PHYSICAL REVIEW A VOLUME 24, NUMBER 1 JULY 1981 Sub-Doppler frequency-modulation spectroscopy of I, G. C. Bjorklund and M. D. Levenson IBM Research Laboratory, San Jose, California 95193 (Received 9 January 1981) Frequency-modulation spectroscopy has been employed to monitor the absorption and dispersion changes induced by the optical saturation of nonzero velocity groups of I, molecules. The use of a high modulation frequency markedly increases the sensitivity of this form of saturation spectroscopy and allows convenient access to molecular velocities well above the thermal average. The problem of detecting small changes in non- uniform absorption profiles continues to bedevil laser spectroscopy. ' Such small effects are im- portant in saturation spectroscopy when the in- homogeneous linewidths of a number of transi- tions overlap and when the number of resonant molecules is small. Even a relatively strong pump can then alter the total absorption by only a few percent. Fluctuations in the power of the probe laser beam often contribute enough noise to unacceptably degrade such spectra. This paper describes a new saturation spectroscopy techni- que which overcomes these difficulties by means of frequency-modulation (FM) spectroscopy. ' We have employed our FM saturation-spectroscopy technique to detect Bennett holes at nonzero axial velocities in I2 vapor and to measure the velocity dependence of the homogeneous linewidth. ' The demonstrated sensitivity of this technique ap- proaches the quantum limit. ' The hyperfine splitting of rovibronic lines of the X - B transitions of the I2 spectrum is by now quite familiar. The homogeneous linewidths of these transitions have been studied by conven- tional saturation spectroscopy and by optical co- herent transient techniques. ~ The former tech- niques revealed that in the absence of collisions, transitions between states with different total angular momenta showed differing homogeneous linewidths. 5 This effect is largest when the or- bital angular momentum is the same order as the angular momentum due to the nuclear spin. For the majority of I2 lines, the orbital angular mo- mentum is far larger, and all of the hyperfine transitions within a given line are expected to have the same homogeneous linewidth and pres- sure-broadening coefficient. The average linewidth and pressure-broadening coefficient can be accurately determined using the photon echo or optical free-induction-decay technique. How- ever, since the splittings between the hyperfine components cannot be suddenly changed by an external perturbation, pulse Fourier-transform optical spectroscopy cannot separate the contri- bution of a single transition from the total coher- ent transient signal. ' When collisions are important, the homogen- eous linewidth can also depend on the molecular velocity. Each transition contributing to the co- herent transient signal corresponds to a different molecular velocity group, but the dephasing rate measured by coherent transients depends only upon the average over transitions and velocities. Mattick et al. and Grossman et al. have shown that there can be considerable velocity depen- dence of the collisional dephasing rate, especial- ly when the interactions with the perturber are relatively short range. ' For hard-sphere interactions, the collisional dephasing rate is expected to scale linearly with the relative veloc- ities of the interacting molecules. Optical techni- ques can specify only one velocity component of one of the collisional partners in a gaseous sam- ple. Averaging over the remaining degrees of freedom reduces the velocity dependence of the measured homogeneous linewidth, especially for slow-velocity groups. The velocity dependence of collisional quench- ing and dephasing rates in I2 are of some funda- mental interest. Because the interactions be- tween the ground-state molecules differ greatly from that between a ground-state and an excited- state molecule, the semiclassical scattering picture previously so successful for vibrational transitions fails and must be replaced by a fully- quantum-mechanical treatment. ' While the aver- age dephasing and quenching cross sections are known to be large, no persuasive model exists for the underlying elastic and inelastic processes. To measure the velocity dependence of the homo- geneous linewidth it is necessary to interact with atoms moving with axial velocities equal to or greater than the average thermal velocity. The optical frequencies required to saturate and 24 166