Bistable behaviour in squeezed vacua: I. Stationary analysis

A time-independent theoretical and numerical analysis of an optical bistable model of two-level atoms in a ring cavity, driven by a coherent field and in contact with a squeezed vacuum field is presented in the two cases of absorptive and dispersive optical bistability (OB). In the former case, a suitable choice of the phase of the squeezed vacuum field reduces the threshold for OB to occur compared with the normal vacuum case. In the latter case, regions of OB are identified as one or two disconnected simple closed curves depending on the cooperation parameter 0pt[0pt]$C \stackrel{> }{< } C_{\rm crit}^{\max}$: $C_{\rm crit}^{\max}$ is the maximum possible value of the critical value of C at fixed values of the squeezed vacuum field parameters. Phase switching effects between different (output) states of the system is investigated in detail. In the absorptive case, one- or two-way optical switching is possible depending on 0pt[0pt]$C \stackrel{> }{< } C_{\rm crit}^{\max}$. We also present results which demonstrate more complicated switching behaviour in the dispersive case