Phase Diffusion in Quantum Dissipative Systems

TL;DR

This paper investigates how quantum phase distributions evolve in dissipative and nondemolition systems, revealing how environmental factors like squeezing and temperature influence phase dynamics differently depending on the interaction type.

Contribution

It provides a detailed analysis of quantum phase diffusion under various environmental interactions, highlighting the contrasting roles of squeezing and temperature.

Findings

Squeezing and temperature jointly affect phase diffusion in nondemolition interactions.

Temperature effects can be counteracted by squeezing in dissipative interactions.

The study introduces a notion of complementarity in atomic systems based on phase distributions.

Abstract

We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum nondemoliton type of coupling, such that there is decoherence without dissipation, as well as when it interacts via a dissipative interaction, resulting in decoherence as well as dissipation. The system is taken to be either a two-level atom (or equivalently, a spin-1/2 system) or a harmonic oscillator, and the environment is modeled as a bath of harmonic oscillators, starting out in a squeezed thermal state. The impact of the different environmental parameters on the dynamics of the quantum phase distribution for the system starting out in various initial states, is explicitly brought out. An interesting feature that emerges from our work is that the relationship between squeezing and temperature effects depends on the type of system-bath interaction. In the case of quantum nondemolition type of interaction, squeezing and temperature work in tandem, producing a diffusive effect on the phase distribution. In contrast, in case of a dissipative interaction, the influence of temperature can be counteracted by squeezing, which manifests as a resistence to randomization of phase. We make use of the phase distributions to bring out a notion of complementarity in atomic systems. We also study the dispersion of the phase using the phase distributions conditioned on particular initial states of the system.