Multiple decoherence-free states in multi-spin systems

TL;DR

This paper introduces a numerical method to identify long-lived quantum states in multi-spin systems by analyzing the null-space of the spin relaxation superoperator, revealing many such states beyond the well-known two-spin singlet.

Contribution

It presents a new numerical procedure for mapping the null-space of the spin relaxation superoperator in multi-spin systems, uncovering numerous long-lived states and their symmetry conditions.

Findings

Identifies multiple long-lived states in n-spin systems (n=4-8).

Shows symmetry requirements maximize the number of these states.

Reveals many states with near-zero eigenvalues beyond two-spin singlet.

Abstract

A numerical procedure is presented for mapping the vicinity of the null-space of the spin relaxation superoperator. The states populating this space, i.e. those with near-zero eigenvalues, of which the two-spin singlet is a well-studied example, are long-lived compared to the conventional T1 and T2 spin-relaxation times. The analysis of larger spin systems described herein reveals the presence of a significant number of other slowly relaxing states. A study of coupling topologies for n-spin systems (n = 4 - 8) suggests the symmetry requirements for maximising the number of long-lived states.