Coherent optical transient study of molecular collisions: Theory and observations

Abstract

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 "CH,F vibration-rotation transition. The echodecay function which provides a signature for the velocity-changing collision diffusion mechanism, is not just a simple exponential in time but exhibits an exp( -Kt') contribution for short times and an exp( -I 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 exp( -K t') 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 hu~& 1, where k is the propagation vector of light, hu is a characteristic velocity jump for a binary collision, and r is the echo-pulse delay time.When kb. u v && 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 "CH,F-"CH,F collision, i.e. , Au = 85 cm/sec" thereby justifying the weakcollision model. The total elastic collision cross section is 430 A'. It follows that elastic collisions lead to velocity thermalization in a time of -5 sec when the "CH,F pressure is 1 mTorr. A comparison is also made of the "CH,F dephasing time v, in a coherent Raman beat decay, which is independent of velocity-changing collisions, with the longitudinal decay time T,. Here, T, 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 v, = T, shows that T, 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 "CH,F transverse dephasing time T, without the effect of elastic collisions while being sensitive to "phase interrupting collisions. " Again, we find that T, = T, so that phase interruptions are negligible. Had such a process dominated the two-pulse echo, an exp(t/T, ) damping would have been noticed with no exp( -K t') contribution. Thus, the present study covers several new aspects of molecular collisions.It represents the first detailed examination of velocit...

Infrared HCN Lineshapes as a Test of Galatry and Speed-Dependent Voigt Profiles

“…From an experimental point of view, reported experiments were performed in the linear interaction regime, which leads to a global response of the sample and makes a detailed analysis intricate. So the interest of experiments in the nonlinear regime, such as saturated absorption or photon echoes experiments, must be emphasized for the analysis of velocity-changing collisions (68,69) or of the speed dependence of relaxation (19)(20)(21)70).…”

Spectroscopic measurement of the softness of ultracold atomic collisions

“…By combining these two measurements, we are able to quantitatively extract the s-wave collisional softness of cold 87 Rb atoms in an optical dipole trap. We obtain good agreement with previously reported theoretical results from molecular dynamics simulations, validating our method and laying the foundations for its application in measuring the softness of other collisional processes.We further show that the coherence decay in an echo experiment is qualitatively different for short and long times [8,9]. This can be used to approximate the softness by combining a Ramsey measurement and an echo measurement in a single, intermediate density regime.…”

“…We further show that the coherence decay in an echo experiment is qualitatively different for short and long times [8,9]. This can be used to approximate the softness by combining a Ramsey measurement and an echo measurement in a single, intermediate density regime.…”

“…They are relevant for atomic clocks, metrology, quantum information, evaporative cooling, atom-ion hybrid systems and more [1][2][3][4][5][6]. Collisions may also have a significant effect on the coherence properties of an ensemble of atoms, providing either elongation [7][8][9][10][11][12][13][14][15][16] or shortening [17,18] of the atomic coherence time.Considering a rapid collisional process compared to other dynamical timescales [19], there exist two extremities for a colliding atom in the center-of-mass frame of the interacting ensemble: "hard collisions", in which the energy of the atom is completely randomized after a single collision, and "soft collisions" in which the atomic energy remains almost unchanged after each collision [14]. We therefore define the "collisional softness" parameter, s, as the number of times an atom has to collide in order for the correlation between its initial and final energies to drop to 1/e [20].…”

“…Defining t tr ≡ τ / √ s, a transition time between the two regimes, an interpolating function can be written to describe the entire dynamics, which is the accurate solution in the limit of soft collisions [9]:…”