Exact quantum dynamics of XXZ central spin problems
Date
2019
Authors
He, Wen-Bin
Chesi, Stefano
Lin, Hai-qing
Guan, Xi-Wen
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American Physical Society
Abstract
We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), the
reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities
characterize the quantum decoherence and entanglement of the system with any number of bath spins, and for
a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field
B, coupling constant A, and longitudinal interaction significantly influence the time scales of the quantum
dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the
resonance condition B = = A, the location of the mth revival peak in time reaches a simple relation tr πN
A m
for a large N. For = 0, N → ∞, and a small polarization in the initial spin coherent state, our analytical result
for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact
dynamical connection between the central spin problems and the light-matter interacting systems in quantum
nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes
while disappearing at strong inhomogeneity.
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Physical Review B
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Journal article
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Open Access
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