Enhanced hyperfine-induced spin dephasing in a magnetic-field gradient

TL;DR

This paper investigates how magnetic-field gradients affect spin coherence in semiconductor quantum dots and donors, revealing significant coherence reductions that can be mitigated or are system-specific, with implications for quantum computing.

Contribution

It provides a theoretical analysis of magnetic-field gradient effects on spin dephasing in quantum dots and donors, highlighting new phenomena and mitigation strategies.

Findings

Magnetic-field gradients can reduce coherence times in GaAs quantum dots by nearly tenfold.

Applying a moderate magnetic field can mitigate dephasing by entering a motional averaging regime.

Finite-size effects cause deviations from Gaussian behavior in small donor systems.

Abstract

Magnetic-field gradients are important for single-site addressability and electric-dipole spin resonance of spin qubits in semiconductor devices. We show that these advantages are offset by a potential reduction in coherence time due to the non-uniformity of the magnetic field experienced by a nuclear-spin bath interacting with the spin qubit. We theoretically study spins confined to quantum dots or at single donor impurities, considering both free-induction and spin-echo decay. For quantum dots in GaAs, we find that, in a realistic setting, a magnetic-field gradient can reduce the Hahn-echo coherence time by almost an order of magnitude. This problem can, however, be resolved by applying a moderate external magnetic field to enter a motional averaging regime. For quantum dots in silicon, we predict a cross-over from non-Markovian to Markovian behavior that is unique to these devices. Finally, for very small systems such as single phosphorus donors in silicon, we predict a breakdown of the common Gaussian approximation due to finite-size effects.