Chirping the probe pulse in a coherent transients experiment

Coherent transients occur when a chirped pump pulse excites a two-level transition. They have been observed with an ultrashort probe pulse. Several studies have been dedicated to using various pump shapes. In this study, the roles of the pump and the probe pulses are reversed. With a Fourier-transform-limited pump pulse followed by a chirped-probe pulse, similar effects can be observed. Finally, the case of two pulses with opposite chirps is considered.

Figure 1

Evolution of the upper-state population under the excitation of a chirped pulse: (a) probability exhibiting coherent transient normalized to unity for long time and (b) corresponding probability amplitude in the complex plane. The symbols correspond to different values of time $\tau$: $-1000$ fs (triangle), 0 fs (circle), 480 fs (diamond), 1090 fs (square), 1840 fs (star), and 4000 fs (cross).

Figure 2

Principle of the excitation scheme. (a) In the case of a chirped pump and a short probe, the probe “freezes” the interaction at time $\tau$. (b) In the case of a short pump and a chirped probe, the pump triggers the interaction between the chirped pulse and the upper two levels at time $-\tau$ (with respect to the chirped pulse).

Figure 3

Two-dimensional mapping of the final-state population (normalized to the population at long time and delay). The vertical axis is the delay between the pump and the probe ($\tau$ in the equations), and the horizontal axis is the time evolution ($t$ in the equations). A vertical cut at 6 ps is plotted on the right-hand side, corresponding to the evolution of the asymptotic value of the final population. This value is the one measured via the experiment. Several horizontal dashed lines are plotted, which correspond to the different cases presented in Fig. 4.

Figure 4

Left: Temporal evolution of the final population during the probe pulse [normalized to the population at long time and delay; see case (f)]. Right: Corresponding probability amplitude plotted in the complex plane. Pump-probe delays are (a) $-1000$, (b) 0, (c) 480, (d) 1090, (e) 1840, and (f) 4000 fs.

Figure 5

Experimental setup: G2, gratings with 600 grooves$/$mm. G1, gratings with 2000 grooves$/$mm. NOPA, noncolinear optical parametric amplifier.

Figure 6

Experimental coherent transients on Rb ($5s$-$5p$ at 795 nm), for a chirp of ${\varphi }_{\mathrm{pr}}^{″}=-1.4\times {10}^5$ fs${}^2$ on the probe (black dots) and the corresponding simulation obtained by numerical resolution of the Schrödinger equation (solid gray line). Curves are normalized to unity at long time.

Figure 7

Experimental coherent transients measured for a chirp of ${\varphi }_{\mathrm{pr}}^{″}=-1.4\times {10}^5$ fs${}^2$ on the probe and sequential chirp values for the pump (${\varphi }_{\mathrm{pu}}^{″}$). Curves are normalized to unity at long time and shifted vertically for clarity. The (a) black-dot solid curve corresponds to transients obtained with a FT-limited pump (see Fig. 6) plotted here for comparison: (b) ${\varphi }_{\mathrm{pu}}^{″}=1.0\times {10}^5$ fs${}^2$ (blue), (c) ${\varphi }_{\mathrm{pu}}^{″}=1.2\times {10}^5$ fs${}^2$ (red), (d) ${\varphi }_{\mathrm{pu}}^{″}=1.4\times {10}^5$ fs${}^2$ (green), and (e) ${\varphi }_{\mathrm{pu}}^{″}=1.5\times {10}^5$ fs${}^2$ (purple). The increasing chirp of the pump gives fewer oscillations in the transients. For opposite chirps (d), the oscillations are completely removed [such as for curve (e)], but the rising time obtained is here the shortest. It is equivalent to the FT-limited cross-correlation duration. The sharp peak around $\tau =0$ is due to the detuning of the central laser wavelength with respect to the resonance wavelength.