extending below the published exclusion bounds included in our comparison, notably the NuSTAR M82 limits. This is a conditional noise-equivalent projection, using the adopted $A/σ_A=1$ stochastic-power criterion and a parameterized technical-noise budget, not a confidence-level exclusion forecast. As a separate readout result, OPO-based total counting reduces the noise-equivalent coupling by approximately $5\%$ relative to matched selective attenuation in a favorable higher-frequency band; $5\%$ internal loss together with a $0.10$-rad pump-phase offset leaves a $3.5\%$ advantage in the stated example. A coherent input with only the final OPO retains this high-frequency benefit, whereas optimized coherent polarimetry remains more sensitive in the baseline. Our results identify both the operating principle of active number conversion and the stability requirements for a future implementation.