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The Wigner distribution function (WDF) for the time-dependent quadratic Hamiltonian system is investigated in the squeezed Schrödinger cat states with the use of Lewis–Riesenfeld theory of invariants. The nonclassical aspects of the system produced by superposition of two distinct squeezed states are analyzed with emphasis on their application into special systems beyond simple harmonic oscillator. An application of our development to the measurement of quantum state by reconstructing the WDF via Autler–Townes spectroscopy is addressed. In addition, we considered particular models such as Cadirola–Kanai oscillator, frequency stable damped harmonic oscillator, and harmonic oscillator with time-variable frequency as practical applications with the object of promoting the understanding of nonclassical effects associated with the WDF. [ABSTRACT FROM AUTHOR]

We investigate the Wigner distribution function of the general time-dependent quadratic-Hamiltonian quantum system with the Lewis–Riesenfeld invariant operator method. The Wigner distribution function of the system in Fock state, coherent state, squeezed state, and thermal state are derived. We apply our study to the one-dimensional motion of a Brownian particle and to the driven oscillator with strongly pulsating mass. [ABSTRACT FROM AUTHOR]