Abstract The spin echo [1 ] discovered by Erwin Hahn in 1950 is one of the most sophisticated phenomena in physics. It demonstrates the fact that the decay of coherence due to the inhomogeneous broadening can be recovered by an ingenious ‘effective time reversal’ technique. Since then, the research on coherent transients has been developed in the field of pulsed magnetic resonance [2]. The advent of the laser stimulated the studies in the optical region. Optical analogues of most of the coherent transients in magnetic resonance have been realized [ 3] except for those in solids, whose mechanisms are based on the spin temperature hypothesis [4] . Thus coherent interactions between radiation and atoms have been extensively studied and the techniques developed have been effectively used in a variety of fields. In the studies of so-called two-level problems the coherence is generated by a direct excitation of the relevant transitions by radiofrequency (r.f.), microwave, or laser fields.
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.
Coherent transient effects are the optical analogs of the many transient phenomena seen in pulsed nuclear magnetic resonance experiments on spin systems. For example, photon-echo and optical nutation are the respective optical equivalents of spin echo and transient nutation of nuclear magnetic resonance. In Stark-switching and frequency-switching techniques the laser field and the molecules are brought into resonance in a sequence of pulses, the rest of the time they remain well off-resonance. So far it has been assumed that the off-resonance field does not have any measureable influence on the experimental results and is utilized to implement a very efficient detection scheme. This work discusses how the off-resonance field affects the coherent transient effects. It is shown here how this field, by inducing changes in the index of refraction as small as 10⁻⁶ produces easily observable effects in photon echo and delayed optical nutation.
Abstract Soon after the discovery of the principal phenomenon of nuclear magnetic resonance (NMR) by Purcellet al.[1] and Blochet al.[2] , it was Hahn [ 3] who realized that spin precession can be observed directly in the rotating frame as a transient phenomenon called free induction decay (FID). In linear response theory, both phenomena, the continuous wave (c.w.) observation and the free precession are related to each other by Fourier transformation. Within the same year, however, Hahn realized that there is more to the motion of spins than just a linear response to radiofrequency field excitation and discovered the spin echo phenomenon [ 4] which led to the foundation of modern NMR spectroscopy and nonlinear optical spectroscopy. In this contribution we want to present a special view on how these early principles of Hahn influenced the development of Optical Excitation and Detection of Spin Precession. For this purpose we consider a very simple physical system, namely an atomic vapour. In optical pumping spectroscopy it is well known that the transmitted light intensity is modulated by irradiating the system with resonant radiofrequency (r.f.) fields [5-8]. By monitoring the transmission of light as a function of the r.f., sublevel splittings of the optically connected states can thus be measured, which are usually not resolved in the Dopplerbroadened optical spectrum.
A major and ongoing focus of our research effort has been the development of laser pulse sequences analogous to those used in nuclear magnetic resonance, to study relaxation phenomena in condensed phases. Sequences of multiple rectangular 90° and 180° pulses with various phases have been used extensively in high resolution and solid state NMR for nearly three decades, and have been shown to enhance forbidden transitions, selectively refocus some intermolecular interactions, or even increase physiological image contrast for tumor identification. By contrast, the conventional approach to optical coherent transient spectroscopy (splitting a single high power pulse into several parts) generates pulse sequences with well defined delays, but generally totally unknown phases; in addition, the pulse shape is not easily controlled. This approach has proven extremely useful in the past, particularly if noncollinear pulses are used to exploit propagation effects, but growing recognition of the fundamental complexity of condensed phase relaxation processes (and the defects of a two-level approximation) reveals a fundamental need for a more powerful approach.
It has been well established that for many metastable electronic levels of impurity ions in insulators, optical coherence times at liquid helium temperatures are limited by magnetic interactions with host nuclear spins. 1 To understand coherence loss in detail, one needs measurements of optical and spin dephasing, magnetic properties and hyperfine structure of impurity ions, and spin dynamics of host nuclei. To this end techniques such as spectral hole burning, 2 coherent transients (e.g. photon echo), 1,3 and optical-rf double resonance 4 have been used. All of these are limited directly or indirectly by optical T2, and have not directly probed the dynamics of host nuclei.