Reduction of the wave packet: Preferred observable and decoherence time scale

TLDR

Environment‑induced destruction of quantum coherence is studied in a simple harmonic‑oscillator model, and its implications for the quantum‑to‑classical transition are briefly explored. The authors propose a new measure of decoherence effectiveness tailored to the model and chosen initial conditions. Decoherence is studied for coherent superpositions of two Gaussian wave packets in position or momentum, and its dependence on the environmental oscillator frequency distribution—particularly a supra‑Ohmic spectrum—is examined. The study shows that decoherence rate depends on the Wigner function peak locations, confirming position as a preferred observable, and that the high‑temperature approximation remains accurate even in the low‑temperature regime.

Abstract

Environment-induced destruction of quantum coherence is investigated in a simple model where the system is a harmonic oscillator, the environment is a collection of harmonic oscillators, and the interaction between them is linear in the position coordinate of the system. We study decoherence for initial states consisting of coherent superpositions of two Gaussian wave packets in either position or momentum. A new measure of the effectiveness of decoherence appropriate to the model and choice of initial conditions is proposed. By studying the dependence of the decoherence rate on the location of the initial peaks of the Wigner function, we clarify the sense in which position is a preferred observable even though position eigenstates are not the pointer states of this model. We analyze decoherence in the low-temperature regime and show that the usual "high-temperature" approximation is remarkably accurate in its domain of applicability. We also examine the relationship between the decoherence process and the frequency distribution of the environment oscillators (in particular, we focus attention on a specific "supra-Ohmic" environment). Implications of our results for the quantum to classical transition in various contexts are briefly explored.