Applications of the master equation of a two-level atom in a narrow-bandwidth squeezed vacuum

In this paper, we derive the time-dependent solution of the effective master equation for the reduced density matrix operator of a two-level atom driven by a coherent laser field and damped by a finite-bandwidth squeezed vacuum. The master equation has the standard form known from the broadband squeezing approaches but with new effective squeezing parameters N˜ and M˜ and new rate coefficients. There are also new terms, proportional to β, which are essentially narrow-bandwidth modifications determined by the parameters γn, δn and the shifts δN and δM. These parameters become zero when the squeezing bandwidth tends to infinity. The effects of the detuning parameter Δ of the driving laser field frequency ωL from the atomic resonance ωA and the squeezing parameters N˜ and M˜ on the atomic inversion, the von Neumann entropy and the resonance fluorescence spectrum are discussed.