Abstract
The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.
Highlights
Since the middle of last century, field–field, atom–field and atom–atom interactions have been regarded as fundamental problems in nonlinear optical phenomena.This is an Open Access article published by World Scientific Publishing Company
We have introduced the problem of the time-dependent interaction between two subsystem governed by su[2] and the su[1, 1] Lie group as interaction between a two-level atom injected in a cavity with parametric amplifer, or through the interaction of a two-level trapped ion in a two-dimensional trap
The solution of the wavefunction in the Schrodinger picture is obtained under a certain integrability condition
Summary
Since the middle of last century, field–field, atom–field and atom–atom interactions have been regarded as fundamental problems in nonlinear optical phenomena. The interaction between three electromagnetic fields represents an important nonlinear parametric interaction in quantum optics.1–10 This type of interaction plays a significant role in many relevant physical phenomena, such as stimulated and spontaneous emission of radiation and coherent Raman and Brillouin scattering.. Researchers generated squeezed light using nondegenerate parametric down conversion to excite a twophoton transition in atomic cesium.12–14 To obtain these types of processes, we have to introduce a Hamiltonian model consisting of a three-wave interaction. Where δij is the Kronecker delta with the properties δij = 1 for i = j and δij = 0 otherwise and λ is the nonlinear coupling parameter that generally depends on the susceptibility χ(2) This has applications in connection with phenomena related to optical phase conjugation..
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