Singlet-triplet decoherence due to nuclear spins in a double quantum dot

TL;DR

This paper provides a quantum analysis of singlet-triplet electron spin decoherence in double quantum dots caused by nuclear spins, revealing long-time saturation behavior, decay transition, and implications for measuring exchange interactions.

Contribution

It introduces a quantum solution accounting for decay without ensemble averaging, contrasting with previous semiclassical models, and explores the effects of exchange interaction and orbital dephasing.

Findings

Long-time saturation value of the singlet-triplet correlator differs from 1/2.

Decay transitions from Gaussian to power law ($ extasciitilde 1/t^{3/2}$) with exchange interaction.

Oscillation phase shift of $3 extpi/4$ enables precision measurement of exchange and Overhauser fields.

Abstract

We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 1/2, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law ($\sim 1/t^{3/2}$) when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\pi/4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence, and find that there is an optimal operating point where orbital dephasing becomes negligible.