Stimulated photon echoes (three-pulse echoes) produced by broadband (incoherent) light pulses are discussed. A switching time corresponding to the reciprocal inhomogeneous width is predicted for the echo signal when the time interval between the first two time-overlapping, mutually coherent pulses is scanned across 0. The effect is demonstrated in an experiment performed with cesium vapor. A new method for fast sampling of atomic or molecular velocity distribution is proposed with potential applications to photodissociation and photofragmentation studies.
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."
Free polarization decay and photon echo were studied experimentally in polar gas 13CH3F at the transition R(4,3) of vibrational mode 0 yields 1 (nu) 3 by Stark switching of molecular levels under irradiation by CW CO2 laser at 9P(32) line. Application of 4.5 mcs pulse to the Stark electrodes inside the gas cell allows to detect the free polarization decay signal, combined with the optical nutation. The sign of the signal corresponds to the increase of absorption in the limit of low intensity (not over 0.01 W/cm2) saturating radiation. Exciting intensity growth till the level of 6.0 W/cm2 implies decrease of signal absolute value, till the change of its sign, while the oscillation of the free polarization decay signal reveals remarkable frequency shift. Such behavior is attributed to the combined action of the dynamic Stark effect of CW radiation field and the levels splitting by the Stark voltage. Two shorter (of about 0.1 and 0.2 mcs) Stark pulses, applied to the gas, generate the photon echo signals detected by the same heterodyne technique. The study of the variations of photon echo parameters versus exciting radiation intensity is in progress.
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 class of molecular two-photon processes, occurring under transient or steady-state conditions, is analyzed exactly for certain cases using a density-matrix formalism. Our results are relevant to the recently observed phenomena of transient coherent Raman beats and steady-state two-photon absorption of oppositely directed laser beams. Lowest-order perturbation theories have shown that these processes are insensitive to the Doppler effect, and consequently the linewidth is unaffected by Doppler broadening and by elastic collisions that change molecular velocity. The solutions presented here are of the same form for the Raman and two-photon problems and reveal significant power-dependent frequency shifts and line broadening that correct the ideal Doppler-free solutions. For the transient case, we assume a molecular three-level quantum structure that can be switched in or out of optical resonance with cw laser radiation by means of a pulsed dc Stark field, but the solutions also apply when resonant optical pulses are introduced. During the resonant condition when the Stark pulse is on, the three levels are prepared in coherent superposition, and during the nonresonant condition following the Stark pulse, the laser field(s) stimulates the coherently prepared sample in a transient two-photon process. One of these processes, the Ramanbeat effect, has been observed in forward scattering, but the second one, transient two-photon emission, should be observable in backward scattering. Bloch-like equations are derived for this three-level problem that facilitate an exact pulse solution for state preparation. Following the pulse, transient decay is well-approximated by a perturbation calculation. For the steady-state case, an exact solution is also obtained and is of interest for continuous-wave spectroscopy or for transient experiments requiring an initial preparation of quantum states, prior to Stark switching. These solutions exhibit a power-dependent line broadening and a frequency shift of magnitude $\ensuremath{\sim}\frac{\ensuremath{\Delta}({\ensuremath{\alpha}}^{2}\ensuremath{-}{\ensuremath{\beta}}^{2})}{({\ensuremath{\Delta}}^{2}+\frac{1}{{T}_{2}^{2}})}$, in agreement with our earlier estimate, where $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are the Rabi flopping frequencies for the two intermediate transitions and $\ensuremath{\Delta}$ is the off-resonance tuning behavior for one of them.
The dependence of the time of the appearance of a Stark (gradient) echo response on the irreversible transverse relaxation time of a system in the nanosecond range and on the width of the excitation region of an inhomogeneously broadened line has been investigated. It has been shown that the use of nonresonant laser pulses with an artificially created spatial inhomogeneity makes it possible to determine the relaxation time in the nanosecond range from the time of the appearance of a Stark (gradient) echo response, which is a more accurate method than the method of determining the relaxation time from the decay of the intensity by varying time intervals of the exposure to inhomogeneous electromagnetic fields.