Experimental arrangement

The experimental setup is depicted in Fig. 1. It used the European Southern Observatory Wendelstein Laser Guide Star Unit (ESO WLGSU) installed next to the William Herschel Telescope (WHT) at the Observatorio del Roque de los Muchachos (ORM) in La Palma (Supplementary Fig. 1). The operation of the WLGSU allows modulation of the beam and pointing the transmitter and receiver telescopes at the same target. The setup incorporated a laser projector telescope and a receiver telescope separated by eight meters. The light source consisted of a continuous-wave Raman-fiber-amplified frequency-doubled laser with a maximum output power of 20 W13. The laser was tuned to the vacuum wavelength of 589.158 nm corresponding to the 3S 1/2 → 3P 3/2 transition of sodium (the D2 line); the linewidth of the laser was measured to be ~2 MHz. The laser system incorporated an AOM (acousto-optic modulator) for on-off amplitude modulation of the beam intensity. The beam polarization was controlled with a set of waveplates following the AOM. The Galilean projector telescope magnified the beam to an output diameter of 30 cm. The receiver consisted of a 40-cm aperture Schmidt–Cassegrain telescope mounted on the WLGSU receiver control unit, equipped with a narrow-band interference filter of 0.30(5) nm bandwidth centered at the sodium D2 line wavelength, a tracking CMOS (complementary metal-oxide-semiconductor) camera and a PMT (photomultiplier tube). A discriminator was used to filter and convert the analog pulses from the PMT into 100 ns TTL (transistor–transistor logic) pulses for the photon counters. The signal was acquired by three independent methods: (a) digitizing and counting the arrival of individual photons (offline mode), (b) directly measuring and averaging the photon-count difference per modulation period (online counter), and (c) directly demodulating the signal from the PMT with a lock-in amplifier.

Fig. 1 Experimental arrangement. A laser projector sends an intensity-modulated beam to the mesosphere where it polarizes sodium atoms. Fluorescence is observed with a second telescope and the received photons are recorded, counted and demodulated with a digitizer, a photon counter, and a lock-in amplifier, respectively. The change in fluorescence is measured as the laser modulation frequency is swept around the Larmor frequency driving the acousto-optic modulator (AOM) using a signal generator. The lock-in amplifier provides the reference to dither the intensity-modulation frequency to discriminate atmospheric scintillation noise Full size image

Each observation run consisted of a discrete frequency sweep of the laser intensity modulation around the predicted Larmor frequency. In order to reduce atmospheric scintillation noise, the frequency of the laser intensity modulation at each step of the sweep (f step ) was dithered with a square-wave function such that

$$f_{{\mathrm{pulse}}}(t) = f_{{\mathrm{step}}} + \delta f \cdot {\mathrm{sgn}}\left[ {{\mathrm{cos}}\left( {2\pi f_{\mathrm{m}}t} \right)} \right],$$ (2)

where f pulse (t) is the frequency of the laser intensity modulation, δf is the excursion of the dither, f m is the dither frequency and sgn is the sign function. The information of the magneto-optical resonance is therefore contained in the amplitude of the alternating signal which oscillates at f m . When f step increases and approaches the magneto-optical resonance, a dip (or peak) occurs depending on the polarity of the reference signal used for demodulation. The opposite situation occurs when the intensity-modulation frequency exceeds the Larmor frequency along the sweep. Therefore, demodulation produces a peak and a dip separated from each other by 2δf and centered at f Larmor . The excursion was varied from δf = 8–45 kHz to find the optimal separation between demodulated peaks, and the dither frequency was fixed at f m = 150 Hz to suppress scintillation noise.

Because some of the sodium atoms decay into the dark F = 1 ground state14, a fraction of the laser power (12%) was detuned by +1.713 GHz in order to maximize the number of available atoms by pumping them back into the F = 2 ground state via the F′ = 2 excited state.

The duty cycle of the laser intensity modulation was varied from 10 to 30%, as a compromise between high return flux and effective optical pumping. Laser polarization was kept circular for all runs in order to prepare the required orientation of the atomic spins along the laser-beam direction. The laser beam pointed in a direction at which the magnetic field vector in the mesosphere was approximately perpendicular to the laser-beam axis, which gives the highest contrast for the magneto-optical resonance. According to the World Magnetic Model (WMM2015)15, the declination and inclination of the magnetic field at La Palma are 5.7° West and 39.1° downwards, respectively. Therefore, observations were carried out at an elevation of about 51° in the northern direction. Nevertheless, pointing at higher elevation up to 75° was also explored in order to reduce the airmass contribution to scintillation and the magnetic field uncertainty due to a shorter sodium layer path along the laser beam. From the WMM2015, the estimated magnetic field strength at 92 km altitude is 0.3735(15) G, corresponding to a predicted Larmor frequency of ~261 kHz.

The duration of each run depended on the frequency range of the sweep and the integration time for each step. About 10 minutes were necessary to perform a sweep of ±75 kHz around the Larmor frequency. During five nights of observations from July 2nd to July 6th 2017, there were 51 successful runs. Laser power, duty cycle and excursion parameters were modified from run to run to investigate their effects on the magneto-optical resonance. The average atmospheric seeing was 0.7 arcsec measured at zenith and at 500 nm, as reported by a seeing Differential Image Motion Monitor (DIMM) collocated at the observatory. Data from the seeing monitor are available online from the website of the Isaac Newton Group of Telescopes (ING)16.

Physical-optics modeling of the mesospheric spot size under these conditions gives an instantaneous full-width-at-half-maximum (FWHM) beam diamater of D FWHM = 36 cm (0.8 arcsec) for a 30-cm launch telescope at an elevation angle of θ EL = 60°, and average mesospheric irradiance of \(I_{{\mathrm{avg}}}^{{\mathrm{meso}}} = 15\) W m−2 for 2-W CW output power (because of the duty cycle and finite AOM efficiency, 10–20% of the average laser power was delivered to the sky). The spot size in the mesosphere was estimated from a long-exposure image taken with the receiver CMOS camera to be 3.1 arcsec (Fig. 2), however, this estimate is subject to the effects of double-pass laser propagation through the atmosphere, beam-wander, and focusing error of the receiver, each of which contribute to broaden the apparent fluorescent spot beyond the instantaneous spot size. Since the spin-precession dynamics occurs on time scales of microseconds, we calculate the irradiance in the mesosphere using the instantaneous beam size obtained from physical-optics17.

Fig. 2 Fluorescence of mesospheric sodium. A five-second-exposure raw image of the sodium fluorescence spot in the mesosphere along with the star HIP113889 obtained with the CMOS camera of the receiver telescope. The estimated long-term spot size is 3.1 arcsec, which comprises broadening due to atmospheric propagation and focusing error of the receiver telescope. Rayleigh scattering from the laser propagation in lower layers of the atmosphere is visible in the bottom-right corner of the image Full size image

Magneto-optical resonances

Figure 3 shows three typical demodulated signals obtained with an online differential counter (Fig. 3a), an offline ratio counter (Fig. 3b), and a lock-in amplifier (Fig. 3c). The online counter reported the real-time difference in the photon counts between two half-periods of the dither signal, averaged over the time of each frequency step (2–3 s). The averaged maximum count difference per dither period of 6.7 ms (150 Hz) was only about seven photon counts, when the frequency reached the Larmor frequency. Therefore, the maximum averaged difference between off-resonance and on-resonance is about 1000 counts s−1 as shown in Fig. 3a. A higher dither frequency would have rejected scintillation noise better, at the cost of fewer photon counts per dither period. The digitizer recorded all photon counts and the ratio between alternating dither sub-periods was calculated. During post-processing, the phase of the square-wave dither signal could be freely adjusted. This is in contrast to the case of the online counter, where a wrong input phase could suppress the signal without the possibility of recovering it in post-processing. The enhancement in fluorescence of the excited sodium atoms when modulating in resonance with the Larmor precession (referred to as contrast) was measured as 18% above the photon flux out of resonance as shown in Fig. 3b. In addition, the lock-in amplifier demodulated the incoming signal into phase and quadrature components, calculating in real time the time-evolution of the resonance, useful for tracking slowly varying magnetic signals. A time constant of 300 ms was used for all measurements with lock-in amplifier.

Fig. 3 Magneto-optical resonances. The resonances were obtained by sweeping the frequency of the intensity-modulated laser beam with three concurrent data acquisition methods. a Online differential counter for a modulation duty cycle of 20% and \(I_{{\mathrm{avg}}}^{{\mathrm{meso}}} = 13\) W m−2. The Larmor frequency lies in the center between the peaks, which are separated by twice the dither excursion δf = 20.2 kHz. b Ratio of the photon counts per dither period averaged over 2 s. The modulation duty cycle was 30%, excursion δf = 30.8 kHz and calculated mesospheric irradiance \(I_{{\mathrm{avg}}}^{{\mathrm{meso}}} = 33\) W m−2. c Lock-in amplifier with time constant of 300 ms, modulation duty cycle 20%, excursion δf = 30.8 kHz, and calculated mesospheric irradiance \(I_{{\mathrm{avg}}}^{{\mathrm{meso}}} = 17\) W m−2. For all resonances, a double Lorentzian fit shows a broad and a narrow width of ~30 and 2 kHz, respectively, consistent with two relaxation mechanisms due to velocity-changing collisions (fast) and spin-exchange collisions (slow) of sodium with N 2 and O 2 molecules. The residuals of the fits are shown below each resonance and obey a normal distribution according to the Gaussian fit of the residuals histograms Full size image

The demodulated signals, consisting of a positive and a negative peak, were fit with superimposed Lorentzians (Fig. 3), following the outcome of a numerical model which is discussed below. The Larmor frequency was estimated as the mid-point between the two peaks. The residuals from the lock-in amplifier signal display small deviations from the fit that may be attributed to slow altitude displacements of the sodium layer centroid during the sweep. Upward displacement of the sodium centroid toward a weaker magnetic field region produces a shift of the magnetic resonance toward lower frequencies, resulting in asymmetries of the observed resonance.

The measured Larmor frequencies from 51 runs are plotted in Fig. 4. The average Larmor frequency was found to be 260.4(1) kHz, representing a geomagnetic field of 0.3720(1) G according to Eq. (1). The WMM2015 prediction for the magnetic field at 92 km altitude is 0.3735(15) G, giving a difference of <0.5% between the model and our observations. Since the magneto-optical signal comprises the contribution from all sodium atoms weighted by their density distribution along the laser interrogated column in the mesosphere, the measured Larmor frequency is most strongly representative of the geomagnetic field at the sodium centroid position. Indeed, due to magnetic field gradients in the vertical direction H in the mesosphere of dB/dH = −1.85 × 10−4 G km−115, equivalent to a Larmor frequency gradient of df Larmor /dH = −0.129 kHz km−1, the position of the Larmor frequency in the magneto-optical resonance could lie at any point within the light-red band shown in Fig. 4, depending on the position of the sodium centroid at the time of the observation.

Fig. 4 Measured Larmor frequency from 51 runs. The red dashed line is the median of all observations. The horizontal light-red band represents the predicted magnetic field between 85 and 100 km altitude according to the WMM2015 magnetic model15. Error bars are the standard error of the estimate of f Larmor Full size image

In addition, spatially separated sodium density peaks (sporadic sodium layers)18 broaden the magneto-optical resonance as a result of atomic spins precessing at different Larmor frequencies due to magnetic field gradients within the sodium layer. Sporadic sodium layers in the mesosphere at La Palma have been detected on average once per night with lifetime from 30 s to several hours19, which makes our technique susceptible to this effect. The spatial accuracy of the magnetic-field measurements could be improved if the vertical sodium profile were independently known, for example, from simultaneous lidar (light detection and ranging) measurements. Because of the absence of such profiles during the present experiment, there is an intrinsic uncertainty in the altitude of the magnetic-field measurements.

Magnetometry

To measure the absolute magnetic field in the mesosphere, a full scan of the magneto-optical resonance was performed so that the Larmor frequency could be determined. If it is desired to measure fluctuations in the magnetic field, the magnetometer can operate with an intensity-modulation frequency fixed at the maximum-sensitivity point along the resonance curve. In this case, magnetic-field variations are reflected in changes of the amplitude of the demodulated signal or in changes of the frequency feedback signal needed to keep the magnetometer locked at a certain point of the resonance curve.

In order to estimate the accuracy of the Larmor-frequency measurements and magnetic-field fluctuations, we use data from a single run with δf = 8 kHz and f m = 150 Hz, as shown in Fig. 5a. The Larmor frequency for this run is 260.12 kHz, corresponding to 0.37170 G, with a standard error for f Larmor of 0.04 kHz (or 0.05 mG). The existence of the narrow peaks in the magneto-optical resonances found in this experiment strongly reduce the uncertainty in the estimate of the Larmor frequency. The highest magnetic-field sensitivity can be found at the minimum of the differentiated fit function of the resonance in Fig. 5b. At the middle point between the two peaks of the reference magneto-optical resonance shown in Fig. 5a, the calculated accuracy is 1.24 mG Hz−1/2, similar to that reported in ref. 12 The highest sensitivity is provided by the slope of the narrower of the two superimposed Lorentzians, where an accuracy of 0.28 mG Hz−1/2 can be reached.

Fig. 5 Estimate of magnetometry accuracy. a A resonance acquired with the lock-in amplifier in good atmospheric conditions (seeing 0.7 arcsec) with δf = 8 kHz. b Magnetometry accuracy level from the derivative of the resonance fit function. The maximum sensitivity of 0.28 mG Hz−1/2 is achieved at the steepest points of the resonance Full size image

In this experiment, a median value of about 12 × 103 counts s−1 was measured during frequency scans, which corresponds to shot noise near 100 counts s−1 or ~1%. The estimate of the noise contributions from the noise analysis (Methods Section and Supplementary Fig. 2) shows a noise floor near 10−2 Hz−1/2, indicating a shot-noise-limited measurement. Random fluctuations of the centroid and the sodium layer profile are strong contributors to the uncertainty in the estimation of the geomagnetic field at a given point in the sodium layer.