Scaling of Dynamical Decoupling for Spin Qubits

TL;DR

This paper studies how the coherence time of spin qubits scales with the number of dynamical decoupling pulses, revealing a power-law relationship and characterizing the environmental noise spectrum.

Contribution

It demonstrates a robust power-law scaling of coherence time with pulse number and models the environmental noise spectrum based on experimental data.

Findings

Power-law scaling of T2 with n_{b} with exponent 0.72

Environmental noise spectrum characterized as (c}) ^{-b} with b  2.6

Model predictions agree well with experimental results for various pulse sequences.

Abstract

We investigate scaling of coherence time, T2, with the number of {\pi}-pulses, n_{\pi}, in a singlet- triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law, T2 = (n_{\pi})^({\gamma}_e), with {\gamma}_e = 0.72\pm0.01, essentially independent of the envelope function used to extract T2. From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S({\omega}) ~ {\omega}^(-{\beta}), yields {\beta} = {\gamma}_e/(1 - {\gamma}_e) = 2.6 \pm 0.1. Model values for T2(n_{\pi}) using {\beta} = 2.6 for CPMG with both even and odd n_{\pi} up to 32 and CDD orders 3 through 6 compare very well with experiment.