Ramsey Envelope Modulation in NV Diamond Magnetometry

TL;DR

This paper investigates the effects of envelope modulation in $^{15}$NV diamond magnetometry under misaligned magnetic fields, deriving theoretical models, validating with experiments, and proposing double-quantum coherence as a mitigation strategy.

Contribution

It provides the first detailed analysis of Ramsey envelope modulation effects in $^{15}$NV magnetometry and demonstrates how double-quantum coherences can suppress these effects.

Findings

Envelope modulation causes magnetic sensitivity loss if uncorrected.

Double-quantum coherences effectively suppress envelope modulations.

Theoretical predictions align with experimental observations.

Abstract

Nitrogen-vacancy (NV) spin ensembles in diamond provide an advanced magnetic sensing platform, with applications in both the physical and life sciences. The development of isotopically engineered $^{15}$NV diamond offers advantages over naturally occurring $^{14}$NV for magnetometry, due to its simpler hyperfine structure. However, for sensing modalities requiring a bias magnetic field not aligned with the sensing NV axis, the absence of a quadrupole moment in the $^{15}$N nuclear spin leads to pronounced envelope modulation effects in time-dependent measurements of $^{15}$NV spin evolution. While such behavior in spin echo experiments are well studied, analogous effects in Ramsey measurements and the implications for magnetometry remain under-explored. Here, we derive the modulated $^{15}$NV Ramsey response to a misaligned bias field, using a simple vector description of the effective magnetic field on the nuclear spin. The predicted modulation properties are then compared to experimental results, revealing significant magnetic sensitivity loss if unaddressed. We demonstrate that double-quantum coherences of the NV $S=1$ electronic spin states dramatically suppress these envelope modulations, while additionally proving resilient to other parasitic effects such as strain heterogeneity and temperature shifts.