Sensitivity of double-resonance alignment magnetometers

We present an experimental study of the intrinsic magnetometric sensitivity of an optical or rf-frequency double-resonance magnetometer in which linearly polarized laser light is used in the optical pumping and detection processes. We show that a semiempirical model of the magnetometer can be used to describe the magnetic resonance spectra. Then, we present an efficient method to predict the optimum operating point of the magnetometer, i.e., the light power and rf Rabi frequency providing maximum magnetometric sensitivity. Finally, we apply the method to investigate the evolution of the optimum operating point with temperature. The method is very efficient to determine relaxation rates and thus allowed us to determine the three collisional disalignment cross sections for the components of the alignment tensor. Both first and second harmonic signals from the magnetometer are considered and compared.

Figure 1

Double-resonance magnetometer geometry using linearly polarized light. Here, $\mathit{k}$ is the direction of the linearly polarized laser beam. The rf field ${\mathit{B}}_1$ (shown here at $t=0$) rotates in a plane perpendicular to the static field ${\mathit{B}}_0$. The linear polarization vector $\mathit{ϵ}$ makes an angle $\gamma$ with the static field ${\mathit{B}}_0$, and the phase of ${\mathit{B}}_1$ is characterized by $\alpha$.

Figure 2

Experimental setup: A cell containing Cs vapor was mounted inside a three-axis Helmholtz coil array all placed inside a three-layer $\mu$-metal shield. The polarization angle $\gamma$, measured with respect to the offset field ${\mathit{B}}_0$, was set by a linear polarizer followed by a half-wave plate $\left(\lambda ∕2\right)$ located outside the shield for ease of access. The laser light traversed the cell and was converted to a current by a nonmagnetic photodiode (PD). All details can be found in the text.

Figure 3

(Color online) Measurements (circles) of the in-phase and quadrature magnetic resonance signals detected as amplitude modulations of the transmitted light power. (a) First harmonic signals. (b) Second harmonic signals. The statistical uncertainty on each data point is represented by the symbol size. The solid lines are fits of the theoretical line shapes given by Eqs. (3a, 5b).

Figure 4

(a) First harmonic DRAM signal amplitude as a function of laser power. (b) Relaxation rates as a function of laser power. Points are measured values, extracted from the fit of the DRAM model [Eqs. (3a, 3b, 3c, 3d)] to the experimental magnetic resonance spectra. The solid lines are fits of the extended DRAM model [Eqs. (11, 12a, 12b, 12c)] to the experimental data. The data were measured at room temperature from a first harmonic DRAM with $\gamma =25.5°$ and ${\omega }_1=2\pi \times 8.3\text{Hz}$.

Figure 5

(a) Second harmonic DRAM signal amplitude as a function of laser power. (b) Relaxation rates as a function of laser power. Points are measured values extracted from the fit of the DRAM model [Eqs. (3a, 3b, 3c, 3d)] to the experimental magnetic resonance spectra. The solid lines are fits of the extended DRAM model [Eqs. (11, 12a, 12b, 12c)] to the experimental data. The data were measured at room temperature from a second harmonic DRAM with $\gamma =90°$ and ${\omega }_1=2\pi \times 8.3\text{Hz}$.

Figure 6

First harmonic DRAM with $\gamma =25.5°$. The upper graph is a contour plot of the NEM as a function of $P_L$ and ${\omega }_1∕2\pi$. The NEM values were calculated using the method developed in Sec. 6A. The cross indicates the position where the NEM is minimum (see Table ). The contour lines start at $40\text{fT}∕\sqrt{\text{Hz}}$ and are spaced by $10\text{fT}∕\sqrt{\text{Hz}}$. The dots indicate the points in parameter space where the NEM has been measured; cf. Sec. 6B. The distribution of the relative difference between calculated and measured values is shown in the lower graph.

Figure 7

Second harmonic DRAM with $\gamma =90°$. The upper graph is a contour plot of the NEM as a function of $P_L$ and ${\omega }_1∕2\pi$. The NEM values were calculated using the method developed in Sec. 6A. The cross indicates the position where the NEM is minimum (see Table ). The contour lines start at $40\text{fT}∕\sqrt{\text{Hz}}$ and are spaced by $10\text{fT}∕\sqrt{\text{Hz}}$. The dots indicate the points in parameter space where the NEM has been measured; cf. Sec. 6B. The distribution of the relative difference between calculated and measured values is shown in the lower graph.

Figure 8

Relaxation rates as a function of laser power, measured at two different temperatures. The empty symbols (◻, ▵, ◇) represent ${\Gamma }_0,{\Gamma }_1,{\Gamma }_2$ measured at $T=25°\text{C}$. The filled symbols (∎, ▴, ◆) represent ${\Gamma }_0,{\Gamma }_1,{\Gamma }_2$ measured at $T=38°\text{C}$. The solid and dashed lines are a fit of the extended DRAM model [Eqs. (12a, 12b, 12c)] to the experimental data. (a) First harmonic DRAM with $\gamma =25.5°$. (b) Second harmonic DRAM with $\gamma =90°$.

Figure 9

Temperature evolution of the relaxation rates extrapolated to zero laser power. The symbols (∎, ▴, ◆) represent ${\Gamma }_{00},{\Gamma }_{10},{\Gamma }_{20}$. The solid lines are fits of Eq. (16) to the experimental data. (a) First harmonic DRAM with $\gamma =25.5°$. (b) Second harmonic DRAM with $\gamma =90°$.

Figure 10

Evolution of the optimum NEM as a function of temperature. (a) First harmonic DRAM with $\gamma =25.5°$. (b) Second harmonic DRAM with $\gamma =90°$. These graphs were calculated from the measurement of the extended DRAM model parameters.