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.
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.
Stimulated photon echo technique with specially chosen linear polarizations of pumping pulses of exciting radiation is applied to investigation of depolarizing collisions in molecular gas SF6 and its mixtures with buffer gases He and Xe. For the first time, the collisional decay rates of population, orientation and alignment of SF6 levels are determined simultaneously. Translational velocity dependence of orientation and alignment collisional decay rates was under investigation. This velocity dependence proved to be negligible within the frames of experimental accuracy both in pure SF6 and in mixtures, which is in agreement with standard theoretical approach accepted for depolarizing collisions. Decay rates of orientation and alignment in pure SF6 have proved lower than velocity changing (elastic) collisions relaxation rate, which allows to conclude, that only some part of elastic collisions participates in destruction of multipole polarization moments of resonant levels. The evidence is obtained for j-dependence of multipole moments relaxation rates SF6.
A stimulated photon echo technique with specially selected linear polarizations of the coherent resonant driver pulses is used to study depolarizing collisions in the molecular gas SF 6 and in mixtures of it with buffer He and Xe. The collisional decay rates of the population, orientation, and alignment in an ensemble of gas particles are determined for the first time in a single experiment. These relaxation rates are measured as a function of the longitudinal translational velocities of the resonant particles. To within the experimental accuracy, no significant dependence of the collisional decay rates on the translational velocities of the particles was observed. This result confirms the conventional theoretical approach to depolarizing collisions. In pure SF 6 the decay rates for the orientation and alignment were lower than the relaxation constant for collisions involving a change in the longitudinal velocity (elastic collisions) that is known from experimental observations of the ordinary photon echo. This means that only some of the elastic collisions participate in destroying the multipole moments of the levels. Evidence is found that the relaxation of the multipole moments created by polarized radiation in a resonant medium of molecular SF 6 gas depends on j , the total angular momentum of the level.
The method of a stimulated photon echo with specially selected linear polarizations of pumping pulses of a coherent resonant radiation is applied to a research of depolarizing collisions in molecular gas SF6 and its mixtures with buffer gases He and Xe. For the first time in one experiment the rates of a collisional decay of three lowest moments of polarization (population, orientation and alignment) are defined in an ensemble of gas particles. These rates of a relaxation are measured as functions on longitudinal velocities of resonant particles. In the frames of an experimental accuracy any noticeable dependence on velocities of particles was not detected both for orientation and alignment neither in pure resonant gas SF6 nor in mixtures. This result confirms the standard theoretical approach to depolarizing collisions. In pure SF6 decay rates of orientation and alignment have proved lesser than relaxation rate constant due to velocity changing (elastic) collisions. It means, that only the part of elastic collisions participates in destruction of multipole polarization moments of resonant levels. In comparison with our previous work the evidence is obtained that the relaxation of multipole moments seems to be j-dependent one in a medium of molecular gas SF6.
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.