## 1 Introduction  
The nonlinear process of multi-frequency Raman generation (MRG) holds the promise of generating high intensity pulses with duration of just single femtoseconds. Such pulses could be used in nonlinear optical experiments for the study of molecular dynamics. MRG generates an ultrabroad spectrum containing several discrete frequency peaks by strongly driving a Raman transition of a molecule using two pump pulses. The peak frequencies of the two pumps are tuned such that the frequency difference equals the Raman frequency. This process was first observed by [PERSON] and co-workers, when they generated several vibrational and rotational Raman orders in hydrogen, when their pump laser was tuned such that two frequency components were output [1]. The advantage of MRG over continuum generation for short pulse generation is that the phase only has to be corrected over several orders rather than the entire spectrum. On the other hand, because the spectrum is discrete, it generates a train of pulses. A pulse train of 1.6 fs pulses was obtained by simply phasing 7 Raman orders from hydrogen using a prism dispersion line and a liquid crystal phase modulator [2]. An even simpler compression technique of placing a few dispersive elements in the path has been shown to create trains of sub-fs pulses [3]. The duration of the pulse train is given by the pulse duration of the pump pulses and so shorter pump pulses would result in fewer pulses in the pulse train leading to more intense pulses. The 1.6 fs pulse train was pumped in the adiabatic regime with nanosecond long pulses. It has been shown that the MRG process can be efficient in the transient regime, where the pump pulses have durations of the coherence time of the Raman transition [4]. However, with short pulses, the MRG process competes with self-phase modulation (SPM), which creates a continuum spectrum under the discrete Raman spectra [5, 6]. To avoid SPM, the short pulses are lengthened by linearly frequency chirping the pulses. We have previously observed that, when using linearly chirped pump pulses, extra peaks appear in the MRG spectrum of sulfur hexafluoride (SF\({}_{6}\)) [7, 8]. These peaks appear on the lower frequency side of the Raman peaks. These red shifted peaks also appear in the MRG spectra with chirped pulse pumping for the gas Raman media of hydrogen [5] as well as in the solid Raman medium, lead tungstate [9], indicating that the origin of the peaks is a fundamental process rather than being material dependent. In order to determine if these red-shifted shoulders were simply the result of four-wave mixing, we have measured the MRG spectra as a function of tuning the instantaneous frequency separation [8]. We showed that the red shifted peaks shift further to the red as the instantaneous frequency separation of the two pump beams is reduced below the Raman frequency until the red-shift saturates. However, the peaks do not blue shift as the frequency separation increases above the Raman frequency, indicating that the shift is not due simply to non-resonant four-wave mixing. If the shifted peaks are not due to non-resonant four-wave mixing then it is most likely due to a Stark shift of the levels. [PERSON] and co-workers noted that when using long pulses in the adiabatic regime, many more Raman orders were observed when the frequencies were tuned to be slightly closer together than the Raman resonance frequency [10]. When the frequencies were further apart than the Raman transition frequency, there was little difference in the generated spectra compared to on-resonance pumping. The authors of this work noted that the enhancement was given for in the in-phase coherent state, but not the anti-phased coherent state. [PERSON] and co-authors derived the two-photon driven coherent state for Raman generation [11].