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arXiv:1801.03750 · Physical Review A

Aspects of the decoherence in high-spin environments: Breakdown of the mean-field approximation

Yamen Hamdouni

Published Aug 25, 2016• 2 citations
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Abstract

The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-$\frac{1}{2}$ 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 $XY$ 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 $XY$ interactions. In the case of a transverse Ising model, we find that the mean-field approximation breaks down for high values of the spin.

DOI
10.1103/physreva.94.022120

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We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XYXYXY, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XYXYXY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.
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We study the decoherence of a central spin-1∕21∕21∕2 induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferromagnetic and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising bath. We present analytic results for the Ising spin chain bath at arbitrary temperature for different distributions of the intrabath interaction strengths. We find clear evidence of non-Markovian behavior in the low temperature regime. We also consider baths described by Ising models on higher-dimensional lattices. We find that interactions lead to a significant reduction of the decoherence. An important feature of interacting spin baths is the saturation of the asymptotic Markovian decay rate at high temperatures, as opposed to the conventional Ohmic boson bath.