Quantum dynamics of a macroscopic magnet operating as environment of a mechanical oscillator

Abstract

We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic: the problem is related with the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. Aim of the work is to understand 1) if, 2) to what extent, and possibly 3) how, the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin-1/2 particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental-spin S constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-S limit. We find an insightful expression for the propagator of the whole system, where we identify an effective "back-action" term, i.e. an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the level-splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field, and the frequency of the oscillator. The time-dependence of the anisotropy is analysed, and its effects on the dynamics of the magnet, as well as its relation with the entangling evolution of the overall system, are discussed.

References in corpus (25)

• Cavity Optomechanics
• The role of quantum information in thermodynamics --- a topical review
• Quantum Computers and Dissipation
• Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode
• Open Quantum Systems. An Introduction
• A nano heat engine beyond the Carnot limit
• 1/f noise: implications for solid-state quantum information
• Non-classical correlations between single photons and phonons from a mechanical oscillator
• A short walk through quantum optomechanics
• Decoherence and 1/f noise in Josephson qubits
• Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing
• Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics
• Quantum-enhanced absorption refrigerators
• Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
• Efficient computation of the Zassenhaus formula
• Dynamics of quantum correlations in colored environments
• Geometric phase with nonunitary evolution in presence of a quantum critical bath
• Classical Simulation of Quantum Noise
• Exploring the quantum critical behaviour in a driven Tavis-Cummings circuit
• Decoherence of a qubit due to a quantum fluctuator or to a classical telegraph noise
• Dicke model and environment-induced entanglement in ion-cavity QED
• Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment
• Parametric representation of open quantum systems and crossover from quantum to classical environment
• Parametric description of the quantum measurement process
• Getting through to a qubit by magnetic solitons

Cited by in corpus (4)

• Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus
• Effective description of the short-time dynamics in open quantum systems
• Thermodynamics of a Periodically Driven Qubit
• Nature and origin of the operators entering the master equation of an open quantum system