Nonlinear spectroscopy of high-spin fluctuations

We investigate theoretically and experimentally fluctuations of high spin ($F>\frac{1}{2}$) beyond the linear response regime and demonstrate dramatic modifications of the spin noise spectra in the high power density probe field. Several effects related to an interplay of high spin and perturbation are predicted theoretically and revealed experimentally, including strong sensitivity of the spin noise spectra to the mutual orientation of the probe polarization plane and magnetic field direction, appearance of high harmonics of the Larmor frequency in the spin noise, and the fine structure of the Larmor peaks. We demonstrate the ability of spin noise spectroscopy to access the nonlinear effects related to the renormalization of the spin states by strong electromagnetic fields.

Figure 1

(a) Energy spectrum of the dressed Hamiltonian (2) for $F=3$ at a fixed magnetic field for various probe beam intensities and $\theta =0$. Arrows indicate transition frequencies. (b) Transition frequencies ${\mathrm{\Omega }}_{M,M+1}$ calculated after Eq. (11) (black dashed lines) and by numerical diagonalization of the Hamiltonian (2) (red solid lines) at $\mathcal{C}|E_0{|}^2/{\omega }_L=1/20$. The arrow indicates the magic angle ${\theta }_m$.

Figure 2

Noise spectra of Faraday rotation, ${\mathcal{N}}_r\left(\nu \right)$, and ellipticity, ${\mathcal{N}}_e\left(\nu \right)$, calculated using Eqs. (9) and (10). Panels (a), (b), and (c) correspond to $\theta =0, \pi /4$, and $\pi /2$, respectively. The parameters of calculation are ${\omega }_L=20$ MHz, $\mathcal{C}|E_0{|}^2/{\omega }_L=1/20$, and $\mathrm{\Gamma }=0.4$ MHz.

Figure 3

Calculated noise spectra of Faraday rotation, ${\mathcal{N}}_r\left(\nu \right)$ (a), and ellipticity, ${\mathcal{N}}_e\left(\nu \right)$ (b), as a function of probe azimuth $\theta$ and frequency $\nu$. The transition frequencies calculated after Eq. (11) are shown as white dotted lines, which are made transparent in the vicinity of the magic angle to not hinder the spectral features. The parameters of calculation are ${\omega }_L=20$ MHz, $\mathcal{C}|E_0{|}^2/{\omega }_L=1/20$, and $\mathrm{\Gamma }=0.4$ MHz.

Figure 4

Energy-level diagram of a cesium atom in the range of the D2 line. The spectral position of the probe light, which was slightly detuned from the center of the D2 optical transition, is shown schematically.

Figure 5

Azimuthal dependence of the ellipticity-noise spectra of Cs atoms, under conditions of resonant probing: experimental data (a) and model (b). The experimental conditions and the parameters of calculation are shown at the top of panels (a) and (b), respectively.