## 1 Introduction  
Coherent Raman spectroscopy of gas-phase rotational wave packets was demonstrated to be a valuable tool for the characterization of temperature, pressure, and composition of gas mixtures. Since molecular rotational spectra are extremely sensitive to the environment, the associated Raman coherence generated with ultrashort laser pulses is commonly used in coherent anti-Stokes Raman scattering (CARS) experiments applied to reacting gases to determine the physical and chemical conditions [1, 2, 3, 4, 5, 6]. Coherent rotational wave packets can also be studied using the alternative technique of stimulated Raman scattering (SRS), and particularly using the impulsive excitation scheme (ISRS), in which excitation of the rotational Raman modes is attained by an ultrafast pump pulse with a duration much shorter than the smaller relevant Raman period [7, 8]. This condition translates into easy access to the low-frequency Raman region (<500 cm\({}^{-1}\)), with commercially available ultrafast sources [9], and for this reason, it is captivating to answer the question of whether the diagnostic capability of CARS can be extended to impulsive SRS. In general, SRS has several advantages over CARS. Among them, the most important difference is in the dependence on dielectric susceptibility (\(|\chi|^{2}\) for CARS, whereas Im(\(\chi\)) for SRS), which results in simpler SRS spectra reproducing those obtained via spontaneous (i.e., linear) Raman. In addition, phase matching is inessential in SRS whereas it troubles CARS arrangements [10]. Moreover, ISRS is realized with a single ultrafast laser beam and a relatively simple setup [11, 12], while single-beam configurations available for CARS [13, 14] need sophisticated sectioning of the spectral content of the laser. As a matter of fact, ISRS was demonstrated in low-frequency Raman characterization of condensed-phase samples in setups equipped with a single low-energy femtosecond source with improved data acquisition rate [15, 16] and signal-to-noise ratio (SNR) [12, 15, 17, 18, 15], allowing the realization of video-rate low-frequency Raman microscopes [18]. On the other hand, low-excitation energy ISRS has never been demonstrated in the gas phase to the best of our knowledge. Low-energy fs pulses in the range of 80 MHz can be easily obtained using a compact commercial fs oscillator as opposed to more complex kHz-rate amplified fs lasers used in gas-phase CARS thermometry. The commonly adopted ISRS setup is based on a Fourier-transform (FT) spectrometer [9, 12, 19], where the sample polarization associated with the vibrational coherent state established by an ultrashort pump pulse interferes with a second, delayed ultrashort (probe) pulse, producing modifications which are detected as a signal. The signal is recorded as a function of the pump-probe delay and is therefore modulated with the same period of the vibrational coherent polarization. An FT of the delay-dependent signal finally gives the frequency spectrum of the vibrational modes. As far as the nature of the signal is concerned, the interference of the probe beam with the sample Raman polarization results in both spectral and refractive effects caused by the occurrence of stimulated Raman gain/loss phenomena and of the Raman-induced Kerr effect [11, 19]. The characteristics and the relative magnitude of these two types of signals were discussed in [17, 19] and more recently reviewed in [9]. In the gas phase, the coherent excitation of nearly equally spaced rotational levels of the sample produces periodic, isolated transients (rotational revivals) at fractional multiples of the fundamental rotational period, due to the recurrent realignment of the molecules. The resulting birefringence was exploited in the so-called Raman-induced polarization spectroscopy (RIPS) technique [20, 21, 22, 23] to study the rotational dynamics and to measure the concentration of gases in mixtures, in layouts equipped with high-energy amplified ultrashort laser sources.