Rotational excitation of molecules with long sequences of intense femtosecond pulses

We investigate the prospects of creating broad rotational wave packets by means of molecular interaction with long sequences of intense femtosecond pulses. Using state-resolved rotational Raman spectroscopy of oxygen, subject to a sequence of more than 20 laser pulses with peak intensities exceeding ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ per pulse, we show that the centrifugal distortion is the main obstacle on the way to reaching high rotational states. We demonstrate that the timing of the pulses can be optimized to partially mitigate the centrifugal limit. The cumulative effect of a long pulse sequence results in a high degree of rotational coherence, which is shown to cause an efficient spectral broadening of probe light via cascaded Raman transitions.

Figure 1

Experimental setup for the generation of long sequences of amplified femtosecond pulses. See text for details.

Figure 2

Temporal profiles of (a) a long periodic pulse train and (b) a dense aperiodic pulse train, 20 pulses each (note different time scales). The four shades of red correspond to one of the four different pathways through the two nested Michelson interferometers.

Figure 3

(a) Experimental setup for coherent rotational Raman spectroscopy implemented in this work. (b) Raman spectrum of room-temperature oxygen gas after the rotational excitation with a single weak transform-limited pulse.

Figure 4

(a) State- and time-resolved Raman spectrogram of ${}^{16}\mathrm{O}_2$ after the excitation by a sequence of five pulses with a period $T$ scanned around the rotational revival time $T_{\text{rev}}$ (vertical solid line). The vertical shaded band represents the length of our Gaussian pulses (FWHM), whereas the shaded horizontal band covers the rotational quantum numbers (shown on the right vertical axis) corresponding to the thermally populated rotational states (population higher than 10%). Light blue markers indicate the time moments at which a coherent rotational wave packet consisting of two states, $|J\rangle$ and $|J+2\rangle$, completes an integer multiple of half rotations $N_J$. The central trajectory (squares) corresponds to $N_J=2J+3$, while the two neighboring sets of circles and triangles represent the cases of $N_J=2J+2$ and $N_J=2J+4$, respectively (see text for details). (b) Raman spectra after a periodic sequence of 20 pulses with $T=T_{\text{rev}}$ (black solid line), $T=0.996T_{\text{rev}}$ (blue dashed line), and $T=1.004T_{\text{rev}}$ (green dotted line).

Figure 5

(a) Raman spectrogram for the rotational excitation by a sequence of two identical periodic pulse trains, five pulses each [same color map as Fig. 4]. The period of each train is fixed at $T_{\text{rev}}$, while the time delay $T_1$ between the two trains is scanned. The integrated signal above reveals the times of maximum total coherence. (b) Alignment-induced birefringence signal as a function of the probe delay after a weak transform-limited pump pulse. (c) Raman response after the rotational excitation by a sequence of 20 pulses: a periodic pulse train with $T=T_{\text{rev}}$ (black solid line) and an optimized pulse train (red dashed line). See text for the optimization procedure. The two trains are illustrated schematically in the top right corner.

Figure 6

(a) Simplified illustration of the first three scattering orders in the process of cascaded Raman scattering. The gray profile represents the Boltzmann distribution of the rotational population (see text for details). (b) Rotational Raman spectra of oxygen gas excited by the optimized train of 28 pulses (see text for the optimization procedure). The four curves correspond to the gas pressures of 1.7 atm (lower blue line), 2.4 atm (middle orange line), 5.1 atm (higher red line), and 6.5 atm (top black line). The first, second, and higher orders of the cascaded Raman scattering are indicated with arrows. More than 235 Raman peaks are observed at higher pressure values, as shown in the inset.

Figure 7

(a) Time-resolved Raman spectrogram (log scale) of oxygen gas excited by the optimized train of 28 pulses (see text for the optimization procedure) under the pressure of 6.5 atm. (b) Raman spectra at the time moments indicated with arrows in the spectrogram: before the first kick (black solid line), at the time of the first kick (blue dashed line), and at the time of the third kick (red dotted line).