Quantum Memory Enhanced Multipoint Correlation Spectroscopy for Statistically Polarized NMR

Nuclear magnetic resonance spectroscopy with solid-state spin sensors is a promising pathway for the detection of nuclear spins at the micro- and nanoscale. Although many nanoscale experiments rely on a single sensor spin for the detection of the signal, leveraging spin ensembles can enhance sensitivity, particularly in cases in which the signal merely originates from statistically polarized nuclear spins. In this work, we introduce multipoint correlation spectroscopy, that combines the advantages of two well-established methods – correlation spectroscopy and quantum heterodyne detection – to enable temporally efficient measurements of statistically polarized samples at the nanoscale with spin ensembles. We present a theoretical framework for this approach and demonstrate an experimental proof of concept with a nitrogen vacancy center in diamond. We achieve single hertz uncertainty in the estimated signal frequency, highlighting the potential applications of the technique for nanoscale nuclear magnetic resonance.

💡 Research Summary

This paper introduces a novel measurement protocol called Multipoint Correlation Spectroscopy (MCS) that combines the strengths of two established nanoscale NMR techniques—Correlation Spectroscopy (CS) and Quantum Heterodyne detection (QDyne)—to achieve highly efficient detection of statistically polarized nuclear spins using ensembles of nitrogen‑vacancy (NV) centers. The authors first review the limitations of CS, which offers √N signal‑to‑noise ratio (SNR) improvement with multiple NVs but suffers from long idle periods between the initial and subsequent phase‑acquisition windows, and of QDyne, which provides rapid, evenly spaced measurements but fails to gain SNR when many NVs are read out simultaneously because the random phases of each sensor average out the statistical polarization signal.

MCS resolves this conflict by employing a long‑lived quantum memory qubit—in this work the intrinsic ^14N nuclear spin of the NV center—to store the phase acquired during an initial sensing interval (ϕ₀). After this storage step, a series of M rapid phase‑acquisition cycles (ϕ₁…ϕ_M) are performed in a QDyne‑like fashion, each time correlating the newly acquired phase with the stored ϕ₀ via conditional gates (C_nNOT_e). The memory’s longitudinal relaxation time (T₁,nuc) can reach seconds, allowing many repetitions (M) without the long dead times that limit conventional CS. Theoretical analysis shows that the measured signal after each k‑th acquisition is

S_k ≈ η