Peculiarities of dissipative dynamics of $\Lambda$-atom driven by a quantized field in squeezed state

The dissipative dynamics of the three-level $\Lambda$-atom driven by a quantized electromagnetic field under the electromagnetically induced transparency (EIT) conditions is investigated both analytically by the Heisenberg–Langevin method and numerically using the quantum Monte Carlo wave function method (QMC method). The impact of the squeezing level of quantized light on the atomic system parameters, which determine the relaxation processes and noise in EIT transparency window, is considered in detail. It is shown that under these conditions quantum properties of light (squeezing) can be transferred to an atom. The work also considers the problem of the propagation of quantum field in squeezed coherent state in the medium of atoms and analyzes the dependence of squeezing level of light at the medium output on the parameters at the input and properties of the medium. The application of the QMC method to numerical simulation of the propagation problem is discussed in the light of the recent experiments on the propagation of squeezed vacuum in the medium under examination.