Quantum Brownian Motion of a Macroscopic Object in a General Environment

TL;DR

This paper derives exact master equations for the quantum dynamics of macroscopic objects interacting with complex environments, enabling analysis of decoherence, entanglement, and quantum behavior in realistic settings.

Contribution

It provides a general framework for modeling the quantum behavior of macroscopic objects in arbitrary environments, including conditions for the validity of center-of-mass approximations.

Findings

Exact master equations for N harmonic oscillators in heat baths

Conditions for center-of-mass approximation validity

Application to nanoelectromechanical systems and macroscopic entanglement

Abstract

For the purpose of understanding the quantum behavior such as quantum decoherence, fluctuations, dissipation, entanglement and teleportation of a mesoscopic or macroscopic object interacting with a general environment, we derive here a set of exact master equations for the reduced density matrix of $N$ interacting harmonic oscillators in a heat bath with arbitrary spectral density and temperature. Two classes of problems of interest to us which these equations can be usefully applied to are that of the quantum dynamics of nanoelectromechanical oscillators and the entanglement evolution of multi-partite macroscopic states such as quantum superposition of mirrors in a high Q cavity. To address a key conceptual issue for macroscopic quantum phenomena we examine the conditions for an assumption often implicitly made in these studies to be valid, namely, that the quantum behavior of a macroscopic object in an environment can be accurately represented by only treating the dynamics of its center-of-mass variable. We also mention how these results can be used to calculate the uncertainty principle governing a macroscopic object at finite temperature.