Cavity-reservoir interaction ($H_I=i\sqrt{\gamma }(a\otimes b^{†}-a^{†}\otimes b)$)

The rotating-wave approximation to a weak quadrature coupling of a cavity mode to a broadband field retains photon-exchange terms and removes counter-rotating pair creation and annihilation. Flat coupling around resonance produces the displayed interaction in units $\hslash =1$. Its short-time propagator is generated by $\sqrt{\gamma }(ad{B}^{†}-a^{†}dB)$; the Gaussian quantum noise Ito table supplies the quadratic drift correction. The resulting passive cavity has the passive cavity input-output transfer function.