Cooperative behavior of atoms irradiated by broadband squeezed light

Abstract

We consider the dynamics of a collection of atoms interacting with a coherent field and a broadband squeezed vacuum. We obtain an exact solution of the master equation and study in detail the types of nonequilibrium steady states that can be generated. We show that in the absence of coherent drive the atoms are in a state whose properties are similar to those of the squeezed vacuum for photons. We demonstrate that the steady state for certain discrete values of the external field strength and detuning is a pure state which is the eigenstate of the non-Hermitian operator cosh(\ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\Vert})${\mathit{S}}^{\mathrm{\ensuremath{-}}}$+sinh(\ensuremath{\Vert}\ensuremath{\xi}\ensuremath{\Vert})${\mathit{S}}^{+}$, where \ensuremath{\xi} is the squeezing parameter associated with the input radiation field. These eigenstates play a very fundamental role in the theory and satisfy the equality sign in the Heisenberg uncertainty relation \ensuremath{\Delta}${\mathit{S}}_{\mathit{x}}$ \ensuremath{\Delta}${\mathit{S}}_{\mathit{y}}$\ensuremath{\ge}1/2\ensuremath{\Vert}〈${\mathit{S}}_{\mathit{z}}$〉\ensuremath{\Vert}. We also present detailed numerical results for the characteristics of the field generated by the collective system.