We have developed a novel atomic magnetometer that uses differential detection of the spatially diverging components of a light field to monitor the Larmor precession frequency of atoms in a thermal vapor. The design is implemented in compact form with a micromachined alkali vapor cell and a naturally divergent light field emitted by a vertical-cavity surface-emitting laser. Operating the magnetometer in differential mode cancels common-mode noise and improves the sensitivity by a factor of 26 over that of single-channel operation. The design is well suited to wafer-level mass production of chip-scale devices.
The experimental setup is shown in Fig. 1A. At the heart of the apparatus is the miniature physics shown in the inset of Fig. 1A. The cell containing 87Rb vapor and a buffer-gas mixture is microfabricated by etching a 1 mm2 hole in a 1 mm thick silicon wafer and sealed by anodically bonding glass wafers to either side. The cell is illuminated by a single VCSEL beam with an output power of 300 μW. The laser is temperature tuned to the center of the collisionally broadened D1 absorption line (795 nm). The beam is uncollimated with a half-intensity, half-angle divergence of 3.8°. The strong central part of the beam is used for optically pumping the atoms, while the diverging wings act as four probe beams, each of which is monitored by a 0.25 mm2 segment of a quadrant photodiode mounted immediately above the cell. By using just a single laser beam to both pump and multiply probe the atoms, without collimating optics, beamsplitters, or mirrors, we are able to demonstrate a core physics assembly for the differential magnetometer with a volume of less than 1 cm3.
Figure 1: [A] Diverging beam magnetometer. (a) Single-layer magnetic shield. (b) Three-dimensional Helmholtz coils. [(d)] Heating coils for laser and cell “hot fingers.” (e) VCSEL baseplate. (f) VCSEL with quarter wave plate on top. (g) 87Rb cell. (h) Quadrant photodiode. [B] A schematic diagram of the operation of the differential magnetometer. The average direction of the pump beam defines the z axis. B0 is the field to be measured, lying at an angle θ to the z axis. θ = 0 for optimal differential signal.
Operation of the differential magnetometer is shown in Fig. 1B. The aim is to measure the Larmor frequency associated with the magnetic field B0 and hence the magnitude of B0. The strong, central part of the circularly polarized laser beam is primarily responsible for optically pumping 87Rb atoms, creating a net atomic spin in the z direction. Spin precession around B0 is coherently driven by the oscillating field Bx = B1∙cos ωt, where B1 = 0.19 μT and ω = 2π×5 kHz. The magnitude of B0 is scanned at 37.4 nT/ms. A resonant response occurs when the frequency of the Larmor precession around B0 matches the driving frequency ω, creating a spin precession of large amplitude. The component of this precessing spin that lies along the ith probe beam determines the absorption of the beam and hence the light intensity reaching the ith photodiode. Passing the output of the ith photodiode through a lock-in amplifier referenced to the driving field Bx enables us to extract the phase and amplitude of the oscillatory part of Mi.
While common-mode noise on each photodiode has the same sign and is subtracted, the signals have opposite sign and hence are added, further improving the signal-to-noise ratio of the differential magnetometer. The differential signal is shown in Fig. 2c and is approximately twice the size of the individual photodiode signals. It has a sensitivity of 28 pT/_Hz at 100 Hz, improving on the single-channel magnetometer by a factor of 26. It is within a factor of 2 of the measured technical and fundamental noise floor of the instrument, which is due to technical electrical noise, Johnson noise, and photon shot noise in roughly equal amounts.
Figure 2: Output of the lock-in amplifier, referenced to the 5 kHz driving field as B0 is slowly scanned with t = 0. (a) photodiode 1, (b) photodiode 2, and (c) differential signal. A doubling of the signal size and a clear reduction of the noise level is evident in the differential signal.
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