Low-noise high-density alkali-metal scalar magnetometer

We present an experimental and theoretical study of a scalar atomic magnetometer using an oscillating field-driven Zeeman resonance in a high-density optically pumped potassium vapor. We describe an experimental implementation of an atomic gradiometer with a noise level below $10\text{fT}{\text{Hz}}^{-1/2}$, fractional field sensitivity below ${10}^{-9}{\text{Hz}}^{-1/2}$, and an active measurement volume of about $1.5{\text{cm}}^3$. We show that the fundamental field sensitivity of a scalar magnetometer is determined by the rate of alkali-metal spin-exchange collisions even though the resonance linewidth can be made much smaller than the spin-exchange rate by pumping most atoms into a stretched spin state.

Figure 1

Schematic of the experimental apparatus. The cell ($3\times 3\times 4{\text{cm}}^3$ with the larger dimension perpendicular to lasers) is heated inside a boron nitride oven and placed in a glass vacuum enclosure pumped out to 0.5 Torr. Coils inside six-layer magnetic shields allow application of magnetic fields and gradients. The gradiometer measurement is obtained by imaging the probe beam onto two-element photodiodes. The signals of the two balanced polarimeters are subtracted at the lock-in.

Figure 2

Absorptive (open symbols) and dispersive (closed symbols) components of the magnetic-resonance polarization rotation signal at $1\mu \text{T}$ (squares), $10\mu \text{T}$ (triangles), and $26\mu \text{T}$ (circles). Solid lines show Lorentzian fits to the data. These data were recorded at the same time and under the same experimental conditions as the high-sensitivity magnetometer measurements.

Figure 3

Noise spectra for (a) $1\mu \text{T}$ and (b) $10\mu \text{T}$. Shown are single-channel spectra (black line with crosses), two-channel difference (gradiometer) spectra (black solid line), and the measured electronic and optical noise (gray solid line) obtained by blocking the pump beam. The dashed black line marks the $14\text{fT}/{\text{Hz}}^{1/2}$ level. Magnetic field noise increases at higher frequencies due to correction for the finite bandwidth of the magnetometer.

Figure 4

The linewidths of Lorentzian fits to the experimental data for absorption (solid points) and dispersion (open points) components of the magnetic resonance in K vapor at $140°\text{C}$. The dotted line is the prediction for rf broadening of the linewidth from Bloch equations with constant $T_1$ and $T_2$, the solid and dashed lines are results of Lorentzian fits to absorption and dispersion line shapes obtained using modified BE with variable $T_2$ discussed in the text. Here $R_{se}=5100{\text{s}}^{-1}$ and $R_{sd}=24{\text{s}}^{-1}$ are fixed from independent measurements, while $R_{op}=840{\text{s}}^{-1}$ is adjusted to fit the measured linewidth at low rf amplitude.

Figure 5

Comparison of transverse polarization components $\left(P_i,P_j\right)$ using full numerical density-matrix evolution (solid points—absorption, open points—dispersion) and modified BE (solid line—absorption, dashed line—dispersion) for $R_{se}/R_{sd}={10}^4$, $R_{op}/R_{sd}=200$, $\gamma B_1/R_{sd}=100$. Lorentzian line shapes are shown with dotted lines for comparison.

Figure 6

Slope of the dispersive part of the resonance curve, given as polarization per angular frequency $d{P}_i/d\omega$. Experiment: Open circles—$R_{op}=220{\text{s}}^{-1}$, open triangles—$R_{op}=625{\text{s}}^{-1}$, solid squares—$R_{op}=1450{\text{s}}^{-1}$. Theory: dash-dotted line—$R_{op}=220{\text{s}}^{-1}$, solid line—$R_{op}=625{\text{s}}^{-1}$, dashed line—$R_{op}=1450{\text{s}}^{-1}$. Temperature $T=140°\text{C}$, $R_{sd}=24{\text{s}}^{-1}$, $R_{se}={5100}^{-1}$.

Figure 7

Comparison of experimental (circles) and theoretical (lines) resonance line shapes. $T=140°\text{C}$, $R_{sd}=24{\text{s}}^{-1}$, $R_{se}=5100{\text{s}}^{-1}$, $R_{op}=625{\text{s}}^{-1}$, $B_1=20\text{nT}$. The model also includes a correction for the polarization-dependent absorption of the pump beam.