## 3 Results  
Measurements were performed as a function of the N\({}_{2}\) pressure in the cell in the range of 1-10 atm. The time-dependent spectral ISRS signals measured at different N\({}_{2}\) pressures using an integration time equal to 100 s, corresponding to 2000 signal averages, are shown in Figure 2a. Clear rotational wave packet interference revivals can be seen at around 2, 4, 8, and 12 ps, especially for the measurements at the highest pressure; however, the signal is detectable down to atmospheric pressure. The positions of the observed revivals are in agreement with published data measured using amplified femtosecond sources [25; 30]. However, the shape of the revivals is different from that reported in previous studies since here we are detecting the spectral ISRS signal. In particular, we can observe that each signal can be described as an alternate of revivals, which can be labeled according to their shape  
Figure 2: (**a**) Time-dependent ISRS signals measured in N\({}_{2}\) at different pressures. (**b**) Same as (**a**) after FT filtering (see text). as \"dispersion\"- or \"peak\"-like, the two shapes being connected by a derivative. Therefore, since the spectral ISRS signal is proportional to the derivative of its refractive counterpart, our data show a revival pattern that is complementary to those reported before. From Figure 2a it can be seen that the revival signals sit on a slowly variable background which does not scale with the sample pressure and is due to a systematic experimental artifact produced by the delay scan mechanism, as verified on a CH\({}_{2}\)Br\({}_{2}\) reference sample. This background can be removed by post-acquisition data processing, e.g., by a 1 THz high-pass FT filter, obtaining much clearer signals as shown in Figure 2b. It is interesting to observe that the dependence of the signal intensity on the sample pressure is not trivial. Notwithstanding the well-known linearity of the SRS signal on sample concentration in condensed matter samples, in the gas phase, many phenomena concur to alter this situation. For example, in femtosecond CARS measurements, the signal dependence on sample concentration is almost linear [14] in the gas phase, differently from the usual quadratic behavior in condensed matter. Accordingly, we expect a sublinear, almost square-root, dependence of the signal intensity on the gas pressure. It is worth observing that improvement of the SNR can be achieved by increasing the laser repetition rate, which improves the statistics of the measurements. In the present experiment, the laser repetition rate is limited to 40 kHz in order to demonstrate a low-average power (<1 mW) operation, but, for example, using a 1 MHz repetition rate (which is a typical maximum figure for a cavity dumper) an SNR improvement of factor five (\(\sqrt{10^{6}/4\cdot 10^{3}}\)) can be foreseen, with a limited average power of only 18 mW, well below the levels commonly used in spontaneous Raman measurements (several hundreds of mW). The use of a higher repetition rate, providing a higher number of pulses during the scan, enables the use of faster delay scan mechanisms [31], thus allowing a shorter measurement time at a fixed number of averages. An experimental implementation of these features will be the subject of future work. As known, the Raman spectrum of the sample can be obtained by a fast Fourier transform (FFT) of the time-dependent ISRS signal; the results of this operation on the data shown in Figure 2b are reported in Figure 3a. The rotational levels of N\({}_{2}\) are visible in the region 50-150 cm\({}^{-1}\) even in the sample at atmospheric pressure and are quite evident in measurements at 7 and 10 atm. The resolution of the data shown in Figure 3a is slightly worse than 2.5 cm\({}^{-1}\) and is due to the available maximum delay.