Optimized Dynamical Decoupling for Spin Ensembles with Large Inhomogeneities

Abstract

Spin ensembles show increasing promise for highly efficient quantum sensing and quantum technologies. However, protecting their coherent properties remains a significant challenge. Dynamical decoupling (DD) typically employs a sequence of fast pulses that aim to reduce the effect of unwanted system-environment interactions. However, the performance of the DD sequences typically suffers in spin ensembles, e.g., due to amplitude and frequency inhomogeneities and control errors. In this work, we compare the performance of an extensive number of DD protocols for coherence protection and quantum sensing in an ensemble of negatively charged NV centers under ambient conditions. We identify the optimal approach that uses rapid adiabatic passage pulses, which are robust to amplitude and frequency inhomogeneity, in combination with the variation of their phases. We experimentally demonstrate an improved signal contrast and an order-of-magnitude increase in memory time with the optimal sequence compared to the widely used XY8 with standard rectangular pulses. We also apply our approach for improved sensing of a weak oscillating field. While our particular demonstration is with NV centers in diamond, the optimized protocol is generally applicable to other spin ensembles and to systems with high amplitude and/or frequency inhomogeneities.

The paper asks how to preserve coherence and perform AC magnetometry in spin ensembles with large microwave-amplitude and resonance-frequency inhomogeneities. It experimentally compares dynamical-decoupling sequences in a room-temperature NV-diamond ensemble at a $1.1$ mT bias field, including XY8/XY16, composite-pulse protocols, interaction-decoupling sequences, smooth amplitude envelopes, and frequency-chirped rapid adiabatic passage (RAP) pulses. The measured relative drive-amplitude inhomogeneity is approximately $27\%$. The best-performing tested combination is KDD16 with Allen–Eberly RAP pulses and half-RAP preparation/readout. Numerical simulations and experimental parameter scans select a $1\,\mu\mathrm{s}$ pulse duration and $7.5$ MHz chirp range. At fixed pulse-center spacing of $1\,\mu\mathrm{s}$, exponential fits give coherence decay times of $49\,\mu\mathrm{s}$ for rectangular-pulse XY8, $131\,\mu\mathrm{s}$ for rectangular-pulse KDD16, $262\,\mu\mathrm{s}$ for sine-shaped KDD16, and $565\,\mu\mathrm{s}$ for KDD16-RAP. RAP-based population oscillations also increase readout contrast from about $17\%$ to $24.5\%$. Amplitude sensing is demonstrated with a non-phase-matched $500$ kHz test field: Bessel-modulated decay fits recover the expected field-amplitude scaling, and weaker applied signals are distinguishable than with rectangular XY8. Frequency scans identify the applied resonance but also show spurious responses that persist under pulse-phase randomization. Larger chirp ranges improve initial contrast while shortening coherence, attributed provisionally to leakage. The optimal sequence depends on the experimental errors; demonstrations are limited to this NV ensemble, and the sensing results do not establish an absolute magnetic sensitivity.