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.
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 report the investigation of molecular M changing kernels using new Stark sublevel photon echo techniques to obtain, for the first time, the entire distribution of discrete M transfer rates. The method exploits the analogy between velocity space, where inhomogeneous broadening is due to Doppler frequency shifts, and M space where an artificial inhomogeneity can be created with a small Stark field. In the presence of the Stark field, random collision induced coherence transfer between M sublevels of an infrared transition of moderate J leads to Stark field dependant degradation of the molecular macroscopic polarization during the echo dephasing-rephasing process. The effects of inelastic (J changing) collisions and elastic velocity changing collisions which are field independent can be eliminated by measuring the ratio of the echo signals with the field on and off as a fuction of either echo time delay or Stark field. The nonexponential decay curve which is obtained is related to the M changing collisions kernel by discrete transformation with the frequency components $\\nu{_{s}}\\Delta $M, where
DeltaM is an integer and
nus is the Stark shift for unit M. In the experiment, the
(V=0,J=4,K=3)longrightarrow(v3=1,J=5,K=3) transition in
CH3P is studied. Acoustooptic (A/0) intensity modulation of 9P32 c.w.
CO2 laser radiation is used for input pulse generation. A novel digital oscillator driver is employed which has no RF leakage, so that A/0 rejected ratios are scattered light limited at
−106:1. Preliminary results yield echo signals with very high signal to background ratio and show completely new nonexponential behavior of the echo decay curve. Applications of both two and three pulse (stimulated) sublevel experiments will be described."
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.
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).