Phase-space studies of backscattering diffraction of defective Schrödinger cat states

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.

Dynamical entropic measure of nonclassicality of phase-dependent family of Schrödinger cat states

“…Another issue discussed in this paper concerns the interaction of the phase-dependent family of the Schrödinger cat (SC) states with the potential barrier in a one-dimensional dispersive channel. This continuation of our previous studies on the SC states in the phase-space formalism 52 allows us to generalize them to the case of the well-separated bimodal state formed by the coherent superposition of two Gaussian wavepackets, each of which moves with an opposite momentum value. It means that each wave packet that is a part of this coherent superposition approaches the other in the configurational space, with an obstacle in the form of a Gaussian barrier between them acting as a scattering centre.…”

“…Besides this, the normalization factor A equals This form of the initial condition can be regarded as a generalization of the result presented in Ref. 52 for the coherent superposition, and we refer to this as the Schrödinger cat state 10 (SC state). For further investigation, we assume that both Gaussians move in the dispersive medium in opposite directions with the same value of the initial momentum, i.e.…”

“…However, for computational reasons, it is more convenient to formulate the equation of motion ( 3 ) slightly differently. Namely, using the Bopp shifts 80 , the Moyal equation can be transformed into the following form 52 . where the first term in the RHS of this equation corresponds to the kinetic term, while the second term in the RHS represents the potential term which is inherently nonlocal 81 .…”

“… . On account of that, we can simplify expression ( 26 ) to the following form with the normalization factor A given by the formula Referring to the previous study 52 , we assume the following values of the parameters which characterize this initial condition, namely , a.u., , and a.u. Owing to this selection of the parameters, the presented initial condition ( 27 ) is the phase-space representation of the SC state given by the superposition of two well-separated and well-localized Gaussians approaching each other with the same momenta.…”