The dynamics of nuclear spins in atomic and molecular environments have been examined in exquisite detail over the past 27 years by the methods of pulsed nuclear magnetic resonance. The early discovery of the spin echo by Erwin Hahn and the transient nutation effect by Henry Torrey initiated the field by introducing coherent transient phenomena to radio-frequency spectroscopy. An entire class of coherent spin transients could be observed by a simple variation of the rf pulse sequence, and from the decay characteristics the various spin-dephasing mechanisms could be examined separately. In short, these methods allowed decomposition of the spin-transition linewidth into its broadening components, and also offered new and versatile ways for performing high-resolution rf spectroscopy.
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.
We demonstrate that frequency-chirped laser excitation pulses may be employed to generate coherent transient signals possessing the same temporal profile as a particular excitation pulse. In comparison with the short, fixedfrequency pulses used in previous studies of this effect, chirped pulses can be temporally longer, of lower intensity, and hence easier to generate. The experiment was performed on the 555.6-nm transition of vapor-phase atomic ytterbium, and pulse-shape information was stored in a coherence between excited-state Zeeman levels. A simple theoretical analysis of our results is presented.
A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}$ which are originated from a single beam at frequency $\ensuremath{\omega}$ but have mutual time delay $\ensuremath{\tau}$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{3}=2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ at $\ensuremath{\omega}$ is calculated as a function of $\ensuremath{\tau}$. Even with the light having a much longer duration than both
T1 (the longitudinal relaxation time) and
T2 (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\ensuremath{\tau}$, represents a decay profile determined mainly by
T2 for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\ensuremath{\tau}}_{c}$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the
T1 effect. However, it does not cause a significant error in the determination of
T2. Moreover, as $\frac{{T}_{2}}{{T}_{1}}\ensuremath{\rightarrow}0$, the trace becomes a single-exponential decay curve determined only by
T2. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\ensuremath{\tau}}_{c}$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.