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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Eigenstates of a time-dependent quadratic Hamiltonian, a kind of generalized squeezed number states

W. S. Liu, Paolo Tombesi

Published May 1, 1992• 1 citation
Publisher
DOI
10.1007/bf02723636

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The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.
The dynamic decoupling of the correlation function hierarchy under the general quadratic Hamiltonian is exploited to extend the results obtained for coherent pumping and squeezing in Ref. . Closed c-number dynamic equations are given explicitly for three- and four-operator averages, for an arbitrary (pure or mixed) initial state of the field. At this level an independent c-number constant of motion appears, related to two-photon correlation properties of the initial state. Extension to higher correlation functions is straightforward. \textcopyright{} 1996 The American Physical Society.