Mapping of the optical frequency comb to the atom-velocity comb

A mode-locked femtosecond laser is used to physically map the laser frequency comb into the velocity comb of the excited Rb atoms at room temperature. Upon resonant excitation by discrete optical frequencies the velocity distribution of the excited Rb atoms shows comblike structure. Simultaneously, velocity-selective population transfer occurs between ground-state hyperfine levels. Both facts are observed by modified direct frequency comb spectroscopy and verified by a detailed density matrix treatment of the multilevel system in resonant field.

Figure 1

Experimental scheme. PD: photodiode. P: polarizer. A: analyzer. FI: Faraday isolator. S: beam stopper. F: neutral density filter.

Figure 2

Hyperfine energy schemes of the ${}^{85,87}\mathrm{Rb}5{}^{2}S_{1∕2}\text{−}5{}^{2}P_{1∕2}$four-level (a) and $5{}^{2}S_{1∕2}\text{−}5{}^{2}P_{3∕2}$ six-level (b) systems with the corresponding relative transition probabilities.

Figure 3

${}^{87}\mathrm{Rb}$ calculated ground-$({\rho }_{11},{\rho }_{22})$ and excited-$({\rho }_{33},{\rho }_{44})$ state hyperfine-level populations for different atomic velocity groups in the case of $5{}^{2}S_{1∕2}\to 5{}^{2}P_{1∕2}$ fs-laser excitation (only a central part of the Doppler-broadened profile is presented).

Figure 4

${}^{85}\mathrm{Rb}$ calculated ground-$({\rho }_{11},{\rho }_{22})$ and excited-$({\rho }_{33},{\rho }_{44})$ state hyperfine-level populations for different atomic velocity groups in the case of $5{}^{2}S_{1∕2}\to 5{}^{2}P_{1∕2}$ fs-laser excitation (only a central part of the Doppler-broadened profile is presented).

Figure 5

${}^{87}\mathrm{Rb}$ calculated ground-$({\rho }_{11},{\rho }_{22})$ and excited-$({\rho }_{33},{\rho }_{44},{\rho }_{55},{\rho }_{66})$ state hyperfine-level populations for different atomic velocity groups in the case of $5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ fs-laser excitation (only a central part of the Doppler-broadened profile is presented).

Figure 6

${}^{85}\mathrm{Rb}$ calculated ground-$({\rho }_{11},{\rho }_{22})$ and excited-$({\rho }_{33},{\rho }_{44},{\rho }_{55},{\rho }_{66})$ state hyperfine-level populations for different atomic velocity groups in the case of $5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ fs-laser excitation (only a central part of the Doppler-broadened profile is presented).

Figure 7

The comparison of the measured and simulated ${}^{85,87}\mathrm{Rb}5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ hyperfine absorption line profiles in the case of $5{}^{2}S_{1∕2}\to 5{}^{2}P_{1∕2}$ fs-laser excitation.

Figure 8

The comparison of the measured and simulated ${}^{85,87}\mathrm{Rb}5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ hyperfine absorption line profiles in the case of $5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ fs-laser excitation.

Figure 9

Relative modulation intensities of four Rb absorption lines as a function of the central fs-laser wavelength.

Figure 10

Relative modulation intensity dependence on the fs-laser power, $5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ fs-laser excitation.

Figure 11

Measured ${}^{85,87}\mathrm{Rb}5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ absorption spectra for $5{}^{2}S_{1∕2}\to 5{}^{2}P_{3∕2}$ fs-laser excitation in the conditions with and without an external magnetic field.

Figure 12

Relative modulation intensity of ${}^{87}\mathrm{Rb}{F}_g=1\to F_e=0,1,2$ absorption line as a function of external magnetic field strength (dots). The solid line is an eye-guiding fit to the experimental data.

Figure 13

Measured ${}^{87}\mathrm{Rb}{F}_g=1\to F_e=0,1,2$ absorption line profiles in the conditions without an external magnetic field and with magnetic field strengths of $18\mathrm{G}$ (minimum in Fig. 12) and $36\mathrm{G}$ (maximum in Fig. 12).