Finite-time quantum-to-classical transition for a Schroedinger-cat state

TL;DR

This paper investigates the finite-time quantum-to-classical transition of Schrödinger cat states in a harmonic oscillator, revealing that nonclassicality can vanish abruptly, challenging the notion that larger states decohere faster.

Contribution

It demonstrates that the quantum to classical transition can occur at a finite time depending on the nonclassicality measure, providing new insights into decoherence and entanglement dynamics.

Findings

Most nonclassicality measures show finite-time death of Schrödinger cat states.

Contrary to common belief, larger macroscopic states do not necessarily decohere faster.

The transition from quantum to classical can be abrupt, not just asymptotic.

Abstract

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schr\"odinger cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum to classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well defined physical meaning and allow a deeper understanding of the quantum to classical transition. Our analysis shows that, for most nonclassicality measures, the Schr\"odinger cat dies after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is prerequisite for entanglement generation our results also bridge the gap between decoherence, which appears to be only asymptotic, and entanglement, which may show a sudden death. In fact, whereas the loss of coherences still remains asymptotic, we have shown that the transition from quantum to classical can indeed occur at a finite time.