Exact dynamics in the inhomogeneous central-spin model

Abstract

We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 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. This formula is evaluated explicitly for initial conditions such that the bath spins are completely polarized at the beginning. For this case we find, after an initial decay, a persistent oscillatory behaviour of the central spin. For a large number of bath spins $N_b$, the oscillation frequency is proportional to $N_b$, whereas the amplitude behaves like $1/N_b$, to leading order. No asymptotic decay due to the non-uniform couplings is observed, in contrast to some recent studies.

7 pages, 3 figures

References in corpus (15)

• Quantum Computation with Quantum Dots
• Electron spin decoherence in quantum dots due to interaction with nuclei
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Electron spin evolution induced by interaction with nuclei in a quantum dot
• Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei
• Decoherence induced by interacting quantum spin baths
• An efficient scheme for numerical simulations of the spin-bath decoherence
• Spin decay and quantum parallelism
• Analytical Solution of Electron Spin Decoherence Through Hyperfine Interaction in a Quantum Dot
• Numerical modeling of the central spin problem using the spin coherent states P-representation
• Entanglement Sharing and Decoherence in the Spin-Bath
• Generating function of correlators in the sl_2 Gaudin model
• Effect of external magnetic field on electron spin dephasing induced by hyperfine interaction in quantum dots
• Finite Size Corrections for the Pairing Hamiltonian
• Quantum versus classical hyperfine-induced dynamics in a quantum dot

Cited by in corpus (81)

• Non-Hermitian Physics
• Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths
• Nuclear Spins in Nanostructures
• Dark state semilocalization of quantum emitters in a cavity
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Nonperturbative master equation solution of central spin dephasing dynamics
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Correlated projection operator approach to non-Markovian dynamics in spin baths
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• 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
• Measurement Induced Continuous Time Crystals
• Dynamics and decoherence in the central spin model in the low-field limit
• Spin-noise in the anisotropic central spin model
• Bang-Bang control of a qubit coupled to a quantum critical spin bath
• Spin polarization through Floquet resonances in a driven central spin model
• Symmetry criteria for quantum simulability of effective interactions
• Integrability and dark states in an anisotropic central spin model
• Control of open quantum systems: Case study of the central spin model
• Influcence of the nuclear electric quadrupolar interaction on the coherence time of hole- and electron-spins confined in semiconductor quantum dots
• Master equation approach to the central spin decoherence problem: the uniform coupling model and the role of projection operators
• From quantum-mechanical to classical dynamics in the central-spin model
• Quantum Rydberg Central Spin Model
• Exact quantum dynamics of XXZ central spin problems
• On the determinant representations of Gaudin models' scalar products and form factors
• Continuous Measurement of a Non-Markovian Open Quantum System
• Quantum quench in the attractive regime of the sine-Gordon model
• 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
• Dynamical correlation functions of the mesoscopic pairing model
• Persistent dark states in anisotropic central spin models
• Persisting correlations of a central spin coupled to large spin baths
• Interacting spins in a cavity: finite size effects and symmetry-breaking dynamics
• 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
• Decoherence of a single spin coupled to an interacting spin bath
• Separable and entangled states in the high-spin XX central spin model
• Hyperfine induced spin and entanglement dynamics in Double Quantum Dots: A homogeneous coupling approach
• Non-interacting central site model: localization and logarithmic entanglement growth
• High Order Coherent Control Sequences of Finite-Width Pulses
• Spin dynamics of a confined electron interacting with magnetic or nuclear spins: A semiclassical approach
• Spins coupled to a Spin Bath: From Integrability to Chaos
• Efficient algorithms for the dynamics of large and infinite classical central spin models
• High-fidelity quantum memory utilizing inhomogeneous nuclear polarization in a quantum dot
• Non-Markovian dynamics in a spin star system: The failure of thermalization
• Theory of box-model hyperfine couplings and transport signatures of long-range nuclear-spin coherence in a quantum-dot spin valve
• Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems
• Quantum simulation of the central spin model with a Rydberg atom and polar molecules in optical tweezers
• Efficient variational approach to dynamics of a spatially extended bosonic Kondo model
• The spin-s homogeneous central spin model: exact spectrum and dynamics
• Nuclear Spin Noise in the Central Spin Model
• Integrability and duality in spin chains
• Quantum phase transition in XXZ central spin model
• Exact dynamics of the homogeneous two-qubit $XXZ$ central spin model with the spin bath prepared in superpositions of symmetric Dicke states
• Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots
• Lattice vs. continuum theory of the periodic Heisenberg chain
• Integrability and quench dynamics in the spin-1 central spin XX model
• Coherence of an extended central spin model with a coupled spin bath
• Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models
• Cross-correlation spectra in interacting quantum dot systems
• Driven dynamics of a quantum dot electron spin coupled to bath of higher-spin nuclei
• On the exact solvability of the anisotropic central spin model: An operator approach
• Quantum bath statistics tagging
• Long-time memory effects in a localizable central spin problem
• Decoherence and energy flow in the sunburst quantum Ising model
• Exact Entanglement dynamics in Three Interacting Qubits
• Perturbative regimes in central spin models
• Kinetic approach to the nuclear-spin polaron formation
• Entanglement and energy transportation in the central-spin quantum battery
• Time dynamics of Bethe ansatz solvable models
• From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions
• Quantum dynamics of Gaudin magnets
• Noise-resistant quantum memory enabled by Hamiltonian engineering
• Symmetry-Enhanced Performance of Dynamical Decoupling
• Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning
• Emergent mirror symmetry in the optimization of the central-spin quantum battery
• Quantifying electron-nuclear spin entanglement dynamics in central-spin systems using one-tangles
• Characterizing the transition from topology to chaos in a kicked quantum system
• Decoherence dynamics of entangled quantum states in the $XXX$ central spin model
• Metastable discrete time-crystal resonances in a dissipative central spin system