81 research outputs found
Parametric oscillator in a Kerr medium: evolution of coherent states
We study the temporal evolution of a coherent state under the action of a
parametric oscillator and a nonlinear Kerr-like medium. We make use of the
interaction picture representation and use an exact time evolution operator for
the time independent part of the Hamiltonian. We approximate the interaction
picture Hamiltonian in such a way as to make it a member of a Lie algebra. The
corresponding time evolution operator behaves like a squeezing operator due to
the temporal dependence of the oscillator's frequency. We analyze the
probability amplitude and the auto correlation function for different
Hamiltonian parameters and we find a very good agreement between our
approximate results and converged numerical calculations.Comment: 11 pages, 3 figure
Approximate coherent states for nonlinear systems
On the basis of the f-deformed oscillator formalism, we propose to construct
nonlinear coherent states for Hamiltonian systems having linear and quadratic
terms in the the number operator by means of the two following definitions: i)
as deformed annihilation operator coherent states (AOCS) and ii) as deformed
displacement operator coherent states (DOCS). For the particular cases of the
Morse and Modified P\"oschl-Teller potentials, modeled as f-deformed
oscillators (both supporting a finite number of bound states), the properties
of their corresponding nonlinear coherent states, viewed as DOCS, are analyzed
in terms of their occupation number distribution, their evolution on phase
space, and their uncertainty relations.Comment: 22 pages, 7 figure
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