Femtotesla Direct Magnetic Gradiometer Using a Single Multipass Cell

We describe a direct gradiometer using optical pumping with opposite circular polarization in two ${}^{87}\mathrm{Rb}$ atomic ensembles within a single multipass cell. A far-detuned probe laser undergoes a near-zero paramagnetic Faraday rotation due to the intrinsic subtraction of two contributions exceeding 3.5 rad from the highly polarized ensembles. We develop analysis methods for the direct gradiometer signal and measure a gradiometer sensitivity of 10.1 $\mathrm{fT}/\mathrm{cm}\sqrt{\mathrm{Hz}}$. We also demonstrate that our multipass design, in addition to increasing the optical depth, provides a fundamental advantage due to the significantly reduced effect of atomic diffusion on the spin-noise time-correlation, in excellent agreement with the theoretical estimate.

Figure 1

(a) V-shaped cell. Image of the sensor including the probe input focuser (F) and polarizer (P), anodically bonded spherical front mirror (FM) and back mirrors (BMs), a $18\times 20\times 30{\mathrm{mm}}^3$ Pyrex cell enclosing both the back mirrors and the atomic vapor, and an output collimation lens (L). (b) Multipass geometry. IR image (camera not shown) of the front mirror with probe-beam spots after $60$ passes through atomic ensembles before exiting the cavity. (c) Layout. Cross-section view of the V-shaped cell within a magnetic shielding with the Pyrex cell enclosed by a boron nitride oven. A magnetic field gradient is applied in the $y$ direction, while the probe beam (input fiber coupled) and the pump beams (free space) propagate in the $x$ and $z$ directions, respectively, as shown in (d). (d) Full experimental sketch. DAQ, data-acquisition card; HWP, half-wave plate; PBS, polarizing beam splitter. (e) Measurement sequence. Optically induced atomic orientation for top and bottom spins, angle tilt by $\pi /2$ pulse, and free Larmor precession in the transverse plane.

Figure 2

Experimental signals. Top: Individual (blue) and differential (red) rotation signals at field $B_z=26\mu \mathrm{T}$, $400\mu \mathrm{W}$ probe power, and $120{}^{\circ }\mathrm{C}$. The inset shows an enlargement of the differential signal with direct cancellation at near-zero gradient. Bottom: Individual signals over a shorter timescale showing a $\pi$ phase difference between the $V_{\mathrm{top}}$ (solid blue line) and $V_{\mathrm{bot}}$ (dashed red line) contributions when the atomic ensembles are polarized with opposite circular polarization. The signals undergo multiple zero crossings over a Larmor period of spin precession (dot-dashed black line).

Figure 3

Top: Finite-gradient gradiometer signal. Gradiometer signal at applied gradients of (from top to bottom) 0.8, 0.5, 0.3, and 0.1 nT/cm. The inset shows the signal in the absence of optical pumping, showing fundamental noise and residual spin excitations. Bottom: Calibration. Experimental (blue points) frequency difference and nominal gradient slope (red line) as a function of applied-magnetic-field difference. The inset shows the frequency-difference scatter over multiple measurements for polarized (blue dots) and unpolarized (black squares) atoms.

Figure 4

Top: Spin-noise spectrum. Experimental spin-noise spectrum (blue points) centered at Larmor frequency ${\nu }_L=96$ kHz and a simple Lorentzian fit (red line) for an unpolarized atomic ensemble under thermal equilibrium at $120{}^{\circ }\mathrm{C}$. Prediction for the spin-noise spectrum including effects of diffusion without free parameters (dashed green line) The inset shows the free-induction-decay signal for low initial polarization, where spin-exchange collisions limit the transverse relaxation time. Bottom: Comparison of diffusion correlation functions. Calculated diffusion correlation function for the V-shaped multipass cell (red line) in comparison with the diffusion correlation function for the cylindrical-mirror multipass cavity [27] used in Ref. [16].