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Physical Review A

Decoherence slowing down in a symmetry-broken environment

Simone Paganelli, FERDINANDO DE PASQUALE, S. M. Giampaolo

Published Nov 22, 2002• 55 citations
Publisher

Abstract

We show how to characterize the temporal evolution of a single qubit interacting with a thermal bath by correlation functions of the bath under quite general hypotheses. The aim is to show how the qubit decoherence time depends on the degree of correlation of the bath. We explicitly study some spin-bath models where every spin of the environment interacts with the qubit either directly or by the mediation of a harmonic oscillator. In both cases we find an increase of the decoherence time as soon as a symmetry breaking occurs in the environment. In the latter case a possible experimental setup is discussed.

DOI
10.1103/physreva.66.052317

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We show how to characterize the temporal evolution of a single qubit interacting with a thermal bath by correlation functions of the bath under quite general hypotheses. The aim is to show how the qubit decoherence time depends on the degree of correlation of the bath. We explicitly study some spin-bath models where every spin of the environment interacts with the qubit either directly or by the mediation of a harmonic oscillator. In both cases we find an increase of the decoherence time as soon as a symmetry breaking occurs in the environment. In the latter case a possible experimental setup is discussed.
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The time evolution of a spin-12\frac{1}{2}21​ particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature TTT is studied. The exact analytical form of the reduced density matrix of the central spin is calculated explicitly for a finite number of bath spins. The case of an infinite number of environmental spins is investigated using the convergence of the rescaled bath operators to normal Gaussian random variables. In this limit, we derive the analytical form of the components of the Bloch vector for antiferromagnetic interactions within the bath, and we investigate the short-time and long-time behavior of reduced dynamics. The effect of the external magnetic field, the anisotropy, and the temperature of the bath on the decoherence of the central spin are discussed.
We study the time evolution of a single spin coupled by exchange interaction to an environment of interacting spin bath modeled by the XY Hamiltonian. By evaluating the spin correlator of the single spin, we observed that the decay rate of the spin oscillations strongly depends on the relative magnitude of the exchange coupling between the single spin and its nearest neighbor J(') and coupling among the spins in the environment J. The decoherence time varies significantly based on the relative coupling magnitudes of J and J('). The decay rate law has a Gaussian profile when the two exchange couplings are of the same order J(') approximately J but converts to exponential and then a power law as we move to the regimes of J(')>J and J(')<J. We also show that the spin oscillations propagate from the single spin to the environmental spins with a certain speed. The effect of varying the anisotropic parameter, external magnetic field, and temperature on the decaying rate of the spin state is also discussed.
We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.
The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-12\frac{1}{2}21​ particles. In this paper we consider environments that are composed of particles of higher spin, and we investigate the consequences on the dynamics of a qubit coupled to such baths via Heisenberg XYXYXY and Ising interactions. It is shown that, while the short time decay in both cases gets faster as the magnitude of the spin increases, the asymptotic behavior exhibits an improvement of the suppression of the decoherence when the coupling is through Heisenberg XYXYXY interactions. In the case of a transverse Ising model, we find that the mean-field approximation breaks down for high values of the spin.