It has been shown recently that molecular gas samples excited with coherent light can display a variety of transient phenomena, similar to those found in nuclear magnetic resonance. This article elucidates how these coherence effects can be used to isolate or unfold molecular collision mechanisms that normally remain hidden within the optical line shape. Elastic collisions, for example, are easily detected here in two-pulse photon echo experiments for a
13CH3F vibration-rotation transition. The echo-decay function which provides a signature for the velocity-changing collision diffusion mechanism, is not just a simple exponential in time but exhibits an $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ contribution for short times and an $\mathrm{exp}(\ensuremath{-}\ensuremath{\Gamma}t)$ decay for long times. This behavior, which is unknown heretofore, contrasts with spin echoes in molecular liquids where Brownian motion leads only to the cubic decay law. An $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ behavior can be understood in terms of a solution of the Fokker-Planck equation which describes the effect of Brownian motion on echo decay. Such a treatment is valid for small phase excursions; in the case of a gas, this implies the Doppler phase factor $k\ensuremath{\Delta}u\ensuremath{\tau}\ensuremath{\ll}1$, where $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ is the propagation vector of light, $\ensuremath{\Delta}u$ is a characteristic velocity jump for a binary collision, and $\ensuremath{\tau}$ is the echo-pulse delay time. When $k\ensuremath{\Delta}u\ensuremath{\tau}\ensuremath{\gg}1$ as in the long-time regime, the Fokker-Planck solution fails. We, therefore, present a new solution to the Boltzmann transport equation using a weak collision model and find agreement with the entire echo time dependence observed. The echo measurements indicate very small changes in longitudinal velocity per
13CH3F-
13CH3F collision, i.e., $\ensuremath{\Delta}u=85$ cm/sec, thereby justifying the weak-collision model. The total elastic collision cross section is 430
A˚2. It follows that elastic collisions lead to velocity thermalization in a time of \ensuremath{\sim}5 sec when the
13CH3F pressure is 1 mTorr. A comparison is also made of the
13CH3F dephasing time ${\ensuremath{\tau}}_{2}$ in a coherent Raman beat decay, which is independent of velocity-changing collisions, with the longitudinal decay time
T1. Here,
T1 represents the molecule-optical interaction time, due largely to jumps in molecular rotation (
J) and orientation (
M) state, and is obtained from a delayed nutation measurement. The fact that the pressure dependent part of ${\ensuremath{\tau}}_{2}={T}_{1}$ shows that
T1 is also independent of velocity diffusion. Futhermore, when a hole is burned in the Doppler distribution, population recovery must be due to inelastic rather than elastic collisions. Optical Carr-Purcell echoes, multiple pulse echoes, provide a direct measure of the
13CH3F transverse dephasing time
T2 without the effect of elastic collisions while being sensitive to "phase interrupting collisions." Again, we find that
T2=T1 so that phase interruptions are negligible. Had such a process dominated the two-pulse echo, an $\mathrm{exp}(\ensuremath{-}\frac{t}{{T}_{2}})$ damping would have been noticed with no $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ contribution. Thus, the present study covers several new aspects of molecular collisions. It represents the first detailed examination of velocity-changing collisions by coherence methods and without the complication of Doppler broadening.
A class of molecular two-photon processes, occurring under transient or steady-state conditions, is analyzed exactly for certain cases using a density-matrix formalism. Our results are relevant to the recently observed phenomena of transient coherent Raman beats and steady-state two-photon absorption of oppositely directed laser beams. Lowest-order perturbation theories have shown that these processes are insensitive to the Doppler effect, and consequently the linewidth is unaffected by Doppler broadening and by elastic collisions that change molecular velocity. The solutions presented here are of the same form for the Raman and two-photon problems and reveal significant power-dependent frequency shifts and line broadening that correct the ideal Doppler-free solutions. For the transient case, we assume a molecular three-level quantum structure that can be switched in or out of optical resonance with cw laser radiation by means of a pulsed dc Stark field, but the solutions also apply when resonant optical pulses are introduced. During the resonant condition when the Stark pulse is on, the three levels are prepared in coherent superposition, and during the nonresonant condition following the Stark pulse, the laser field(s) stimulates the coherently prepared sample in a transient two-photon process. One of these processes, the Ramanbeat effect, has been observed in forward scattering, but the second one, transient two-photon emission, should be observable in backward scattering. Bloch-like equations are derived for this three-level problem that facilitate an exact pulse solution for state preparation. Following the pulse, transient decay is well-approximated by a perturbation calculation. For the steady-state case, an exact solution is also obtained and is of interest for continuous-wave spectroscopy or for transient experiments requiring an initial preparation of quantum states, prior to Stark switching. These solutions exhibit a power-dependent line broadening and a frequency shift of magnitude $\ensuremath{\sim}\frac{\ensuremath{\Delta}({\ensuremath{\alpha}}^{2}\ensuremath{-}{\ensuremath{\beta}}^{2})}{({\ensuremath{\Delta}}^{2}+\frac{1}{{T}_{2}^{2}})}$, in agreement with our earlier estimate, where $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are the Rabi flopping frequencies for the two intermediate transitions and $\ensuremath{\Delta}$ is the off-resonance tuning behavior for one of them.
Elastic velocity-changing collisions have been observed for the first time to our knowledge in a nonpolar molecule by photon-echo studies of SF(6) using a frequency-switched CO(2) laser that we have developed. The photon-echo decay is nonexponential and reveals the velocity-changing collision cross section to be sigma(vc) = 180 A(2), with an average velocity change per collision of Deltau = 155 cm/sec. Using delayed optical nutation, we also determine the cross section for the population decay rate (1/T(1)) to be sigma(pop)=335 A(2). To within experimental accuracy, we find that phaseinterrupting collisions are not important (T(1) approximately T(2)). A comparison of these cross sections with those for the polar molecule (13)CH(3)F is made.
The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.
Method of stimulated photon echo with specially chosen linear polarizations of exciting pulses of coherent resonant radiation is applied for investigation of collisional decay of orientation and alignment in molecular gas SF6 and its mixtures with buffers He and Xe. These relaxation rates are measured as a function of longitudinal velocities. Within experiment accuracy, no remarkable velocity dependence of depolarizing collisions rates was detected. This result confirms conventional approach of depolarizing collisions theoretical treatment.
Two different time-resolved spectroscopic techniques are discussed theoretically and demonstrated experimentally in dilute gases. The first technique involves extending the advantages of Stark-effect based time-resolved spectroscopy to non-polar molecules. This involves the development of a stable, TEM₀₀ mode, cw, CO₂ laser capable of switching rapidly and controllably between two frequencies. Design problems and output characteristics are discussed. The frequency switchable laser is applied to the CO₂ 10.6 μm P(16) coincidence with the non-polar molecule SF₆. The population relaxation time, T₁, is measured using two-pulse delayed nutation. The decay of induced dipoles is studied using the phenomenon of photon echoes. It is found that the echoes decay in a manner characteristic of dephasing dominated by velocity-changing collisions. A fit of the data to a model for such decays gives values of γ(ab) ≡ 1/T₂ (the non-velocity-changing contribution to the dipole decay rate), Γ(VC) (the total probability of a velocity-changing collision per unit time), and Δu which is related to the mean velocity change of SF₆ upon a velocity changing collision. A comparison with the published results of the similar Stark experiments on C¹³ H₃F are made. The second technique involves the development of an alternative to the pulsed excitation typically used in time-resolved T₁ studies. This involves inversion of a portion of the velocity distribution by adiabatic rapid passage (ARP) techniques. The center of this portion is then probed in the manner of previous delayed nutation experiments. The system preparation is shown theoretically to be different and simpler than the pulse case. In addition, ARP preparation gives a larger signal than two-pulse delayed nutation experiments. ARP experiments on N¹⁴H₃ and N¹⁵H₃ are described and compared to two-pulse delayed notation experiments. The single exponential decay best fits to the data from the two methods are found to be in agreement. We would expect the N¹⁵H₃ results to be very similar to the N¹⁴H₃ results, though reduced rotational resonance effects in its upper state should give it an overall slower decay. It is indeed found that the decay appears to be a simple exponential as did the N¹⁴H₃ data over the time range studied. The pressure dependent single exponential decay rate for N¹⁵H₃ is however roughly 45% larger than the rate for N¹⁴H₃ in the pressure range from 0.5 to 9 mTorr.