Balancing coherent and dissipative dynamics in a central-spin system

TL;DR

This paper derives exact expressions for the steady-state time in a central-spin quantum system, revealing an optimal dissipation rate that minimizes this time and demonstrating logarithmic growth with system size, relevant for quantum information applications.

Contribution

It provides the first analytical solution for steady-state time in a central-spin system, highlighting the benefits of dissipation optimization and collective effects for scalable quantum systems.

Findings

Optimal dissipation rate minimizes steady-state time.

Steady-state time grows logarithmically with system size.

Collective enhancement significantly improves scalability.

Abstract

The average time required for an open quantum system to reach a steady state (the steady-state time) is generally determined through a competition of coherent and incoherent (dissipative) dynamics. Here, we study this competition for a ubiquitous central-spin system, corresponding to a `central' spin-1/2 coherently coupled to ancilla spins and undergoing dissipative spin relaxation. The ancilla system can describe $N$ spins-1/2 or, equivalently, a single large spin of length $I=N/2$. We find exact analytical expressions for the steady-state time in terms of the dissipation rate, resulting in a minimal (optimal) steady-state time at an optimal value of the dissipation rate, according to a universal curve. Due to a collective-enhancement effect, the optimized steady-state time grows only logarithmically with increasing $N=2I$, demonstrating that the system size can be grown substantially with only a moderate cost in steady-state time. This work has direct applications to the rapid initialization of spin qubits in quantum dots or bound to donor impurities, to dynamic nuclear-spin polarization protocols, and may provide key intuition for the benefits of error-correction protocols in quantum annealing.