Experimental study of laser-detected magnetic resonance based on atomic alignment

We present an experimental study of the spectra produced by optical–radio-frequency double resonance in which resonant linearly polarized laser light is used in the optical pumping and detection processes. We show that the experimental spectra obtained for cesium are in excellent agreement with a very general theoretical model developed in our group [Weis, Bison, and Pazgalev, Phys. Rev. A 74, 033401 (2006)] and we investigate the limitations of this model. Finally, the results are discussed in view of their use in the study of relaxation processes in aligned alkali-metal vapors.

Figure 1

Geometry of double resonance spectroscopy involving linearly polarized light. The oscillating field ${\mathit{B}}_1$ rotates in a plane perpendicular to the static field ${\mathit{B}}_0$. The linear polarization vector $\mathbf{ϵ}$ makes an angle $\gamma$ with the static field ${\mathit{B}}_0$, and the phase of ${\mathit{B}}_1$ is characterized by $\alpha$.

Figure 2

Sketch of the experimental setup. A paraffin-coated glass cell containing Cs vapor was placed inside a three-layer mumetal shield. The shield contained Helmholtz coils to produce the static magnetic field ${\mathit{B}}_0$, and radio-frequency coils to produce the rotating magnetic field ${\mathit{B}}_1$. The distributed feedback (DFB) diode laser was stabilized to the $F_g=4\to F_e=3$ transition of the Cs $D_1$ line by means of a dichroic atomic vapor laser lock (DAVLL). A linear polarizer followed by a half wave plate $(\lambda ∕2)$ were used to prepare linearly polarized light at an angle $\gamma$ with respect to ${\mathit{B}}_0$. The transmitted light power after the cell was monitored by a nonmagnetic photodiode (PD) whose signal was amplified by a low-noise transimpedance amplifier and analyzed by a lock-in amplifier. The function generator driving the rf field also served as reference for the lock-in amplifier. The resonance spectra were recorded by a personal computer which controlled the rf frequency scan.

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 smaller than the symbol size. The solid lines (blue) are fits of the theoretical line shapes given by Eqs. (3) with three independent relaxation rates. The dashed lines (red) are fits of the theoretical line shapes given by Eqs. (3) with only one independent relaxation rate $\Gamma \equiv {\Gamma }_0={\Gamma }_1={\Gamma }_2$. The details of the experimental conditions and fit results are in the text.

Figure 4

(Color online) Dispersive component of the magnetic-resonance signal oscillating at frequency $\omega$ measured under the following conditions: the angle between the linear polarization vector and the static field was $\gamma =25°$, the laser light power was $0.1\mu \mathrm{W}$, and the rf field Rabi frequency was ${\omega }_1∕\left(2\pi \right)=4.8\mathrm{Hz}$. Graph (a) (blue) was measured with a rotating rf field and graph (b) (red) with an oscillating rf field. The solid line is a fit of the theoretical line shape to the curve obtained with the rf rotating field. The slight difference in linewidth suggests that the Rabi frequency in the two measurements was not perfectly equal although we increased the amplitude of the oscillating rf field by a factor 2.

Figure 5

(Color online) Angular dependence of the amplitude of the first (blue, solid line) and second (red, dashed line) harmonic signals on the angle $\gamma$ between the light polarization $\mathbf{ϵ}$ and the magnetic offset field ${\mathit{B}}_0$. Each experimental data point is the result of a measurement and fit of the magnetic-resonance spectra as explained in Sec. 4. The measurements were made using a light power of $0.07\mu \mathrm{W}$ and a rf field Rabi frequency of $2.4\mathrm{Hz}$. The lines were found by fitting the $h_{\omega }$ and $h_{2\omega }$ functions given by Eqs. (2) to the experimental data.

Figure 6

Resonance spectra measured with an angle $\gamma =75°$ and for different Rabi frequencies of the rf field: (a) ${\omega }_1∕\left(2\pi \right)=0.95\mathrm{Hz}$, (b) ${\omega }_1∕\left(2\pi \right)=2.4\mathrm{Hz}$, (c) ${\omega }_1∕\left(2\pi \right)=4.8\mathrm{Hz}$. The left column shows in-phase and quadrature components of the first-harmonic signal, and the right column shows in-phase and quadrature components of the second-harmonic signal. For these measurements, the light power was $0.1\mu \mathrm{W}$.

Figure 7

Saturation of the resonant absorptive signals $A_{\omega }$ and $A_{2\omega }$ as a function of the Rabi frequency ${\omega }_1∕\left(2\pi \right)$ of the rf field. (a) On-resonance amplitude of the first-harmonic signal measured for an angle $\gamma =25.5°$. (b) On-resonance amplitude of the second-harmonic signal measured for an angle $\gamma =90°$. For these measurements, the light power was fixed to $0.1\mu \mathrm{W}$. The solid lines are fits of the DRAM theoretical model [Eqs. (6)] to the experimental data.

Figure 8

Global amplitude factor $g_{\omega }{\mathcal{A}}_0$ from Eq. (5) of the first-harmonic resonance signal as a function of the laser power $P_L$ measured for $\gamma =25.5°$. Each experimental data point is the result of a measurement and a fit of the magnetic-resonance spectra as explained in Sec. 4. For these measurements, the Rabi frequency of the rf field was fixed at ${\omega }_1∕\left(2\pi \right)=3.8\mathrm{Hz}$. The solid line is a fit of the function given by Eq. (7) to the experimental data. The dashed lines represent the quadratic parts of the fit function and the linear asymptote to Eq. (7) which has a zero crossing at the saturation power $P_{\omega }^{\mathrm{sat}}=0.67\left(3\right)\mu \mathrm{W}$.

Figure 9

Relaxation rates as a function of the laser power $P_L$ measured for $\gamma =25.5°$. Each triplet $(\Gamma 1,\Gamma 2,\Gamma 3)$ is the result of a measurement and a fit of the magnetic-resonance spectra as explained in Sec. 4, starting from the same experimental data which were used for Fig. 8. The circles represent ${\Gamma }_0∕\left(2\pi \right)$, the squares ${\Gamma }_1∕\left(2\pi \right)$ and the triangles ${\Gamma }_2∕\left(2\pi \right)$. The solid lines are linear fits to the experimental data.