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arXiv:quant-ph/0406001 · Physical Review E

Decoherence by a chaotic many-spin bath

José Lages, V. V. Dobrovitski, Mikhail I. Katsnelson, Hans A. De Raedt, B. N. Harmon

Published Aug 31, 2005• 60 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreve.72.026225

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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 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 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 spin-bath environment. It is shown that the connectivity and the coupling strength between the spins in the environment are of crucial importance for the decoherence of the central system. For the anisotropic spin bath, changing the connectivity or coupling strength changes the decoherence of the central system from Gaussian to exponential decay law. The initial state of the environment is shown to affect the decoherence process in a qualitatively significant manner.
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.
We study the quantum-classical correspondence for systems with interacting spin particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of individual spins. Our analysis of the Lyapunov spectra reveals that the largest Lyapunov exponent agrees with the Lyapunov exponent that determines the local instability of each individual spin moving under the influence of all other spins. Within this picture, we introduce a rigorous and simple test of ergodicity for the spin motion, and use it to identify when classical chaos is both strong and global in phase space. In the quantum domain, our analysis of the Hamiltonian matrix in a proper representation allows us to obtain the conditions for the onset of quantum chaos as a function of the model parameters. From the comparison between the quantum and classical domains, we demonstrate that quantum quantities, such as the local density of states (LDoS) and the shape of the chaotic eigenfunctions written in the noninteracting many-body basis, have well-defined classical counterparts. We also find a relationship between the Kolmogorov-Sinai entropy and the width of the LDoS, which is useful for studies of many-body dynamics.
In this review, we discuss the decoherence and thermalization of a quantum spin system interacting with a spin bath environment, by numerically solving the time-dependent Schrödinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.