Abstract
The coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function. This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. Propagation of this state in the phase space is described by the Moyal equation which is solved for the case of a dispersive medium with a Gaussian barrier in the above-barrier reflection regime. Formally, this regime constitutes conditions for backscattering diffraction phenomena. Dynamical quantumness and the degree of localization in the phase space of the considered state as a function of its imperfection are the subject of the performed analysis. The obtained results allow concluding that backscattering communication based on the defective Schrödinger cat states appears to be feasible with existing experimental capabilities.
Highlights
The coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function
The aim of our work is to investigate the coherent dynamics of a defective superposition of two Gaussian wavepackets in the backscattering diffraction regime[16,17] using the phase-space representation of the quantum theory[18,19,20,21,22,23,24]
Eq (30)] is the initial condition for the Moyal equation of motion (14). It is solved numerically by applying the second-order split-operator method according to Eq (18). By using this method we can investigate the dynamical properties of the considered state in a dispersive medium with an internal perturbation which breaks its homogeneity
Summary
The coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. The possibility of creating non-classical states, e.g. the above mentioned Schrödinger cat states, raises natural questions about their dynamics in dispersive media and the accompanying effects This problem is rarely analyzed in d etail[11,12,13,14], it seems to be important for applications in quantum c ommunications[15] and Scientific Reports | (2021) 11:11619. Problems related to a quantum state’s transmission or detection because of decoherence which destroys the quantum interference
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