Interaction of a finite train of short pulses with an atomic ladder system

When a train of optical pulses interacts with a medium, the time between pulses and the pulse-to-pulse phase jump have a profound effect on the outcome of the interaction. For a near-infinite train of regularly separated pulses having a constant pulse-to-pulse phase jump, as in the output of a frequency comb laser interacting with a ladder system, excitation of that system has been previously calculated and compared with experiment. In that case, the number of pulses in the train is very large, and the energy per pulse is very small. In the present work, the other extreme is experimentally examined: A small number of regularly spaced optical pulses are made to interact with a three-level ladder system in atomic rubidium. The pulses have been amplified, possibly placing the interactions into a nonperturbative regime. The experimental results are compared to a simple intuitive model and found to be in good general agreement. However, some aspects of the experimental results seem to be at odds with the simple model.

Figure 1

The effect of a sinusoidal spectral phase, like that of Eq. (4), on a Gaussian transform-limited input pulse. Here the curve of pulselike structures is $E_{\mathrm{out}}$ (blue online), while the boxy curve shows the absolute phase of each pulse, relative to some arbitrary zero (red online).

Figure 2

Landscape plot of Rb${}^{+}$ counts vs. $T$ and ${\varphi }_0$ for $A=2.5332$, which gives rise to a train of 11 significant pulses. The structures correspond to constructive and destructive interferences of Eqs. (1) and (2) from the $5s$-$5p$ and $5p$-$5d$ transitions. In taking the data, ${\varphi }_0$ ranged from 0 to $2\pi$. In order to make clearer the diagonal structures, the data were copied and replotted so as to artificially extend the range of the ${\varphi }_0$ axis to $4\pi$.

Figure 3

Landscape plots of Rb${}^{+}$ counts vs. $T$ and ${\varphi }_0$ for various numbers, $N$, of pulses in the train. Plots (a), (b), and (c) have $N=3$, 7, and 11, corresponding to $A=0.3672$, 1.3152, and 2.5332, respectively.

Figure 4

Values of the Bessel function argument as a function of the desired number of pulses in the train for $f=0.05$. The points are from direct computation, while the solid curve is a fit to the indicated power law.