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Journal of Modern Optics

Reconstruction of the Wigner function of the Schrödinger-cat state via time-dependent Autler-Townes spectroscopy

Tasnim Azim, Sajid Qamar, Muhammad Suhail Zubairy

Published Jan 1, 2002• 11 citations
Publisher

Abstract

Equivalent descriptions of the quantum state of the radiation field can be formulated in terms of the quasiprobability distributions such as P-representation, Q-representation, and the Wigner distribution function. The paper presents a physical and more realistic model for the reconstruction of the Wigner distribution function of the Schrödinger-cat state using time-dependent Autler-Townes spontaneous emission spectroscopy.

DOI
10.1080/09500340110087183

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Equivalent descriptions of the quantum state of the radiation field can be formulated in terms of the quasiprobability distributions such as P-representation, Q-representation, and the Wigner distribution function. The paper presents a physical and more realistic model for the reconstruction of the Wigner distribution function of the Schrödinger-cat state using time-dependent Autler-Townes spontaneous emission spectroscopy.
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A review of the definition of Crystallized Schrödinger cat states and their statistical properties is presented. The associated Wigner and Husimi quasi-probability distribution functions are also calculated together with the second moment of the Husimi function. The Hamiltonian formulation of the Nöther's theorem is used to get the linear time dependent invariants of until general quadratic Hamiltonians in the quadratures of the electromagnetic field. By means of these invariants, the evolution of Crystallized Schrödinger cats is studied, thus we have explicit time dependent expressions for the means and dispersions of the quadratures of the electromagnetic field together with the corresponding Wigner and Husimi functions. By means of these results, we establish some conditions on the parameters of the Crystallized cat states to have the description of non-classical light.
The Wigner distribution function for the time-dependent quadratic Hamiltonian system in the coherent Schrodinger cat state is investigated. The type of state we consider is a superposition of two coherent states, which are by an angle of π out of phase with each other. The exact Wigner distribution function of the system is evaluated under a particular choice of phase, δc, q. Our development is employed for two special cases, namely, the Caldirola–Kanai oscillator and the frequency stable damped harmonic oscillator. On the basis of the diverse values of the Wigner distribution function that were plotted, we analyze the nonclassical behavior of the systems.
We present a scheme to reconstruct a two-mode entangled state in a high-QQQ cavity from the spontaneous emission spectrum in a driven four-level atomic system. The two modes of the cavity field drive the upper three levels of the atom and thus the spontaneous emission spectrum contains the information about the photon statistics of the cavity field. Wigner function of the driving field is recovered from the photon statistics in a straightforward manner.