Experiments exploiting similarities for coherence collisional evolution in velocity space and in M space are reported. Generally, there is a total outgoing rate from any state and incoming rates (kernels) from neighboring states. Collision-induced velocity changes, ΔV, are studied with lasers by measuring the Doppler frequency Δ V/λ (λ = optical wavelength). To obtain information about coherence M transfer, it is only necessary to associate a frequency with each ΔM. This idea is demonstrated by measuring two-pulse photon echo intensity Ie for 13CH3F in a small dc Stark field. Acoustooptic modulation of infrared cw laser radiation, polarized parallel to the Stark field, is used to excite a number of uncoupled M → M transitions on the R(4,3) line. Each transition has a resonance frequency, vo + M· vs (vs is M = 1 Stark shift, Hz). A most remarkable result is obtained for large echo delays T with ΔVT/λ >> 1, all ΔV. The shape of the curve ln[ Ie(o)/ Ie(V)] vs Stark voltage V tends to that of the dominant coherence ΔM transfer kernel itself. Physically this arises because, for large T, the macroscopic coherence is preserved only for collisions where the frequency changing due to M transfer compensates the Doppler shift due to the ΔV, i.e., Δ V/λ + ΔM-·vs = 0. Generalizations are discussed.
Collision-induced coherence transfer between infrared molecular transitions is studied using a technique that permits the complete distribution of accompanying velocity changes to be determined in a simple way. The experiments are carried out by measuring the intensity of two pulse photon echoes as a function of applied Stark field at fixed large echo time delay. The velocity change distribution for coherence-transfer collisions is obtained directly as the shape of the echo intensity versus Stark field curve. Previously unpublished data for dipole-quadrupole and van der Waals interactions are presented, and a theory of coherence-transfer velocity-changing kernels is developed that is in good agreement with the data.
Radiator reorientation kernels are measured in Stark-tunable infrared transitions of 13CH3F. The dominant (ΔM = 1) kernel is obtained by a scale transformation from the shape of a two-pulse photon-echo intensity versus Stark voltage curve, at fixed large echo time delay. The quantum-mechanical transport equation in the presence of coherence M transfer and a dc electric field is reviewed, and the applications of photon echoes in a tunable Stark field to measure reorientation collision kernels are discussed.
We describe a new Stark sublevel photon echo technique for measuring fluctuations in macroscopic coherences. This idea is applied to the Stark tunable infrared (λ = 9 μm) R(4, 3, V3 = 0 → 1) transition of 13CH3F to measure, for the first time, the radiator reorientation velocity changing kernels WΔ M (Δv) which describe the rates (per unit velocity) at which the radiator orientation M changes by an amount ΔM accompanied by a velocity change Δv.1 In the experiments, two pulse photon echoes are obtained using a laser field polarized along an applied weak de Stark field ( z ^ direction) which shifts each M transition by Mvs (Hz).
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 simple application of the Stark-pulse technique, developed by Brewer and Shoemaker, demonstrates optical free induction decay-the optical analog of free induction decay in NMR. A molecular sample which is coherently prepared by a cw laser beam exhibits such a decay when it is suddenly switched out of resonance by a Stark field. Observations are presented for a nondegenerate Doppler-broadened infrared transition of N
H2D, where the sample is optically thin, and the decay behavior can be compared quantitatively with a solution of the Bloch equations. When the molecular sample is prepared under steady-state conditions, the solutions are analytic; for pulse excitation, a numerical solution is required. The treatment invokes a hard-collision relaxation model. Such characteristics as the abrupt termination of the decay and the related edge echo, which result from Doppler dephasing, can be examined for Stark pulses of finite extent.