One- and two-photon transitions driven by a femtosecond pulse train and a cw laser in Rb vapor


Abstract
: We use an ultrashort pulse train and a cw laser to investigate one- and two-photon transitions in Rb vapor. The action of the two lasers, combined with a 1 GHz repetition rate, allows a velocity selective spectroscopy of the hyperfine levels of the 5P and 5D states. Moreover, the experimental data are well described in the frequency domain picture.
In most high-resolution atomic spectroscopy experiments with frequency combs [1], a cooled and trapped sample is employed or a vapor in which a two-photon transition under counterpropagating beams is allowed [2], such that only one group of atoms, with specific velocity, is investigated as the femtosecond (fs) laser repetition rate is scanned. On the other hand, in systems with Doppler-broadening where coherent accumulation processes are present a velocity selective spectroscopy is also possible. In this latter case, however, if the frequency separation in the comb is of order of 100 MHz, as usually used, the resolution is limited by the superposition of the hyperfine transitions.

Recently, we have shown that an fs laser with 1 GHz frequency separation of the optical modes allows us to resolve the hyperfine levels, and also to investigate the coherent processes induced by the train of ultrashort pulses [3]. Under the high repetition rate of the fs laser the necessary condition for the coherent accumulation of population and coherence is much better fulfilled, and moreover, it enables to probe the position of a single mode within the Doppler profile of the rubidium D1 or D2 line.

In this work, we investigate the combine action of an ultrashort pulse train and a cw diode laser over the one- and two-photon transitions in a rubidium Doppler broadening sample. A diagrammatic scheme of the experimental setup is presented in Fig. 1(a). The 1 GHz Ti:sapphire laser can excite the 5S - 5P1/2 or 5S - 5P3/2 - 5D transitions at 795 nm and 780+776 nm, respectively. A diode laser, with a linewidth of about 1 MHz, is used to excite the 5S1/2 - 5P3/2 transition. The two beams are overlapped in the center of a sealed Rb vapor cell in a counterpropagating configuration.


Fig. 1. (a) Experimental diagram. (b) Diode beam transmission variation induced by the fs pulse
train in one-photon transition, as a function of the diode frequency. (c) Variation of the ground
state population and (d) Energy levels of 85Rb, for the experimental situation defined in (b). (e)
Fluorescence at 420 nm (lower curve), due to two-photon transitions and the saturated absorption
signal (upper curve) as a function of the diode laser frequency.
For the one-photon transition experiment, the data acquisition is performed using a lock-in amplifier. In this case, a chopper provides the reference frequency and the lock-in signal represents the probe beam transmission variation induced by the fs pulse train. In the two-photon experiment, the fluorescence emitted by spontaneous decay from 6P state to 5S is collected at 90 grades, detected with a photomultiplier tube and recorded on a digital oscilloscope.

Fig. 1(b) shows the transmission variation of the diode laser beam induced by the fs pulse train, Delta_T, as a function of the diode frequency for the Doppler line 5S1/2, F = 3 - 5P3/2. The vapor cell is kept at room temperature, and the Rabi frequencies are: Omega_cw = 0.08gama (for the diode laser) and Omega_m = 0.13gama (for each mode of the frequency comb), where gama is the relaxation rate of the excited states. A scheme of the relevant level structure is presented in Fig. 1(d). All the hyperfine transitions driven by the 1 GHz laser can be resolved, resulting in four resonances with the modes of the frequency comb. Moreover, the diode beam probes these resonances in three different transitions of the D2 line: F = 3 − F′′ = 2,3,4. These resonances explain the two similar sets of six peaks, separated by 362 MHz, shown in Fig. 1(b). Each pair of positive and negative peaks, 36 MHz distant, reflects the optical pumping induced by the 1 GHz laser between the two hyperfine levels of the ground state 5S1/2. The observed linewidths are dominated by the power broadening due to the two lasers, although the laser drifts and the magnetic field broadening in the unshielded Rb cell also contribute to the width.

The result of Fig. 1(b) can be explained by a simple model consisting of two independent three-level lambda systems interacting with the modes of the frequency comb. In the steady-state regime and for a weak diode beam, we can solve the Bloch equations. The analytical solution for the ground state population, probed by the diode laser, is used to describe the interaction with the two excited hyperfine levels, 362 MHz distant. As the diode beam probes these resonances in three different transitions, we add them weighted by their electric transition dipole moments. Fig. 1(c) shows the analytical result for the population variation, Delta_Tcalc, of the state Rb 85, 5S1/2,F = 3.

Fig. 1(e) shows the fluorescence signal (red line) at 420 nm, for a fixed repetition rate (fR), as the diode frequency is scanned over the four Doppler-broadened D2 lines of the Rb 85 and Rb 87. In this case, the vapor cell is heated to ≈ 80oC. The spectrum consists of several narrow peaks over a flat background. The narrow peaks are due to the two-photon transition excited by both lasers: the diode laser (5S - 5P3/2) and the different modes of the frequency comb (5P3/2 - 5D); while the background is due only to the excitation by the frequency comb. In the same scan we can observe simultaneously peaks associated to the excitation of the 5D3/2 and 5D5/2 states. We also see two peaks, separated of one fR in optical frequency of the diode laser, that correspond to the same transition excited by two neighboring modes of the frequency comb. The saturated absorption curve (blue line) is used to calibrate the diode frequency. In this experiment, the repetition rate is phase-locked to a signal generator with 1 Hz resolution, in way that we can resolve all the hyperfine levels of excited 5D states. In addition, the experimental spectra can be understood using a simple mode consisting of independent three-level cascade systems interacting with two cw lasers.

In conclusion, we have shown that coherent processes such as the two-photon transitions and the optical pumping between hyperfine levels of rubidium atoms can be well resolved using a 1 GHz fs laser. Moreover, the experimental results are well described by the interaction of the atomic vapor with a frequency comb.

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

References


1. J. Ye and S. T. Cundiff, eds., Femtosecond Optical Frequency Combs Technology: Principle, Operation, and Application (Springer, New York, 2004).
2. J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg, and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor,” Phys. Rev. A 81, 043840 (2010).
3. Marco P. Moreno and Sandra S. Vianna, “Femtosecond 1 GHz Ti:sapphire laser as a tool for coherent spectroscopy in atomic vapor,” J. Opt. Soc. Am. B 28, 2066-2069 (2011).