Equilibration in closed quantum systems: Application to spin qubits

TL;DR

This paper investigates how quantum systems, specifically spin qubits in quantum dots, reach equilibrium by deriving bounds on equilibration and analyzing spin dynamics through exact diagonalization.

Contribution

It introduces an observable-based approach to equilibration, deriving bounds and applying them to the central spin model in quantum dots with exact numerical analysis.

Findings

Small nuclear spin environments can induce significant equilibration of electron spins

Derived bounds relate observable fluctuations to equilibration times

Exact diagonalization confirms rapid equilibration in realistic quantum dot models

Abstract

We study an observable-based notion of equilibration and its application to realistic systems like spin qubits in quantum dots. On the basis of the so-called distinguishability, we analytically derive general equilibration bounds, which we relate to the standard deviation of the fluctuations of the corresponding observable. Subsequently, we apply these ideas to the central spin model describing the spin physics in quantum dots. We probe our bounds by analyzing the spin dynamics induced by the hyperfine interaction between the electron spin and the nuclear spins using exact diagonalization. Interestingly, even small numbers of nuclear spins as found in carbon or silicon based quantum dots are sufficient to significantly equilibrate the electron spin.