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.
Photon echo and free induction decay, i.e., representative coherent optical transients, are described for two level system whose transition frequency is modulated by the Gaussian-Markoffian process. Photon echo signal is shown to decay biexponentially and to be effective in fixing the magnitude and the correlation time of the frequency modulation. Then we present the transition of the free induction decay rate against laser intensity from the Bloch type at the weak laser field into the Redfield one at the strong laser field.
Resonant microwave coherence transfer between two levels pairs (
a−aprime) and (
b−bprime) of two molecular species A and B has been observed. A and B are either different molecules or the same molecule in states uncoupled by collision induced transitions. The frequencies of the two transitions
arightarrowaprime and
brightarrowbprime are nearly equal and can be transiently brought in coincidence by applying a suitable Stark field. The coherence transferred from A-molecules to the B-molecules is detected by the techniques of time resolved spectroscopy. The observed phenomena may be interpreted either by collision induced effects between collision partner molecules or by collective effects. The contribution of these two effects are roughly estimated.
Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (
T2) and population (
T1) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime
T1 is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.
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.