Quantum mechanical treatment of large spin baths

Abstract

The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number $N_{\mathrm{eff}}\approx 10^4$ to $10^6$ of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit $N_{\mathrm{eff}}\to \infty$ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a non-interacting bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not become completely classical. The data obtained by the proposed iEoM approach is tested successfully against data from other, established approaches. Thus, the iEoM mapping extends the set of theoretical tools which can be used to understand the spin dynamics in large CSMs.

18 pages, 9 figures

References in corpus (27)

• Coherent control of a single electron spin with electric fields
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Nuclear spin physics in quantum dots: an optical investigation
• Spin decoherence of a heavy hole coupled to nuclear spins in a quantum dot
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Quantum many-body theory of qubit decoherence in a finite-size spin bath
• Electron spin decoherence of single Nitrogen-Vacancy defects in diamond
• Nuclear Spins in Nanostructures
• Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin-bath
• Quantum many-body theory of qubit decoherence in a finite-size spin bath. II. Ensemble dynamics
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Quantum Decoherence of the Central Spin in a Sparse System of Dipolar Coupled Spins
• Nonperturbative master equation solution of central spin dephasing dynamics
• Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot
• Hyperfine interaction induced decoherence of electron spins in quantum dots
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• Two-color spin noise spectroscopy: Using spin fluctuation correlations to reveal homogeneous linewidths within quantum dot ensembles
• Electrically-Driven Reverse Overhauser Pumping of Nuclear Spins in Quantum Dots
• Nuclear spin dynamics and Zeno effect in quantum dots and defect centers
• From quantum-mechanical to classical dynamics in the central-spin model
• Spin echo decay at low magnetic fields in a nuclear spin bath
• Non-equilibrium nuclear spin distribution function in quantum dots subject to periodic pulses
• Influence of the nuclear Zeeman effect on mode locking in pulsed semiconductor quantum dots
• Spin noise in a quantum dot ensemble: from a quantum mechanical to a semi-classical description
• Efficient algorithms for the dynamics of large and infinite classical central spin models
• Long-time coherence in fourth-order spin correlation functions
• Comparison of the Iterated Equation of Motion Approach and the Density Matrix Formalism for the Quantum Rabi Model

Cited by in corpus (9)

• Magnetic field dependence of the electron spin revival amplitude in periodically pulsed quantum dots
• Determining the validity of cumulant expansions for central spin models
• Nuclear frequency focusing in periodically pulsed semiconductor quantum dots described by infinite classical central spin models
• Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems
• Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots
• Solomon equations for qubit and two-level systems: Insights into non-Poissonian quantum jumps
• Strong quenches in the one-dimensional Fermi-Hubbard model
• Exact Model Reduction for Continuous-Time Open Quantum Dynamics
• Truncated Wigner approximation for the bosonic model of large spin baths