[Paper Review] DC Magnetometry at the $T_2$ Limit

Ashok Ajoy, Yixiang Liu+1 more|arXiv (Cornell University)|Nov 15, 2016

Magnetic Field Sensors Techniques3 citations

TL;DR

This paper introduces an ancilla-mediated frequency upconversion technique that enables DC magnetometry at the $T_2$ coherence limit by converting static magnetic fields into detectable AC signals via a nuclear spin ancilla. The method achieves quantum lock-in detection with noise filtering bandwidths near $1/T_2$, demonstrating $\approx 6\mu$T/$\sqrt{\textrm{Hz}}$ sensitivity and narrow-band noise filtering below 64 kHz, enabling high-sensitivity vector magnetometry at the nanoscale.

ABSTRACT

Sensing static or slowly varying magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging and materials science. Several versatile magnetometry platforms have emerged over the past decade, such as electronic spins associated with Nitrogen Vacancy (NV) centers in diamond. However, their high sensitivity to external fields also makes them poor sensors of DC fields. Indeed, the usual method of Ramsey magnetometry leaves them prone to environmental noise, limiting the allowable interrogation time to the short dephasing time T2*. Here we introduce a hybridized magnetometery platform, consisting of a sensor and ancilla, that allows sensing static magnetic fields with interrogation times up to the much longer T2 coherence time, allowing significant potential gains in field sensitivity. While more generally applicable, we demonstrate the method for an electronic NV sensor and a nuclear ancilla. It relies on frequency upconversion of transverse DC fields through the ancilla, allowing quantum lock-in detection with low-frequency noise rejection. In our experiments, we demonstrate sensitivities better than 6uT/vHz, comparable to the Ramsey method, and narrow-band signal noise filtering better than 64kHz. With technical optimization, we expect more than an one order of magnitude improvement in each of these parameters. Since our method measures transverse fields, in combination with the Ramsey detection of longitudinal fields, it ushers in a compelling technique for sensitive vector DC magnetometry at the nanoscale.

Motivation & Objective

• To overcome the $T_2^*$ limitation in DC magnetometry caused by environmental noise and $1/f$ noise.
• To enable long interrogation times up to the $T_2$ coherence time for improved field sensitivity.
• To develop a method for high-sensitivity vector DC magnetometry using a single NV center with a nuclear spin ancilla.
• To demonstrate quantum lock-in detection of DC fields via frequency upconversion and dynamical decoupling.
• To achieve noise filtering bandwidths near $1/T_2$ for enhanced signal-to-noise ratio.

Proposed method

• The method uses a nitrogen-vacancy (NV) center electron spin as a sensor and a $^{14}\textrm{N}$ nuclear spin as an ancilla to up-convert transverse DC magnetic fields into oscillating fields at a tunable frequency $\omega_0$.
• The upconverted AC signal is measured using a CPMG dynamical decoupling sequence, enabling quantum lock-in detection at $\omega_0$.
• The technique leverages the narrow bandwidth of the dynamical decoupling filter ($\sim 1/T_2$) to suppress both environmental noise and low-frequency signal noise.
• Quantum interpolation is applied to achieve sub-timing-resolution sampling of the signal peak, enabling precise measurement of the $^{14}\textrm{N}$ signal at $\approx 20.8$ ps resolution.
• Monte Carlo fitting with error propagation is used to estimate uncertainties in fit parameters and experimental error bars.
• The system performs dual band-pass filtering: it filters both sensor noise and signal noise, effectively extending the effective coherence time to $T_2$.

Experimental results

Research questions

• RQ1 Can DC magnetic fields be measured with sensitivity limited by $T_2$ rather than $T_2^*$ in NV center magnetometry?
• RQ2 Can ancilla-mediated frequency upconversion enable quantum lock-in detection of DC fields?
• RQ3 To what extent does the method suppress low-frequency noise in both the signal and the sensor environment?
• RQ4 Can the technique achieve sub-timing-resolution sampling of the signal peak using quantum interpolation?
• RQ5 What is the achievable sensitivity and noise filtering bandwidth in a practical implementation?

Key findings

• The method achieves a magnetic field sensitivity of approximately $6\mu$T/$\sqrt{\textrm{Hz}}$, comparable to conventional Ramsey-based methods.
• Narrow-band noise filtering is demonstrated to be better than 64 kHz, enabling effective suppression of low-frequency noise.
• Quantum interpolation enables effective sampling resolution of $\approx 20.8$ ps, far below the hardware timing resolution, allowing precise peak detection at $\approx 60.45$ ns.
• The experimental signal lineshape closely matches a theoretical modified sinc-function with slight asymmetry, confirming the accuracy of the model.
• Chevron patterns in the data match those from two-spin exchange dynamics, validating the coherence and fidelity of the quantum interpolation process.
• With technical optimization, the authors project more than a tenfold improvement in both sensitivity and noise filtering bandwidth.