Coupling between cw lasers and a frequency comb in dense atomic samples - Experiment

1. Introduction
2. Experiment

The simplified scheme of the experimental setup together with the relevant hyperfine structure of the 87Rb isotope is presented in figure 1. The frequency comb is generated by a modelocked Ti:sapphire laser (MIRA 900B-Coherent) with a pulse duration of ~ 150 fs and repetition rate of 76 MHz. A homemade external cavity diode laser with a linewidth of about 1 MHz is used as a probe beam. The two beams are overlapped, with orthogonal linear polarizations, forming a small angle at the centre of the sealed Rb vapour cell, in a configuration that can be co- or counter-propagating. The vapour cell is 5 cm long and contains both 85Rb and 87Rb isotopes in their natural abundances, with no buffer gas. The cell is heated in order to control the atomic density.
The central wavelength of the femtosecond laser is tuned at 780 nm (D2 resonance line) with a maximum average power of 350 mW and a spectral bandwidth of the order of 8 nm. The average power per mode of the fs laser is of the order of a few µW, and the comb linewidth is negligible compared with the diodelaser linewidth2. The fs beam is chopped at 1.8 kHz and focused to a diameter of about 120 µm at the centre of the Rb cell, resulting in a peak electric field of approximately 40 MV/m, which is kept constant in all measurements. The diode-laser beam with a maximum average power of 240 µW is also focused at the centre of the cell with a beam waist of ~ 100 µm, and its intensity can be varied using neutral-density filters. The probe frequency is scanned across the Doppler-broadened hyperfine transitions at a rate of 200 MHz/s. A saturated absorption setup (not shown) is used to calibrate the probe detuning. The transmission of the cw beam, after passing through cell and a linear analyser, is detected simultaneously with two photodiodes (PD1 and PD2) as a function of its detuning.

The signal from photodetector PD1 is processed by a lockin amplifier employing the chopper frequency as a reference. The lock-in output is monitored and recorded on a digital oscilloscope, together with the signal from photodetector PD2. In this way, whereas the PD2 signal provides the total transmission of the probe beam after passing through the cell, the PD1 signal, after the lock-in, represents the probe-beam transmission variation induced by the fs pulse train.
Measurements of the coupling between the two beams for three different diode intensities are displayed in figure 2. Each picture shows the transmission variation of the cw beam induced by the fs pulse train as a function of the diode frequency, when the diode laser scans the hyperfine transitions and the fs laser is tuned to 780 nm. The temperature of the cell is kept constant at 304 K and the two beams are co-propagating through the cell. The average power of the diode beam is (a) 4 µW , (b) 80 µW and (c) 240 µW .
In figure 2(a) we clearly see the frequency comb of the fs laser impressed in the Doppler profile of the Rb atoms. 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 here 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 [9]. For a weak probe beam, a structure in the modulation can be observed as a direct consequence of a population transfer between the two ground hyperfine levels of Rb induced by the frequency comb. An extensive study of this velocity-selective optical pump (VSOP) process in the D1 and D2 lines of Rb and Cs atoms at room temperature was conducted by Pichler’s group [10–13].

As the diode power increases, we observe, figures 2(b) and (c), that the visibility of themodulations decreases whereas the absorption of the diode beam induced by the fs laser increases throughout the whole Doppler profile. This behaviour is in agreement with previous experimental results [13].
We also investigate the dependence of the coupling between the two beams with the atomic density. Figure 3 presents the experimental results for four different atomic densities when the two beams are counter-propagating and the average power of the cw beam is kept constant at 4 µW. Each row in figure 3 corresponds to one temperature of the Rb cell, with the two frames in each rowobtained simultaneously while the diode laser is scanned across the transitions of the D2 line of 87Rb. In the left column we present the signals from photodetector PD1, whereas the signals from photodetector PD2 are present in the right column. The signal from PD2 clearly shows the increase in the absorption of the diode beam as the Rb-cell temperature is increased revealing strong absorption for high temperatures: the diode’s intensity after the cell almost vanishes over a large range of frequencies throughout the Doppler profile.
In figure 3(a) we observe the frequency comb of the fs laser impressed in the Doppler profile as in figure 2(a). For these experimental conditions of cw beam intensity and atomic density, is always negative, 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, figures 3(b) and (c), we observe positive values for transmossion on the red side of the Doppler profile, indicating decrease in the absorption of the diode beam due to the fs pulse train. The small value of transmossion in the central region is a consequence of the strong absorption of the diode beam for those frequencies.

The results shown in figure 3 indicate that, depending on the atomic density, the fs pulse train plays different roles if the diode frequency is on the blue or red side of the hyperfine transitions. A similar behaviour is also observed for the other transitions of the D2 line of 87Rb. A comparison of the signal for the transitions from Fg = 1 and Fg = 2 is shown in figure 4, for the same experimental conditions.