Backward generation of echoes with three-pulse excitation is discussed in solid and gaseous systems. The backward echo in gases is possible as in solids but with different combinations of incident pulse directions. The first experiments in a gas were performed on the atomic sodium D 1 line in both the nanosecond and the picosecond region. Furthermore, we have observed the first backward echo in a molecular system, that is, in both of the X Σ -A Σ and X Σ -B I I transitions of Na 2 . Decays of the echoes were measured as a function of buffer gas (Ar) pressure, and collisional cross sections due to phase interrupting collisions were evaluated for each of the above cases.
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.
Backward photon echo and its decay were observed in the X Σ - A Σ transition of Na 2 undergoing collisions with Ar buffer gas. By using the quantum mechanical transport equation, expressions of the various collisionaI cross sections are presented. The results are applied to the experimtent, and several kinds of cross sections are obtained for the Na 2 -Ar system. Furthermore by assuming the Gaussian collision kernel, two parameters of the population kernel are derived for the Na 2 ( X Σ )-Ar collisions.
The effect of velocity-changing collisions in an extended-pulse photon echo is studied. In an extended-pulse photon echo, the second excitation pulse has a duration comparable with the relaxation time of an atomic system. We present an analytic solution of the quantum-mechanical transport equation in the perturbation-theory limit and apply it to the extended-pulse photon echo. It is found that the decay rate of the echo signal due to velocity-changing collisions is significantly modified by the variation of the second pulse's duration. The results are compared with those of conventional theories of two- and three-pulse echoes using temporally narrow excitation pulses. A physical interpretation of the results is given using both time- and frequency-domain arguments.