Three-level atom in a broadband squeezed vacuum field. I. General theory

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Abstract
A complete treatment of a three-level ladder system interacting with a broadband squeezed vacuum field is presented. It is assumed that the ground state and the second excited state are decoupled in the electric-dipole approximation, and are tuned close to the sum frequency of the incident squeezed vacuum field. Using Zwanzig’s projection-operator techniques, we derive the master equation, assuming that the system interacts with a broadband squeezed vacuum field in one or more dimensions. It is shown that, in the first case, the squeezed vacuum introduces new decay constants and frequency-shift parameters. These have the same dependence on the atom-radiation coupling parameter as the ordinary vacuum decay rate and frequency shift, the only major difference being that they are multiplied by the squeezing parameters M and N. In more dimensions, the decay constants and frequency-shift parameters depend on the solid angle Ω over which the squeezing is propagated. For Ω=0 these correspond to the usual Einstein A coefficients and Lamb shifts of the atomic levels, while for large Ω they are similar to those for the one-dimensional squeezed vacuum.

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