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arXiv:0709.1383 · Physical Review E

Decoherence induced by an interacting spin environment in the transition from integrability to chaos

Armando Relaño, J. Dukelsky, Rafael A. Molina

Published Oct 26, 2007• 13 citations
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Abstract

We investigate the decoherence properties of a central system composed of two spins 12 in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like linear entropy or fidelity does not depend on the dynamical regime of the bath. We interpret the latter results as due to a comparable complexity of the Hamiltonian for both the integrable and the fully chaotic limits.

DOI
10.1103/physreve.76.046223

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We investigate the decoherence properties of a central system composed of two spins 12 in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like linear entropy or fidelity does not depend on the dynamical regime of the bath. We interpret the latter results as due to a comparable complexity of the Hamiltonian for both the integrable and the fully chaotic limits.
We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the system's density matrix, the linear entropy, and the fidelity of the central system decay differently for chaotic and non-chaotic baths. Therefore, knowledge of the basic parameters of the bath (strength of the system-bath interaction, and the bath's spectral density of states) is not always sufficient, and much finer details of the bath's dynamics can strongly affect the decoherence process.
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.
We study the decoherence of two coupled spins that interact with a chaotic spin-bath environment. It is shown that connectivity of spins in the bath is of crucial importance for the decoherence of the central system. The previously found phenomenon of two-step decoherence (Phys. Rev. Lett. {\bf 90}, 210401 (2003)) turns out to be typical for the bath with a slow enough dynamics or no dynamics. For a generic random system with chaotic dynamics a conventional exponential relaxation to the pointer states takes place. Our results confirm a conjecture of Paz and Zurek (Phys. Rev. Lett. {\bf 82}, 5181 (1999)) that for weak enough interactions the pointer states are eigenstates of the central system.
Fidelity is a convenient tool to study the sensitivity of quantum motion under Hamiltonian perturbations. In this paper we first show that classical chaos can produce the dephasing necessary to suppress quantum interference, even in the absence of any environment. To this end we consider the fidelity of mixed states, which takes into account interference amplitudes, and directly relate its decay to the decay of an appropriate classical correlation function, which is totally unrelated to quantum phases. We then discuss the dephasing in a two-qubit system, induced by the coupling to a single-particle, deterministic chaotic environment. The latter is shown to behave as a pure dephasing many-body object which induces decoherence in the system; memory effects are also taken into account.
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.
The environment of an open quantum system is usually modelled as a large and complex many-body quantum system. However, the question of how large and complex this many-body quantum system must be in order to play the role of a genuine environment and thus generate decoherence is an often elusive key-point in the literature. In this work, by studying the reduced dynamics of a spin connected to a generic spin chain, we show that the physical mechanism responsible for generating stronger decoherence on the reduced spin relies mostly on the chaotic behaviour of the chain. More interestingly, even in the case of an extremely short spin chain composed of two spins, by analyzing the decoherence dynamics of the reduced system we are able to reproduce the whole integrable to chaos transition. Finally, we discuss implications on quantum control experiments and show that quantum chaos reigns over the best degree of control achieved, even in small chains.