## 4 Experiment: Preparing Molecules with Two Independent CW Laser Beams  
In this section, we discuss our experiment where we have prepared the molecular coherence by using two independent laser beams. Figure 4 shows the simplified schematic of this experiment. Similar to the pump laser, the Stokes laser system starts with an ECDL, but now near a wavelength of 1.55 \(\upmu\)m. We amplify the Stokes ECDL output to 20 W with an erbium-doped fiber amplifier. A PDH setup similar to that of the pump laser keeps the Stokes beam resonant with the cavity. When we lock both lasers to the cavity and adjust the frequency difference of the two lasers to within about a GHz of the Raman transition resonance, \(\
u_{pump}-\
u_{Stokes}\approx\
u_{ab}\), the two beams efficiently drive the molecular coherence. The established molecular coherence then mixes with the driving lasers to produce the anti-Stokes and second Stokes sidebands at wavelengths of 807 nm and 2.94 \(\upmu\)m, respectively. These sidebands are only observed when the lasers are tuned to within about 1 GHz of the Raman transition. For these experiments, we reduce the gas pressure to a sufficiently low value such that Raman lasing on the vibrational Stokes beam is negligible; _i.e._, if we lock only the pump laser to the cavity there is no substantial Raman generation. The Raman lasing needs to be suppressed because the Stokes beam generated through Raman lasing interferes with the cavity lock of the 1.55 \(\upmu\)m beam. Figure 5 shows the power of the generated 807 nm  
Figure 3: The conversion efficiency from the mixing beam to the 636 nm anti-Stokes sideband as the incident pump power is varied at a constant D\({}_{2}\) pressure of 0.3 atm. The solid line is a theoretical calculation without any adjustable parameters, based on the measured transmitted powers of the pump and the Stokes beams through the cavity. anti-Stokes beam as a function of the two-photon detuning at a molecular gas pressure of 0.01 atm. This pressure value is about three orders of magnitude lower than those traditionally used in stimulated Raman scattering experiments. It is important to note that, just as in the 90 THz mixing experiment described above, the cavity mirrors do not have a high reflectivity at the anti-Stokes wavelength, so the 807 nm beam is generated in a single pass through the system. We generate a maximum CW anti-Stokes power exceeding 1 mW, which is an order of magnitude larger than our previous experiments that relied on Raman lasing to generate the Stokes beam [30]. The predicted established molecular coherence in this experiment is more than an order of magnitude higher than what was achieved in the mixing experiment, \(|\rho_{ab}|\approx 1\times 10^{-3}\). Although the established molecular coherence in this experiment is much higher, we have not yet been able to translate this increase into an increase in the mixing efficiency experiment of the previous section. When we increase the molecular gas pressure, the dynamics of Raman lasing and instabilities in the locking performance substantially reduce the intra-cavity intensities for the pump and the Stokes beams. One of our immediate goals is to increase the established molecular coherence and operate at higher pressures in the two-beam setup and thereby increase the mixing efficiency. We believe that the intra-cavity intensities in our experiment are currently limited by the large free-running linewidths of the ECDLs (about 0.5 MHz) and by imperfect locking electronics. Due to these limitations, we are able to couple at best 10% of the incident power in each laser beam to the cavity.