Real-time Amplitude and Phase Estimation of AC Fields with Diamond Spins

Abstract

Nitrogen-vacancy centers in diamond have been shown to be capable of detecting AC magnetic fields with high sensitivity, spectral resolution, and spatial resolution. However, most studies so far have focused on the regime of time-averaged or time-correlated measurements, while little attention has been paid to the single-shot regime. Here we show that the amplitude and phase of an AC field can be retrieved from a single pair of two consecutive measurements. We demonstrate this concept by measuring a 4 MHz AC field with a per-shot amplitude and phase sensitivity of 78 nT and 63 mrad, respectively, at a temporal resolution of 320 us. We also investigate the effects and quantify the errors resulting from probe frequency detunings, as well as operating in the strong field regime. Moreover, we showcase the ability of the measurement protocol to dynamically change the probe frequency in real-time. This work advances the use of NV centers for real-time measurements of AC magnetic fields.

Figures (4)

• Figure 1: Protocol for real-time magnetic field amplitude and phase estimation. (a) Bloch sphere representation of a TLS subject to a MW driving field and an AC probe field. (b) Phasor representation of the amplitude and phase of three different measurement points, plotted in terms of its I and Q components. (c) Proposed real-time phase-sensitive AC sensing protocol. The protocol utilizes a well-defined time delay between a pair of sequential measurements. An example CPDD control sequence used in this work is shown in the inset. (d) Simplified schematic of the experimental setup. The NV diamond sample is placed on top of a CPW used to deliver the MW control pulse sequence and is surrounded by a 8-turn planar coil loop to deliver AC test signals.
• Figure 2: Demonstration of real-time AC sensing. (a)(i) Measured PL response as a function of input AC magnetic field strength. The red solid line is expected behavior from theory following Eqs. \ref{['eq:eq3']} and \ref{['eq:eq4']}, with the slope of the fit equal $4.85$ mV/$\upmu$T. The residual is plotted in (ii). (b) Measured phase response with the phase of the test field swept from [0, $2\pi$]. The red solid line represents the ideal case where $\phi_{\mathrm{test}} = \phi_{\mathrm{meas.}}$ and the residual is plotted in (ii). (c) Time trace of the measured (i) in-phase, quadrature, (ii) amplitude and phase component of a time-varying AC test field, with amplitude and phase changes applied every $320$ ms. The corresponding IQ diagram is plotted in (d) and the white crosses indicate expected location based on $R_{\mathrm{test}}$ and $\phi_{\mathrm{test}}$. For each set point (white cross), 1000 data points were measured (i.e., $320 \; \upmu \mathrm{s}$ per data point over 320 ms) and represented as a density map with dark (light) red indicating high (low) sample density. (e) Amplitude and (f) phase Allan deviation calculated from a 10 s time trace. Shaded areas represent the uncertainty.
• Figure 3: Errors arising from frequency detunings and large amplitudes. (a) Measured amplitude response as a function of AC test frequency swept in $10$ kHz steps, with the CPDD sequence resonantly tuned to $f_{\mathrm{probe}}=4$ MHz for different values of $N$. A separate set of measurements scanned over a smaller frequency range in $1$ kHz steps is shown in the inset. (b) IQ diagrams at selective frequency detunings, with the test signal phase swept from [0, $2\pi$]. (c) Extracted major axis, semi-major axis and the (d) calculated ellipticity as a function of frequency detuning. (e) Measured phase rotation as a function of frequency detuning. Solid lines are expected behavior calculated using an idealized model. (f) Selective IQ diagrams in the high field non-linear regime with the test signal phase swept from [0, $2\pi$].
• Figure 4: Demonstration of real-time frequency tracking. Measured (ii) amplitude and (iii) phase response of a time-varying AC test signal with frequency changes applied every 1.28 s (a) without and (b) with frequency tracking enabled by dynamically adjusting the probe frequency in (i). Each measurement was taken every $320 \; \upmu$s, totaling 4000 data points per frequency change. Dotted gray lines indicate expected set values. Corresponding IQ diagrams (c) without and (d) with frequency tracking. Each color indicates a different probe frequency and the sample density is represented by the shade of each color (i.e., dark (bright) = high (low) sample density).