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arXiv:quant-ph/0611242 · Physical Review A

Decoherence induced by interacting quantum spin baths

Davide Rossini, Tommaso Calarco, Vittorio Giovannetti, Simone Montangero, Rosario Fazio

Published Mar 26, 2007• 199 citations
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Abstract

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, $XY$, 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 $XY$ 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.

DOI
10.1103/physreva.75.032333

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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.
Optical lattices can be used to simulate quantum baths and hence they can be of fundamental help to study, in a controlled way, the emergence of decoherence in quantum systems. Here we show how to implement a pure dephasing model for a two-level system coupled to an interacting spin bath. In this scheme it is possible to implement a large variety of spin environments embracing Ising, XY and Heisenberg universality classes. After having introduced the model, we calculate exactly the decoherence for the Ising and the XY spin bath model. We find universal features depending on the critical behaviour of the spin bath, both in the short- and long-time limits. The rich scenario that emerges can be tested experimentally and can be of importance for the understanding of the coherence loss in open quantum systems.
We introduce, and determine decoherence for, a wide class of non-trivial quantum spin baths which embrace Ising, XY and Heisenberg universality classes coupled to a two-level system. For the XY and Ising universality classes we provide an exact expression for the decay of the loss of coherence beyond the case of a central spin coupled uniformly to all the spins of the baths which has been discussed so far in the literature. In the case of the Heisenberg spin bath we study the decoherence by means of the time-dependent density matrix renormalization group. We show how these baths can be engineered, by using atoms in optical lattices.
The reduced dynamics of a single qubit or two qubits coupled to an interacting quantum spin bath modeled by an XXZXXZXXZ spin chain is investigated. By using the method of a time-dependent density matrix renormalization group (t-DMRG)(t\text{-DMRG})(t-DMRG), we go beyond the uniform coupling central spin model and nonperturbatively evaluate the induced decoherence and entanglement. It is shown that both the decoherence and the entanglement strongly depend on the phase of the underlying spin bath. We show that in general, spin baths can induce entanglement for an initially disentangled pair of qubits. Furthermore, when the spin bath is in the ferromagnetic phase because the qubits directly couple to the order parameter, the reduced dynamics shows an oscillatory type behavior. On the other hand, only for the paramagnetic and the antiferromagnetic phases do the initially entangled states suffer from an entanglement sudden death. By calculating the concurrence, the finite disentanglement time is mapped out for all of the phases in the phase diagram of the spin bath.
We investigate the reduced dynamics of single or two qubits coupled to an interacting quantum spin bath modeled by a XXZ spin chain. By using the method of time‐dependent density matrix renormalization group (t‐DMRG), we evaluate nonperturbatively the induced decoherence and entanglement. We find that the behavior of both decoherence and entanglement strongly depend on the phase of the underlying spin bath. We show that spin baths can induce entanglement for an initially disentangled pair of qubits. We observe that entanglement sudden death only occurs in paramagnetic phase and discuss the effect of the coupling range.
We investigate the reduced dynamics of two qubits coupled to an interacting quantum spin bath modeled by a XXZ spin chain. By using the method of time-dependent density matrix renormalization group (t-DMRG), it is shown that when the spin bath is in an ordering state, the reduced dynamics of qubits strongly depends on the range of the spin chain that qubits coupled to. Only for ordering spin baths, both decoherence and entanglement show qualitatively different behaviors when the coupling range changes. In particular, In particular, we find that in the parametic regime where there is no ordering in the bath, the coupling range is irrelevant. On the other hand, for ordering spin baths, when the coupling range increases from local coupling to infinite range coupling, the reduced dynamics of qubits exhibits a transition in which initially entangled states no longer suffers from the entanglement sudden death when the coupling range is large.
This paper analyzes the decoherence induced on a single qubit by the interaction with a spin chain with nontrivial internal dynamics (XYXYXY-type interactions). The aim of the paper is to study the existence and properties of the so-called universal regime, in which the decoherence time scale becomes independent of the strength of the coupling with the environment. It is shown that, although such a regime does exist, as previously established by Cucchietti et al. [Phys. Rev. A 75, 032337 (2007)], it is not a clear signature of a quantum phase transition in the environment. In fact, this kind of universality also exists in the absence of quantum phase transitions. A universal regime can be related to the existence of an energy scale separation between the Hamiltonian of the environment and the one characterizing the system-environment interaction. The results presented also indicate that in the strong-coupling regime the quantum phase transition does not produce an enhancement of decoherence (as opposed to what happens in the weak-coupling regime).