Quantum Decoherence of the Central Spin in a Sparse System of Dipolar Coupled Spins

Abstract

The central spin decoherence problem has been researched for over 50 years in the context of both nuclear magnetic resonance and electron spin resonance. Until recently, theoretical models have employed phenomenological stochastic descriptions of the bath-induced noise. During the last few years, cluster expansion methods have provided a microscopic, quantum theory to study the spectral diffusion of a central spin. These methods have proven to be very accurate and efficient for problems of nuclear-induced electron spin decoherence in which hyperfine interactions with the central electron spin are much stronger than dipolar interactions among the nuclei. We provide an in-depth study of central spin decoherence for a canonical scale-invariant all-dipolar spin system. We show how cluster methods may be adapted to treat this problem in which central and bath spin interactions are of comparable strength. Our extensive numerical work shows that a properly modified cluster theory is convergent for this problem even as simple perturbative arguments begin to break down. By treating clusters in the presence of energy detunings due to the long-range (diagonal) dipolar interactions of the surrounding environment and carefully averaging the effects over different spin states, we find that the nontrivial flip-flop dynamics among the spins becomes effectively localized by disorder in the energy splittings of the spins. This localization effect allows for a robust calculation of the spin echo signal in a dipolarly coupled bath of spins of the same kind, while considering clusters of no more than 6 spins. We connect these microscopic calculation results to the existing stochastic models. We, furthermore, present calculations for a series of related problems of interest for candidate solid state quantum bits including donors and quantum dots in silicon as well as nitrogen-vacancy centers in diamond.

25 pages, 26 figures

References in corpus (27)

• Single-shot read-out of an individual electron spin in a quantum dot
• Universal dynamical decoupling of a single solid-state spin from a spin bath
• Fault-Tolerant Quantum Dynamical Decoupling
• How to Enhance Dephasing Time in Superconducting Qubits
• Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Quenching Spin Decoherence in Diamond through Spin Bath Polarization
• Quantum many-body theory of qubit decoherence in a finite-size spin bath
• Electron spin decoherence of single Nitrogen-Vacancy defects in diamond
• Electron Spin Dephasing due to Hyperfine Interactions with a Nuclear Spin Bath
• Room-temperature manipulation and decoherence of a single spin in diamond
• Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation
• Pure quantum dephasing of a solid state electron spin qubit in a large nuclear spin bath coupled by long-range hyperfine-mediated interactions
• Restoring Coherence Lost to a Slow Interacting Mesoscopic Bath
• Electron spin decoherence in isotope-enriched silicon
• Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem
• Comparison of dynamical decoupling protocols for a nitrogen-vacancy center in diamond
• Quantum computing by optical control of electron spins
• Dangling-bond spin relaxation and magnetic 1/f noise from the amorphous-semiconductor/oxide interface: Theory
• Quantum many-body theory of qubit decoherence in a finite-size spin bath. II. Ensemble dynamics
• Electron spin phase relaxation of phosphorus donors in nuclear spin enriched silicon
• Anomalous decoherence effect in a quantum bath
• Hybrid solid state qubits: the powerful role of electron spins
• Concatenated dynamical decoupling in a solid-state spin bath
• Decoherence induced by anisotropic hyperfine interaction in Si spin qubits
• Electrostically defined few-electron double quantum dot in silicon
• Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath

Cited by in corpus (1)

• On the determinant representations of Gaudin models' scalar products and form factors