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Title: Decoherence induced by interacting quantum spin baths

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 bathmore » we resort to the numerical time-dependent density matrix renormalization group.« less

Authors:
; ;  [1];  [2];  [3];  [1];  [4]
  1. NEST-CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa (Italy)
  2. Dipartimento di Fisica, Universita di Trento and BEC-CNR-INFM, I-38050 Povo (Italy)
  3. (United States)
  4. (SISSA), Via Beirut 2-4, I-34014 Trieste (Italy)
Publication Date:
OSTI Identifier:
20982279
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032333; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; COUPLING; DECAY; DENSITY MATRIX; HAMILTONIANS; HEISENBERG MODEL; INFORMATION THEORY; ISING MODEL; LOSSES; ONE-DIMENSIONAL CALCULATIONS; QUANTUM COMPUTERS; QUANTUM DECOHERENCE; QUANTUM ENTANGLEMENT; QUBITS; RENORMALIZATION; SPIN; TIME DEPENDENCE

Citation Formats

Rossini, Davide, Giovannetti, Vittorio, Montangero, Simone, Calarco, Tommaso, ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, Fazio, Rosario, and International School for Advanced Studies. Decoherence induced by interacting quantum spin baths. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.032333.
Rossini, Davide, Giovannetti, Vittorio, Montangero, Simone, Calarco, Tommaso, ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, Fazio, Rosario, & International School for Advanced Studies. Decoherence induced by interacting quantum spin baths. United States. doi:10.1103/PHYSREVA.75.032333.
Rossini, Davide, Giovannetti, Vittorio, Montangero, Simone, Calarco, Tommaso, ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, Fazio, Rosario, and International School for Advanced Studies. Thu . "Decoherence induced by interacting quantum spin baths". United States. doi:10.1103/PHYSREVA.75.032333.
@article{osti_20982279,
title = {Decoherence induced by interacting quantum spin baths},
author = {Rossini, Davide and Giovannetti, Vittorio and Montangero, Simone and Calarco, Tommaso and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138 and Fazio, Rosario and International School for Advanced Studies},
abstractNote = {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},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • 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 introduce the quantum theory of the electron spin decoherence in a nuclear spin bath and the dynamical decoupling approach for protecting the electron spin coherence. These theories are applied to various solid-state systems, such as radical spins in molecular crystals and NV centers in diamond.
  • The coherence time of an electron spin decohered by the nuclear spin environment in a quantum dot can be substantially increased by subjecting the electron to suitable dynamical decoupling sequences. We analyze the performance of high-level decoupling protocols by using a combination of analytical and exact numerical methods, and by paying special attention to the regimes of large interpulse delays and long-time dynamics, which are outside the reach of standard average Hamiltonian theory descriptions. We demonstrate that dynamical decoupling can remain efficient far beyond its formal domain of applicability, and find that a protocol exploiting concatenated design provides best performancemore » for this system in the relevant parameter range. In situations where the initial electron state is known, protocols able to completely freeze decoherence at long times are constructed and characterized. The impact of system and control nonidealities is also assessed, including the effect of intrabath dipolar interaction, magnetic field bias and bath polarization, as well as systematic pulse imperfections. While small bias field and small bath polarization degrade the decoupling fidelity, enhanced performance and temporal modulation result from strong applied fields and high polarizations. Overall, we find that if the relative errors of the control pulse flip angles do not exceed 3%, decoupling protocols can still prolong the coherence time by up to 2 orders of magnitude.« less
  • The spurious interaction of quantum systems with their environment known as decoherence leads, as a function of time, to a decay of coherence of superposition states. Since the interactions between system and environment are local, they can also cause a loss of spatial coherence: correlations between spatially distant parts of the system are lost and the equilibrium states can become localized. This effect limits the distance over which quantum information can be transmitted, e.g., along a spin chain. We investigate this issue in a nuclear magnetic resonance quantum simulator, where it is possible to monitor the spreading of quantum informationmore » in a three-dimensional network: states that are initially localized on individual spins (qubits) spread under the influence of a suitable Hamiltonian apparently without limits. If we add a perturbation to this Hamiltonian, the spreading stops and the system reaches a limiting size, which becomes smaller as the strength of the perturbation increases. This limiting size appears to represent a dynamical equilibrium. We present a phenomenological model to describe these results.« less
  • The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence--the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state--and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ('surface hops') and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single descriptionmore » of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schroedinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.« less