He, Wen-BinChesi, StefanoLin, Hai-qingGuan, Xi-Wen2020-05-272020-05-272469-9950http://hdl.handle.net/1885/204689We 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.This work is supported by the National Key R&D Program of China No. 2017YFA0304500, the key NSFC Grant No. 11534014, and NSFC Grant No. 11874393. S.C. acknowledges support from the National Key R&D Program of China No. 2016YFA0301200 and NSFC (Grants No. 11574025, No. 11750110428, and No. 1171101295).H.-Q.L. and S.C. acknowledge financial support from NSAF U1530401 and computational resources from the Beijing Computational Science Research Center (CSRC). X.-W.G. thanks CSRC, where part of this paper was prepared, for kind hospitality.application/pdfen-AU© 2019 American Physical Society201910.1103/PhysRevB.99.1743082019-12-19