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arXiv:1612.03099 · SciPost Physics

Decoherence and pointer states in small antiferromagnets: A benchmark test

Hylke C. Donker, Hans A. De Raedt, Mikhail I. Katsnelson

Published Mar 23, 2017• 8 citations
arXivHTMLPDF

Abstract

We study the decoherence process of a four spin-1/2 antiferromagnet that is coupled to an environment of spin-1/2 particles. The preferred basis of the antiferromagnet is discussed in two limiting cases and we identify two exact pointer states. Decoherence near the two limits is examined whereby entropy is used to quantify the robustness of states against environmental coupling. We find that close to the quantum measurement limit, the self-Hamiltonian of the system of interest can become dynamically relevant on macroscopic timescales. We illustrate this point by explicitly constructing a state that is more robust than (generic) states diagonal in the system-environment interaction Hamiltonian.

DOI
10.21468/scipostphys.2.2.010

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Abstract We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum, non-relativistic particles. We solve the Schrödinger equation for the wave function of this tripartite system using exact diagonalization. Although computational limitations on the size of the Hilbert space prevent us from exploring the regime where the device and environment consist of a truly macroscopic number of degrees of freedom, we nevertheless see clear evidence of decoherence: after tracing out the environment, the density matrix describing the system and measuring device evolves quickly towards a matrix that is close to diagonal in a subspace of pointer states. We measure the speed with which decoherence spreads in the relativistic quantum field theory for a range of parameters. We find that it is less than the speed of light but faster than the speed of the massive charges in the initial state.
In this manuscript, we analyze the dynamics of a model in which two spin-1/2 systems are each coupled noncommutingly to a static environmental field and to a self-Hamiltonian, while also being mutually coupled through a σy(1)σy(2)σ_y^{(1)}σ_y^{(2)}σy(1)​σy(2)​ interaction. By constructing an exact solution that exploits parity symmetry, and by applying the stationary-phase approximation (the saddle-point method) in the continuum limit of the environmental field, we show that coherence associated with the ordinary isolated stationary point decays as t−1t^{-1}t−1, whereas, under the resonance condition at which the local effective fields of the two spins cancel each other, only the coherence between a pair of maximally entangled, Bell-type states- the eigenbasis of the inter-system coupling-survives, decaying via the anomalously slow power law t−1/2t^{-1/2}t−1/2. Through a comparison with the pointer-basis theory of W. H. Zurek and coworkers (the 1981 and 2005 models), we further reveal a mechanism not reducible to local coupling: in this system, the pointer observable is determined not by the individual system-environment couplings but by a statistical resonance condition between the two environments.
The two-dimensional Heisenberg antiferromagnet with an additional isotropic coupling to ``environmental'' spin degrees of freedom is studied by exact diagonalization of small clusters to examine the effect of decoherence from first principles. The dynamical correlation function for the staggered order parameter $c(\ensuremath{\omega})$ is calculated for two systems containing 101010 and 181818 electronic spins coupled to two environmental spins. The evolution of spectral weight in the main macroscopic quantum coherence resonance is followed as a function of environmental coupling and spin anisotropy and is discussed in connection with theoretical work on decoherence.
Quantum decoherence is widely regarded as the principal dynamical mechanism through which classical behaviour emerges from quantum dynamics. This review presents a technical account of decoherence as an open-system phenomenon, emphasizing its mathematical framework, microscopic models, experimental evidence, and foundational implications. Starting from system-environment interactions and reduced density operators, we introduce completely positive trace-preserving maps and Lindblad master equations. We then discuss pure dephasing, pointer-state selection, quantum Brownian motion, spin-boson dynamics, and collisional decoherence. Experimental evidence from atom and molecular interferometry, superconducting qubits, and mesoscopic platforms is examined. Finally, the review assesses the role of decoherence in the quantum measurement problem. Decoherence explains preferred-basis selection and practical suppression of interference, but it does not independently account for the occurrence of a unique measurement outcome.
We study the decoherence of two coupled spins that interact with a chaotic spin-bath environment. It is shown that connectivity of spins in the bath is of crucial importance for the decoherence of the central system. The previously found phenomenon of two-step decoherence (Phys. Rev. Lett. {\bf 90}, 210401 (2003)) turns out to be typical for the bath with a slow enough dynamics or no dynamics. For a generic random system with chaotic dynamics a conventional exponential relaxation to the pointer states takes place. Our results confirm a conjecture of Paz and Zurek (Phys. Rev. Lett. {\bf 82}, 5181 (1999)) that for weak enough interactions the pointer states are eigenstates of the central system.