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Decoherence by engineered quantum baths

Rossini, D, Calarco, T, Vittorio Giovannetti, Montangero, S, Rosario Fazio

Published May 5, 2006• 21 citations
OpenAlex

Abstract

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.

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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.
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 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.
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.
The decoherence and entanglement dynamics of two interacting qubits coupled through Heisenberg XY interactions to a spin bath in thermal equilibrium are studied. The exact form of the reduced density matrix is derived for finite and infinite numbers of environmental spins. It is shown that decoherence can be minimized at low bath temperatures and strong coupling between the qubits. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The relation between the fidelity and the concurrence is also investigated.
Decoherence of a central spin coupled to an interacting spin bath via inhomogeneous Heisenberg coupling is studied by two different approaches, namely an exact equations of motion (EOMs) method and a Chebyshev expansion technique (CET). By assuming a wheel topology of the bath spins with uniform nearest-neighbor XXXXXX-type intrabath coupling, we examine the central spin dynamics with the bath prepared in two different types of bath initial conditions. For fully polarized baths in strong magnetic fields, the polarization dynamics of the central spin exhibits a collapse-revival behavior in the intermediate-time regime. Under an antiferromagnetic bath initial condition, the two methods give excellently consistent central spin decoherence dynamics for finite-size baths of $N\ensuremath{\le}14$ bath spins. The decoherence factor is found to drop off abruptly on a short time scale and approach a finite plateau value which depends on the intrabath coupling strength nonmonotonically. In the ultrastrong intrabath coupling regime, the plateau values show an oscillatory behavior depending on whether N/2N/2N/2 is even or odd. The observed results are interpreted qualitatively within the framework of the EOM and perturbation analysis. The effects of anisotropic spin-bath coupling and inhomogeneous intrabath bath couplings are briefly discussed. Possible experimental realization of the model in a modified quantum corral setup is suggested.
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.