Chiral basis for qubits and spin-helix decay

TL;DR

This paper introduces a chiral basis for qubits based on transverse spin helices with kinks, enabling better analysis of topological quantum states and their decay, with applications to spin helix relaxation in cold atom experiments.

Contribution

It proposes a novel chiral basis for qubits that simplifies the study of transverse spin components and topological states, and provides an explicit universal decay function for spin helices.

Findings

Diagonalization of spin operators in the chiral basis

Universal function for spin helix relaxation

Application to cold atom experiment data

Abstract

We propose a qubit basis composed of transverse spin helices with kinks. Unlike the usual computational basis, this chiral basis is well suited for describing quantum states with nontrivial topology. Choosing appropriate parameters the operators of the transverse spin components, $\sigma_n^x$ and $\sigma_n^y$, become diagonal in the chiral basis, which facilitates the study of problems focused on transverse spin components. As an application, we study the temporal decay of the transverse polarization of a spin helix in the XX model that has been measured in recent cold atom experiments. We obtain an explicit universal function describing the relaxation of helices of arbitrary wavelength.