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arXiv:2007.02279 · Physical review. B./Physical review. B

Coherence of an extended central spin model with a coupled spin bath

Pengcheng Lu, Hailong Shi, Like Cao, Xiao-Hui Wang, Tao Yang, Junpeng Cao, Wen‐Li Yang

Published May 22, 2020• 8 citations
arXivHTMLPDF

Abstract

We study an extended central spin model with an isotropic nearest-neighbor spin-exchange interaction among the bath spins. The system is controllable by external magnetic fields applied on the central spin and the bath, respectively. We construct a basis set of the Hilbert space and express the Hamiltonian of the extended model into a series of $2\ifmmode\times\else\texttimes\fi{}2$ block matrices to obtain the exact solution of the model successfully. Therefrom, the coherence and the spin polarization of the central spin are investigated. We find that if the couplings among the bath spins are antiferromagnetic, the central spin has good coherence and polarization at low temperatures. Moreover, the decoherence is greatly suppressed at the critical point where the strengths of the central and the bath magnetic field take the same value. A dephasing phenomenon is identified when the initial state of the central spin is unpolarized.

DOI
10.1103/physrevb.101.184307

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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.
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 many-body dynamics of an electron spin−1/2 qubit coupled to a bath of nuclear spins by hyperfine interactions, as described by the central spin model in two kinds of external field, are studied in this paper. In a completely polarized bath, we use the state recurrence method to obtain the exact solution of the X X Z central spin model in a constant magnetic field and numerically analyze the influence of the disorder strength of the magnetic field on fidelity and entanglement entropy. For a constant magnetic field, the fidelity presents non-attenuating oscillations. The anisotropic parameter λ and the magnetic field strength B significantly affect the dynamic behaviour of the central spin. Unlike the periodic oscillation in the constant magnetic field, the decoherence dynamics of the central spin act like a damping oscillation in a disordered field, where the central spin undergoes a relaxation process and eventually reaches a stable state. The relaxation time of this process is affected by the disorder strength and the anisotropic parameter, where a larger anisotropic parameter or disorder strength can speed up the relaxation process. Compared with the constant magnetic field, the disordered field can regulate the decoherence over a large range, independent of the anisotropic parameter.
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We study the dynamics of a single spin 1∕21∕21∕2 coupled to a bath of spins 1∕21∕21∕2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. For initially completely polarized bath spins and small magnetic field, we find persistent oscillations of the central spin about a nonzero mean value. For a large number of bath spins Nb{N}_{b}Nb​, the oscillation frequency is proportional to Nb{N}_{b}Nb​, whereas the amplitude behaves as 1∕Nb1∕{N}_{b}1∕Nb​, to leading order. No asymptotic decay of the oscillations due to the nonuniform couplings is observed, in contrast to some recent studies.
The time evolution of a spin-12\frac{1}{2}21​ particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature TTT is studied. The exact analytical form of the reduced density matrix of the central spin is calculated explicitly for a finite number of bath spins. The case of an infinite number of environmental spins is investigated using the convergence of the rescaled bath operators to normal Gaussian random variables. In this limit, we derive the analytical form of the components of the Bloch vector for antiferromagnetic interactions within the bath, and we investigate the short-time and long-time behavior of reduced dynamics. The effect of the external magnetic field, the anisotropy, and the temperature of the bath on the decoherence of the central spin are discussed.