Phase-space quantum profile of P\"oschl-Teller two-level systems

TL;DR

This paper explores the phase-space quantum dynamics of P"oschl-Teller potentials using Wigner functions, revealing non-classical features and quantifying non-Gaussianity, with implications for experimental quantum systems.

Contribution

It provides a detailed phase-space analysis of P"oschl-Teller two-level systems, quantifies non-Gaussianity, and demonstrates the construction of bipartite continuous-variable quantum states.

Findings

Wigner functions show non-classical, non-linear patterns.

Quantum wells can approximate Gaussian behavior in quantum-classical studies.

Bipartite systems of continuous variables are separable under certain criteria.

Abstract

The quantum phase-space dynamics driven by hyperbolic P\"oschl-Teller (PT) potentials is investigated in the context of the Weyl-Wigner quantum mechanics. The obtained Wigner functions for quantum superpositions of ground and first-excited states exhibit some non-classical and non-linear patterns which are theoretically tested and quantified according to a non-gaussian continuous variable framework. It comprises the computation of quantifiers of non-classicality for an anharmonic two-level system where non-Liouvillian features are identified through the phase-space portrait of quantum fluctuations. In particular, the associated non-gaussian profiles are quantified by measures of {\em kurtosis} and {\em negative entropy}. As expected from the PT {\em quasi}-harmonic profile, our results suggest that quantum wells can work as an experimental platform that approaches the gaussian behavior in the investigation of the interplay between classical and quantum scenarios. Furthermore, it is also verified that the Wigner representation admits the construction of a two-particle bipartite quantum system of continuous variables, $A$ and $B$, identified by $\sum_{i,j=0,1}^{i\neq j}\vert i_{_A}\rangle\otimes\vert j_{_B}\rangle$, which are shown to be separable under gaussian and non-gaussian continuous variable criteria.