Dynamics of cavity fields with dissipative and amplifying couplings through multiple quantum two-state systems

Abstract

We consider simultaneous dissipative and amplifying coupling of cavity fields to multiple two-state systems. We derive a master equation for optical field in a leaky cavity coupled to a reservoir through multiple two-state systems. In our previous works we have limited our study to systems where the reservoir either solely absorbs energy (detector setup) or adds energy (amplifying setup) to the cavity through a single two-state system. In this work we allow both interactions simultaneously and derive a reduced dynamic model for the optical field. We also generalize our model to cover the coupling of the field to several two state systems and discuss its connection to macroscopic interaction, e.g., in semiconductors. Our model includes four physical parameters: the field two-state system coupling $\ensuremath{\gamma}$, the excitation and deexcitation couplings of the two-state system by the reservoir ${\ensuremath{\lambda}}_{A}$ and ${\ensuremath{\lambda}}_{D}$, respectively, and the mirror losses of the cavity $C$. We solve the steady-state fields at different regimes of these physical parameters. Furthermore, we show that, depending on the parameters, our model can describe the operation of a detector, a light emitting diode, or a laser.