Kalka M, Spisak BJ, Woźniak D, Wołoszyn M, Kołaczek D. Dynamical entropic measure of nonclassicality of phase-dependent family of Schrödinger cat states.
Sci Rep 2023;
13:16266. [PMID:
37758979 PMCID:
PMC10533523 DOI:
10.1038/s41598-023-43421-2]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 09/23/2023] [Indexed: 09/29/2023] Open
Abstract
The phase-space approach based on the Wigner distribution function is used to study the quantum dynamics of the three families of the Schrödinger cat states identified as the even, odd, and Yurke-Stoler states. The considered states are formed by the superposition of two Gaussian wave packets localized on opposite sides of a smooth barrier in a dispersive medium and moving towards each other. The process generated by this dynamics is analyzed regarding the influence of the barrier parameters on the nonclassical properties of these states in the phase space below and above the barrier regime. The performed analysis employs entropic measure resulting from the Wigner-Rényi entropy for the fixed Rényi index. The universal relation of this entropy for the Rényi index equal one half with the nonclassicality parameter understood as a measure of the negative part of the Wigner distribution function is proved. This relation is confirmed in the series of numerical simulations for the considered states. Furthermore, the obtained results allowed the determination of the lower bound of the Wigner-Rényi entropy for the Rényi index greater than or equal to one half.
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