Dynamics of Non-classicality Measures in the Decohering Harmonic Oscillator

TL;DR

This paper investigates how non-classicality measures evolve in a harmonic oscillator coupled to a Markovian bath, revealing a peak in non-classicality during decoherence and introducing improved classical state sets for analysis.

Contribution

The study introduces a new set of classical states for better non-classicality calculations and demonstrates the effectiveness of Wigner function negativity as a practical measure.

Findings

A non-trivial peak in non-classicality as a function of quantum number n during decoherence.

Wigner function negativity correlates well with other non-classicality measures.

New classical states improve the accuracy of non-classicality assessments.

Abstract

We show that eigenstates |n> of the harmonic oscillator coupled to a linear Markovian bath demonstrate a non-trivial behavior in the dynamics of measures of non-classicality. Specifically, as the system undergoes decoherence, a time-dependent peak in non-classicality as a function of n emerges. We find this effect studying the dynamics of several non-classicality measures previously presented in the literature which compare quantum states to the set of all classical states. In studying these measures we introduce a novel set of classical states for the purpose of calculations which improve upon the results obtainable using these measures. In addition, following in the footsteps of Kenfack and \'Zyczkowski, we show that the negative volume of the Wigner function agrees well with all the non-classicality measures while being otherwise calculationally significantly more tractable. Finally, we explore the dynamics of non-classicality of several other states.