Amplitude-modulated indirect pumping of spin orientation in low-density cesium vapor

A recently demonstrated technique of continuous indirect pumping enables a high level of atomic spin polarization to be generated in thermal alkali-metal vapors, without compromising the coherence lifetime through power broadening from the pump laser. The indirect pumping process combines optical excitation and spin-exchange collisions. Here we describe the pumping process and the role of spin-exchange collisions for the case of amplitude-modulated optical excitation. We demonstrate that effective spin-exchange decoherence is modified by the measurement geometry and dynamics. Decoherence changes are studied through magneto-optical-rotation signals. The studies presented here are particularly important for optimizing the performance of an atomic magnetometer operating in the quantum nondemolition configuration in a nonzero-magnetic-field environment.

Figure 1

(a) Cesium $6{}^2{S}_{1/2}\to 6{}^2{P}_{3/2}$ transition ($D2$ line) energy structure. The arrows represent the frequency of the laser beams used in the experiments (solid, pump, and dotted, probe). (b) Geometry of the experiment. A circularly polarized light beam propagating along the $z$ axis optically pumps the sample of Cs atoms. A linearly polarized probe beam propagates along the $y$ direction. The polarization of the probe light is parallel to the $z$ direction. The polarization state of the light after traversing the atomic sample is measured with a balanced polarimeter. The weak field $B$ is oriented in the $xz$ plane.

Figure 2

Evolution of the atomic collective spin state $F$ (red arrow) in the presence of a static magnetic field $B$ (defining the quantization axis, green arrow). (a) Configuration of rf spectroscopy experiment. A circularly polarized laser beam pumps atoms along the direction of the static magnetic field $(z$ axis). A weak rf magnetic field generates a spin component orthogonal to the magnetic field (atomic ground-state coherence), which leads to precession of the collective spin vector around the $z$ axis. (b) A circularly polarized laser beam pumps atoms along the $z$ axis. The presence of the magnetic field directed in the $xz$ plane results in the precession of the collective spin vector. (c) Precession of the atomic spin in a magnetic field along the $x$ axis.

Figure 3

Width of rf resonance observed for the $F=4$ manifold versus pump laser power (static magnetic field 1.86 $\mu \mathrm{T}$). Experimental signals were measured for 10 $\mu \mathrm{W}$ probe laser power and $0.8\times {10}^{11}{\mathrm{cm}}^{-3}$ atomic density. The black line marks the value of $\mathrm{\Delta }{\omega }_0$, i.e., the minimum value of the linewidth recorded in rf spectroscopy.

Figure 4

The magneto-optical-rotation signal recorded as a function of the frequency of pump laser amplitude modulation (solid black line). The fit is marked by the dotted (red) line while the two individual Lorentzian components of the fit are shown with the dashed (blue) lines. The experimental signal was measured for 100 $\mu \mathrm{W}$ probe laser power, 2900 $\mu \mathrm{W}$ pump laser power amplitude modulated with an $8\%$ duty cycle, and $0.3\times {10}^{11}{\mathrm{cm}}^{-3}$ atomic density.

Figure 5

Dependence of the amplitudes (a) and widths (b) of spectral profiles for amplitude-modulated indirect pumping on the pump beam power for two values of the angle between the direction of the magnetic field and $z$ axis (${10}^{\circ }$, blue dots; ${75}^{\circ }$, red diamonds). Experimental signals were measured for 10 $\mu \mathrm{W}$ probe laser power and $0.8\times {10}^{11}{\mathrm{cm}}^{-3}$ atomic density.

Figure 6

Dependence of the amplitudes (a) and widths (b) of the spectral profiles (black dots) for amplitude-modulated indirect pumping on the angle between the magnetic field and the pump beam propagation direction ($z$ axis). The amplitude of the magnetic field was kept constant over the course of this measurement to give a Larmor frequency of 1 kHz. The dashed red curve in (a) shows modifications of the signal amplitude caused by the change of character of the optical excitation, while blue triangles show the contribution from line narrowing. The dashed red line in (b) shows the changes to the linewidth resulting from geometrical considerations, while the solid red line represents the value of $\mathrm{\Delta }{\omega }_0$, i.e., the minimum value recorded in rf spectroscopy at the same atomic density. Experimental signals were measured for a 1500 $\mu \mathrm{W}$ pump laser power amplitude modulated with $8\%$ duty cycle, 10 $\mu \mathrm{W}$ probe laser power, and $0.33\times {10}^{11}{\mathrm{cm}}^{-3}$ atomic density.

Figure 7

Dependence of the amplitudes (a) and widths (b) of spectral profiles for amplitude-modulated indirect pumping on the amplitude of the magnetic field (in terms of the Larmor precession frequency) directed along the $x$ axis. Experimental signals were measured for a 1500 $\mu \mathrm{W}$ pump laser power amplitude modulated with a $12\%$ duty cycle, 10 $\mu \mathrm{W}$ probe laser power, and $0.33\times {10}^{11}{\mathrm{cm}}^{-3}$ (red dots) and $1.2\times {10}^{11}{\mathrm{cm}}^{-3}$ (blue diamonds) atomic densities. Solid red and dashed blue lines (b) represent the value of $\mathrm{\Delta }{\omega }_0$, i.e., the minimum value recorded in rf spectroscopy at the same atomic density.

Figure 8

Two phases in the course of a single period of the atomic spin precession: Optical excitation, marked by two square pulses, creates the atomic coherence (the amplitude is marked with a red solid line) and the atomic coherence relaxation in the absence of the pump light.