Scaling Behavior in the Decoherence of Decoupled Multi-spin System

TL;DR

This paper investigates how decoherence times scale with the number of spins in a decoupled multi-spin system, revealing scale-invariant behavior within a Zeeman manifold and inverse square root scaling across different manifolds, relevant for quantum technology.

Contribution

It provides a detailed analysis of decoherence scaling laws in multi-spin systems, extending understanding to various Zeeman configurations and dynamical decoupling scenarios.

Findings

Decoherence times are scale-free within a Zeeman manifold.

Decoherence times scale inversely with the square root of the number of spins across manifolds.

Results inform the scalability of spin-based quantum technologies.

Abstract

We study the scaling of decoherence of decoupled electron spin qubits due to hyperfine interaction. For a superposed state consisting of product states from a single Zeeman manifold, both $T_2^*(n)$ and $T_2(n)$ are scale-free with respect to $n$ and the number of basis states, $m$. For a superposed state made up of states from different Zeeman manifolds, both $T_2(n)$ and $T_2^*(n)$ are roughly inversely proportional to $\sqrt{n}$. Our results can be extended to other decoherence mechanisms, including in the presence of dynamical decoupling, which allow meaningful discussions on the scalability of spin-based coherent solid state quantum technology.