Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot

Abstract

The spin of an electron trapped in a quantum dot is a promising candidate implementation of a qubit for quantum information processing. We study the central spin problem of the effect of the hyperfine interaction between such an electron and a large number of nuclear moments. Using a spin coherent path integral, we show that in this limit the electron spin evolution is well described by classical dynamics of both the nuclear and electron spins. We then introduce approximate yet systematic methods to analyze aspects of the classical dynamics, and discuss the importance of the exact integrability of the central spin Hamiltonian. This is compared with numerical simulation. Finally, we obtain the asymptotic long time decay of the electron spin polarization. We show that this is insensitive to integrability, and determined instead by the transfer of angular momentum to very weakly coupled spins far from the center of the quantum dot. The specific form of the decay is shown to depend sensitively on the form of the electronic wavefunction.

13 pages, 4 figures, accepted by PRB

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• Numerical modeling of the central spin problem using the spin coherent states P-representation
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Cited by in corpus (63)

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• Three stage decoherence dynamics of electron spin qubits in an optically active quantum dot
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• Intrinsic spin fluctuations reveal the dynamical response function of holes coupled to nuclear spin baths in (In,Ga)As quantum dots
• Exponential decay in a spin bath
• Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. II. Beyond Linear Response of Spin Baths
• Spin decoherence due to a randomly fluctuating spin bath
• Dynamics and decoherence in the central spin model using exact methods
• Hyperfine interaction dominated dynamics of nuclear spins in self-assembled quantum dots
• Dynamic Nuclear Polarization in Double Quantum Dots
• An improved semiclassical theory of radical pair recombination reactions
• Dephasing of electron spin qubits due to their interaction with nuclei in quantum dots
• Spin-noise in the anisotropic central spin model
• Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions
• Semi-classical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath
• Quadrupolar and anisotropy effects on dephasing in two-electron spin qubits in GaAs
• Influcence of the nuclear electric quadrupolar interaction on the coherence time of hole- and electron-spins confined in semiconductor quantum dots
• From quantum-mechanical to classical dynamics in the central-spin model
• Master equation approach to the central spin decoherence problem: the uniform coupling model and the role of projection operators
• Quantum Rydberg Central Spin Model
• Electron spin synchronization induced by optical nuclear magnetic resonance feedback
• Spin echo decay at low magnetic fields in a nuclear spin bath
• Quantum model for mode locking in pulsed semiconductor quantum dots
• Non-equilibrium nuclear spin distribution function in quantum dots subject to periodic pulses
• Conservation laws protect dynamic spin correlations from decay: Limited role of integrability in the central spin model
• Magnetic field dependence of the electron spin revival amplitude in periodically pulsed quantum dots
• Long-term Dynamics of the Electron-nuclear Spin System of a Semiconductor Quantum Dot
• Simple and accurate method for central spin problems
• Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots
• Determining the validity of cumulant expansions for central spin models
• Persisting correlations of a central spin coupled to large spin baths
• Spectrum and Screening cloud in the central spin model
• Spin noise in a quantum dot ensemble: from a quantum mechanical to a semi-classical description
• Nuclear frequency focusing in periodically pulsed semiconductor quantum dots described by infinite classical central spin models
• Spin dynamics of a confined electron interacting with magnetic or nuclear spins: A semiclassical approach
• Efficient algorithms for the dynamics of large and infinite classical central spin models
• Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots
• The theory of coherent dynamic nuclear polarization in quantum dots
• Dynamic mean-field theory for dense spin systems at infinite temperature
• Long coherence of electron spins coupled to a nuclear spin bath
• The spin-s homogeneous central spin model: exact spectrum and dynamics
• Phase-Sensitive Probes of Nuclear Polarization in Spin-Blockaded Transport
• Efficient variational approach to dynamics of a spatially extended bosonic Kondo model
• Long-time coherence in fourth-order spin correlation functions
• Quantum phase transition in XXZ central spin model
• Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots
• Quantum mechanical treatment of large spin baths
• Coherence of an extended central spin model with a coupled spin bath
• Cross-correlation spectra in interacting quantum dot systems
• Spin textures in strongly coupled electron spin and magnetic or nuclear spin systems in quantum dots
• Understanding the dynamics of randomly positioned dipolar spin ensembles
• Signatures of long-range spin-spin interactions in an (In,Ga)As quantum dot ensemble
• Fourth-order spin correlation function in the extended central spin model
• Electron spin-flip correlations due to nuclear dynamics in driven GaAs double dots
• Long-time memory effects in a localizable central spin problem
• Electron Spin Noise under the Conditions of Nuclei Induced Frequency Focusing
• Dissipative evolution of a two-level system through a geometry-based classical mapping
• Self-Quenching of Nuclear Spin Dynamics in Central Spin Problem
• Dark states in an integrable XY central spin model
• Simulation of nonequilibrium spin dynamics in quantum dots subjected to periodic laser pulses
• Truncated Wigner approximation for the bosonic model of large spin baths