Optical-field-induced dips and splits in nonlinear spectra of selective reflection from high-density atomic vapor

TL;DR

The paper addresses nonlinear selective reflection spectra in high-density rubidium vapor where self-broadening dominates Doppler width, and distinguishes homogeneous versus inhomogeneous broadening using hole-burning and derivative spectroscopy. It employs a pump–probe setup and analyzes $\mathrm{d}R/\mathrm{d}\nu$ to resolve spectral features, interpreting results within the dressed-atomic-states framework. At low to moderate densities the spectra are inhomogeneously broadened with optically saturated dips, while at the highest density a strong pump field produces two symmetric, homogeneously broadened resonances with spacing linked to the generalized Rabi frequency; the relation $\Delta\nu_{\text{SP}} [\text{GHz}] \approx 2.53\sqrt{I_{\text{pump}}[\text{kW cm}^{-2}]}$ captures this behavior. The findings illuminate the transition between broadening regimes and provide a route to study many-body interatomic interactions in dense gases using dressed-state spectroscopy, with potential implications for quantum devices and nanoscale systems.

Abstract

We discuss nonlinear spectra of selective reflection from high-density rubidium atomic vapor, where the self-broadening of the resonant transition $5S_{1/2}-5P_{3/2}$ dominates over the Doppler width. In the experiments, the hole-burning technique with probe and pump lasers is used. The reflection of weak probe beam is investigated at four atomic densities in the range $(1.2\text{--}3.6)\times10^{17}$~cm$^{-3}$ and various pump beam intensities. To enhance the spectral resolution, the frequency derivative $\text{d}R/\text{d}ν$ of the reflection coefficient $R$ is analyzed. Increasing the atomic number density changes the character of self-broadening from inhomogeneous to homogeneous. At the highest density, the strong pump field splits the observed spectra into two homogeneously broadened symmetric resonances. The appearance of the optical-field-induced resonances can be explained within the framework of "dressed atomic states" approach. At lower densities the spectral profiles are inhomogeneously broadened. Spectral profiles of the frequency derivative are separated by optically saturated dips. The width of such dips is a combination of the homogeneous component of self-broadening and intensity-dependent field broadening. Careful study of the transition from inhomogeneous to homogeneous broadening may initiate further development of the theory of interatomic interactions in high density atomic gas media.

Figures (4)

• Figure 1: Optical layout of the setup. Two orthogonally polarized laser beams from pump and probe lasers are combined by polarizing beam splitter (PBS) and focused by lens (L) at internal surface of the cell window. The reflected probe beam is directed by a mirror (M) to a photodiode (PD) through Glan--Thompson polarizer (GT). The frequency of the pump laser is measured by a wavemeter (WM, High-Finesse/Angstrom WS-U). The frequency scan and single-mode regime of the probe laser are monitored by observing saturated absorption in a vapor cell and resonances of reference Fabry--Perot cavity (FPI). The setup also includes the following optical elements: BS--beam splitter, BD--beam dump, QWP--quarter-wave plate, ND--neutral-density filter.
• Figure 2: Spectral dependence of normalized reflection coefficient $(R - R_0)/R_0$ for the probe beam, measured at four number densities: (a) $N_1 = 1.2 \times 10^{17}$ cm$^{-3}$ ($\Gamma_0/2\pi = 13.2$ GHz), (b) $N_2 =1.7 \times 10^{17}$ cm$^{-3}$ ($\Gamma_0/2\pi = 18.7$ GHz), (c) $N_3 = 2.5 \times 10^{17}$ cm$^{-3}$ ($\Gamma_0/2\pi = 27.5$ GHz), and (d) $N_4 = 3.6 \times 10^{17}$ cm$^{-3}$ ($\Gamma_0/2\pi = 39.6$ GHz). Zero frequency corresponds to the transition $5S_{1/2} (F = 3)-5P_{3/2} (F' = 4)$ in $^{85}$Rb atoms.
• Figure 3: Frequency derivatives of the reflection coefficient $\text{d}R/\text{d}\nu$ at four different number densities $N_1$, $N_2$, $N_3$, $N_4$ and three selected values of the pump beam intensity (a) $I_\text{pump}=0$ kW/cm$^2$, (b) $I_\text{pump}=4.8$ kW/cm$^2$, (c) $I_\text{pump}=8.8$ kW/cm$^2$. The bottom curves show saturated-absorption spectra of the probe beam for the reference rubidium cell. The frequency scale in panel (a) is the same as in Fig. \ref{['fig2']}. Zero frequency corresponds to the transition $5S_{1/2} (F = 3)-5P_{3/2} (F' = 4)$ in $^{85}$Rb atoms. Horizontal dashed lines show the "zero" levels. Vertical dotted lines indicate the location of the pump laser frequencies. Marks (x) indicate crossing of the derivative curves with the "zero" levels (dashed lines).
• Figure 4: The values of measured splitting $\Delta\nu_{\text{SP}}$ are shown as data points. The lines are results of fit by a linear function $\Delta\nu_{\text{SP}}=a\Delta\nu+b$, where $a$--slope of the fitting line, $b$--intercept of fitting line with the vertical axis. The inset shows the slope dependence on the atomic number density $N$.