Spin-noise spectroscopy under resonant optical probing conditions: Coherent and nonlinear effects

Highly sensitive Faraday rotation spectroscopy is used to measure the fluctuating magnetization noise of noninteracting rubidium atoms under resonant and nonresonant optical probing conditions. The spin-noise frequency spectra, in conjunction with the probe light detuning with respect to the $D_2$ transition, reveal clear signatures of coherent coupling of the participating electronic levels. The results are explained by extended Bloch equations, including homogeneous and inhomogeneous broadening mechanisms. Our measurements further indicate that spin noise originating from excited states is governed at high intensities by collective effects.

Figure 1

(a) $D_2$ transition (${}^2{S}_{1/2}\to {{}^{2}P}_{3/2}$) for the case of ${}^{87}$Rb. The bold arrow indicates the transition that corresponds to zero detuning in the following. Neighboring ground and excited states are coherently coupled. (b) Experimental spin noise setup. A liquid crystal retarder (LCR) switches the polarization analysis between sensitivity on linear or circular birefringence, respectively (details are found in the text).

Figure 2

Off-resonant spin-noise difference spectrum measured at $1.8\mathrm{mT}$ and $45\mu \mathrm{T}$ (terrestrial magnetic field), respectively.

Figure 3

Spin-noise power density in color coding as a function of laser detuning $\Delta$ (abscissa) and noise frequency $\nu$ (ordinate) for cell A (pure ${}^{87}$Rb). The black (upper) curve shows the absorption spectrum, and the red (lower) curve shows the integrated noise power, neglecting spin noise at noise frequencies centered at $0\mathrm{MHz}$. Zero detuning corresponds to the $F=2\to F^{\prime }=3$ transition of ${}^{87}$Rb. (a), (b) Experimental data with probe laser intensities $I_l=1.8$ and $I_l=14.1\mathrm{W}/{\mathrm{cm}}^2$. (c), (d) Calculations corresponding to the experimental data in (a) and (b), respectively. All graphs depict spin-noise difference spectra.

Figure 4

(a) Calculated and measured absorption spectra for cell B (natural rubidium). (b) Measured spin noise spectra of cell B with a probe laser intensity of $I_l=7.8\mathrm{W}/{\mathrm{cm}}^2$ for different laser frequencies. At low detuning, spin noise of the excited $5{}^2{P}_{3/2}$ states ($g_F=2/3$) becomes significant. The fit curves with the three calculated Larmor frequencies for $g_F=1/3$, $1/2$, and $2/3$ are shown as solid lines. (c) Spin noise spectra calculated by the extended Bloch model corresponding to the experimental data shown in (b).