Competition between a cw laser and a frequency comb interacting with a Rb vapor

Abstract: We investigate the transmission of a cw laser interacting with rubidium vapor and a frequency comb. The results reveal various regimes of competition and the importance of optical pumping and power broadening of the lasers.

In the last decade femtosecond (fs)-lasers have been established as an essential tool for coherent control and highresolution spectroscopy, with applications in several branches of science [1, 2]. In particular, when the fs-laser frequency comb directly excites the atomic samples it is possible to combine the temporal, ultrafast aspect of femtosecond lasers with the spectral resolution of its frequency comb [3]. Direct excitation of samples by a frequency comb, however, requires a deeper understanding of the various processes responsible for the medium response to the pulse-to-pulse phase change of the fs laser. Most of the previous works considered only the frequency comb exciting the atoms. The introduction of a second, cw laser in the experiments allows to probe the action of the fs laser over the various velocity groups of a room-temperature atomic vapor [4].

We report on a new study on the coupling between cw lasers and a frequency comb. We experimentally investigate this coupling process as a function of atomic density and both laser intensities. The frequency comb is generated by a mode-locked Ti:sapphire laser with 150 fs pulse duration and 76 MHz repetition rate. A home-made external cavity diode laser with 1 MHz linewidth is used as a probe beam. The two beams are overlapped, with orthogonal linear polarizations, in the center of a Rb vapor cell, in a co- or counter-propagating configuration. The vapor cell, containing both 85Rb and 87Rb isotopes, is heated in order to control the atomic density.

The central wavelength of the fs laser is kept at 780 nm (D2 line) and the diode frequency is scanned across the Doppler-broadened 87Rb 5 2S1/2 to 5 2P3/2 hyperfine transitions. The transmission of the cw beam, after passing through the cell and a polarizer, is detected by a photodiode as a function of its detuning. The signal is processed by a lock-in amplifier and gives the diode-beam transmission variation induced by the fs pulse train.

Our experimental results show a strong dependence of the cw laser absorption with the intensity of both lasers and the atomic density. At room temperature and for weak probe beam we clearly observe the frequency comb of the fs laser impressed in the Doppler profile of the Rb atoms, in agreement with recent results [5-6]. In this situation, where the atomic relaxation times are greater than the laser repetition period, the resonances of the fs laser field and the atomic system are determined by the frequency comb rather than the spectrum of a single pulse. The modulation observed is due to the coherent accumulation effect in the excitation process, and is determined by constructive and destructive interferences between the coherences excited by the sequence of pulses from the fs laser [5,7] .

The dependence of the coupling between the two beams with the atomic density is presented in Figure 1, for a counter-propagating configuration. Each row corresponds to the diode-transmission variation for one temperature of the Rb cell, while the diode laser is scanned across the Fg = 1 to Fe = 0,1,2 transitions of 87Rb. For these experimental conditions of cw beam intensity and atomic density, the diode-transmission variation is always negative in Fig. 1a, indicating that the presence of the fs pulse train leads to an increase of the diode beam absorption for all frequencies in the Doppler profile. As we increase the atomic density, Figs. 1b and 1c, we observe positive values for the diode-transmission variation in the red side of the Doppler profile, indicating decrease in the absorption of the diode beam due to the fs pulse train. For the highest atomic density, two distinct regions are clearly observed: one with positive values for the diode-transmission variation on the low-frequency side of the Doppler profile and the other with negative values for diode-transmission variationon the high-frequency side. The small value of diode-transmission variationin the central region is a consequence of the strong absorption of the diode beam for those frequencies.
We also investigate the dependence of the coupling between the two beams with the diode intensity. As the diode power increases, the visibility of the modulations decreases whereas the absorption of the diode beam induced by the fs laser increases throughout the whole Doppler profile.

In order to understand the fundamental aspects behind the experimental results, a theoretical model considering the interaction of the two lasers with a four-level system, in all orders of the fields, was developed. We model the atom with two ground states, in order to allow for the various optical pumping conditions of the system, and two excited states, to account for the orthogonal polarization of the two beams. The atomic population and coherences are calculated by numerical integration of the Bloch equations, using a fourth order Runge-Kutta routine. To compare with the experimental results we calculated the difference, of the imaginary part of the coherence between the two levels connected by the diode laser, with and without the presence of the fs laser. For low cw laser intensities we obtain a reduction of the diode beam absorption induced by the fs beam for both kinds of transitions. As the cw laser intensity increases, we find an intensity region where the two kinds of transitions, closed and open, present different behaviors with respect to absorption. While for the closed transitions we continue to obtain an increase of the diode transmission, for the open transition the fs beam induces an increase of the absorption of the diode beam for all frequencies within the Doppler profile. This distinct behavior can be understood if we note that for the closed transition only the fs beam can transfer population between the two ground states. However, for the open transition, there is a competition between the two lasers in the population transfer process, and the diode laser may prevail when its area is large enough.
Our results reveal the existence of various regimes of competition between the two lasers, depending on their relative intensities and on the nature, open or closed, of the atomic transition excited by the cw laser. A clear qualitative explanation for the observed behaviors is provided by a Bloch equation treatment of the problem considering the atom as a four-level system.

This work was supported by CNPq, FACEPE and CAPES (Brazilian Agencies).

[1] A. H. Zewail, Femtochemistry: Ultrafast dynamics of the chemical bonds (Word Scientific: Singapore, 1994).
[2] Jun Ye and S. Cundiff , Femtosecond Optical Frequency Comb Technology: Principle, Operation and Application} (New York: Springer,2005).
[3] A. Marian, M. Stowe, J. Lawall, D. Felinto, and J. Ye, Science 306, 2063 (2004).
[4] D. Aumiler, T. Ban, H. Skenderovic, and G. Pichler, Phys. Rev. Lett. 95, 233001 (2005).
[5] D. Felinto, C. A. Bosco, L. H. Acioli, S. S. Vianna, Opt. Comm. 215, 69 (2003).
[6] T. Ban, D. Aumiler, H. Skenderovic, G. Pichler, Phys. Rev. A, 73, 043407 (2006).
[7] D. Felinto, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 70, 043403 (2004).