Revival Hamiltonians, Phase Operators and Non-Gaussian Squeezed States

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Abstract
The phase operators P ± of the electromagnetic field, whose classical analogues are exp (∓ iθ), θ being the classical phase, and the number operator N associated with a harmonic oscillator mode are used to construct a class of operators T m = N(P −)m and T + m = (P +)m N, m = 1, 2,…. It is shown that T m, T + m and N satisfy a simple algebra. T m and T + m are used to construct model Hamiltonians H m describing the coupling of a two-level atom to a field that leads to decay and exact revivals in the atomic dynamics. In the second part of the paper, a family of unitary operators U m is constructed in terms of T m and T + m. For m = 1 and m = 2 the states generated by U m from the vacuum are non-Gaussian squeezed states. The variance properties of the squeezed states so constructed are analysed and compared with those of the Gaussian squeezed states. It is shown that the non-Gaussian squeezed states constructed in this paper have small values for the variance product that rise only logarithmically with for large values of , the mean number of quanta.