Atomic Magnetometer Multisensor Array for rf Interference Mitigation and Unshielded Detection of Nuclear Quadrupole Resonance

An array of four ${}^{87}\mathrm{Rb}$ vector magnetometers is used to detect nuclear quadrupole resonance signals in an unshielded environment at 1 MHz. With a baseline of 25 cm, the length of the array, radio-frequency interference mitigation is also demonstrated; a radio-station signal is suppressed by a factor of 20 without degradation to the signal of interest. With these compact sensors, in which the probe beam passes through twice, the fundamental limit to detection sensitivity is found to be photon-shot noise. More passes of the probe beam overcome this limitation. With a sensor of similar effective volume, $0.25{\mathrm{cm}}^3$, but $25\times$ more passes, the sensitivity is improved by an order of magnitude to $1.7\pm 0.2\mathrm{fT}/\sqrt{\mathrm{Hz}}$.

Figure 1

Top view of the 2-pass sensor array. In the inset, a Twinleaf sensor, held down with nylon bolts, is shown with a nickel for perspective; all connections, including those for heating and temperature measurement, are fiber optic. Table 1 gives the pump and probe powers measured at the fiber mating connectors, denoted by a black dot above. A square pair of coils, separation and side length of 21 cm, provide real-time calibration of the sensors, while the net static field $B_0\widehat{z}$, which is kept parallel to the pump beam, is set by field coils that are not shown here. The NQR sample, sodium nitrite, sits inside the rf excitation coil and is situated 2 cm above the sensor array.

Figure 2

A 90-90 spin-lock spin-echo sequence [52], rf duration $t_e=t_r=100\mu \mathrm{s}$, with $N$ echoes, is used to excite the sample. The $Q$ of the tuned excitation coil is spoiled, so that the stored energy quickly dissipates before the light of duration $t_p$ pumps the sensor. The light is adiabatically ramped down to avoid perturbations, before the signal is acquired during $t_a$. Values are given in Table 2.

Figure 3

The ESR calibration for the calibration coil, Fig. 1, determines the field values in the 2-pass sensors for the measured voltage input $V_{\mathrm{in}}$. Normalized data are fit to $\sin (\gamma \alpha V_{\mathrm{in}}{t}_{\mathrm{rf}}/2)$, where the calibration constant $\alpha$ is given in the legend. Data are taken with the oven at a reduced set point, $100°\mathrm{C}$, to avoid nonlinearity in the measurement.

Figure 4

By varying light duration $t_p$ the polarization buildup rate can be measured, Fig. 8. By varying $\tau$, the time in the dark after the polarization is fully built up, relaxation rates which characterize the sensor can be determined, Fig. 9 and Table 1. By varying the rf pulse strength, Fig. 3, the magnetic field can be calibrated. Details for buildup, vary-$\tau$, and ESR experiments can be found in Table 3.

Figure 5

In the $\parallel$ orientation, a 60-Hz magnetic field is found to oscillate the resonance frequency of the magnetometer by $\pm 2\mathrm{kHz}$, resulting in a fluctuation in the phase and size of the complex signal, as shown above for inner sensor 1. The effect can also be seen in the large and periodic 60-Hz noise spikes in the inset of Fig. 10. Such examples of a 60-Hz noise can be found in other works [21].

Figure 6

The 50-pass sensor [(b), (c)] is an order of magnitude more sensitive than the 2-pass sensor. Representative data for the 2-pass sensors, taken using inner sensor 2, is shown in (a). (c) Low probe power, 0.4 mW, yields better sensitivity than (b) higher power, 1.2 mW. As discussed in the text, looking at noise with the pump or probe light turned off, with the field detuned, and under matched filtering gives insight into the dominant noise sources. Filtering is applied to all time domain data, duration 1 ms, except those explicitly labeled as unfiltered. Because of a long dwell time for (a), digital filtering effects can be observed towards the edges of the spectra.

Figure 7

The free induction decay (FID) of the signal under heterodyne detection after a $\pi /2$ pulse behaves as the Bessel function $J_1\{2\theta (t)\}{e}^{i\mathrm{\Delta }\omega t+\phi }$, solid lines, where $\mathrm{\Delta }\omega$ is the angular off resonance from the spectrometer frequency, $\phi$ is the receiver phase, and an analytic solution [56] for $\theta (t)$ is derived from Eq. (3) with $P=P_T$. From this fit it is found ${\theta }_{\max }=\theta (t=0)=20.56\pm 0.02\mathrm{rad}$.

Figure 8

The buildup of signal as a function of pump duration is shown for the 2-pass sensors in the main graph, and for the 50-pass sensor in the inset. The NQR data and sensitivity measurements are taken with pump times close to 1 ms, to accommodate the echo train timing.

Figure 9

The factor of 8 light narrowing reveals 92% spin polarization in the 50-pass cell, as measured at a 1-MHz Larmor frequency. The delay $\tau$ between the 5-ms-long light pulse and the resonant rf pulse, Fig. 4, is given in the legend, while the relaxation rate, $\mathrm{\Gamma }=1/T_2$, as a function of $\tau$ values is in the inset. The probe power used for this particular measurement is $3\times$ higher than what is listed in Table 1.

Figure 10

When the resonance frequency is matched to a radio station, blue lines, the 100-fT test signal is lost in the interference, as can be seen in both the 1D spectra (a) and the 2D spectra (b). The standard deviation about the mean $\sigma$ of the 100 scans, dashed lines, is indistinguishable from the root mean square of the data, rms. Using all four sensors, and the rejection algorithm described in the text, the signal can now be distinguished from the interference (c) and (d), and can be compared to the case when there is little interference, red lines. (e) Looking at the on-resonance projection coefficients, ${\lambda }_S={\lambda }_S^{\prime }+i{\lambda }_S^{\prime \prime }$ for the signal and ${\lambda }_I={\lambda }_I^{\prime }+i{\lambda }_I^{\prime \prime }$ for interference, one can clearly see the signal separated out from the interference distribution.

Figure 11

The interference signal is plotted for the sensor array as a function of position, normalized to $d$, revealing the quadratic component is more significant in the $\perp$ orientation than in the $\parallel$. In the graph, the signals have been normalized to the complex signal of inner sensor 1, Fig. 1, to better show the functional dependence. The interference is, however, more than an order of magnitude higher for the $\parallel$ orientation.

Figure 12

The strong rf pulse used to excite the sodium-nitrite sample induces a phase-dependent ringing in the magnetometer which is reduced by averaging, solid red line, over the phase-cycled data, dashed and dotted data. Calibration data, taken just before and after the NQR echo train, are used to correct for drift in the magnetic field. Each curve corresponds to an average over $N$ echoes, Table 2. The NQR signal is more than 2 orders of magnitude smaller than the calibration signal and would not be easily seen on the scale displayed.

Figure 13

The NQR signal detected by the two inner sensors is measured as a function of the excitation field strength. The difference in the results comes from asymmetric placement of the sensors with respect to the sodium nitrite sample; for RFIM the placement is made symmetric as shown in Fig. 1.