Until now all reported studies of transient spectroscopy with incoherent light, including photon echo and pump-probe spectroscopy, were concerned with two-level systems where quasi-monochromatic light of only one frequency couples the two levels.[1-4] However, there exist various coherent transient phenomena where light of two or more frequencies are concerned, and time resolution of the transient spectroscopies using these phenomena are also expected to be limited not by the duration of used light pulses but by the correlation time of the radiation fields.[5]
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.
A detailed theoretical analysis is presented of the dephasing signal measured in four-beam picosecond time-resolved stimulated-Raman-gain experiments. The analytical expressions derived are successful in simulating observations on the CS2 model system under various experimental conditions. It is established that the tail of the curve for sufficiently long delay times is uniquely determined by the vibrational Raman term that yields the vibrational dephasing time T2. It is also found that the rotational dephasing time cannot be fundamentally determined from the rotational Raman peak centered around zero delay. Furthermore, it is shown that the coherence properties of the stimulating laser fields, as distinguished from their pure pulse-envelope properties, are crucially important in determining the time resolution of the experiments and for explaining several experimental phenomena observed under mismatched excitation-pulse conditions. In this respect, the domain model for mode-locked pulses has proved to be useful. It is found that the time resolution of the dephasing measurements is determined by the combined pulse-coherence time of the driving fields and not by the cross-correlation width of the pulse envelopes.
Spontaneous vibrational Raman scattering is a ubiquitous form of light-matter interaction whose description necessitates quantization of the electromagnetic field. It is usually considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming field. When probing an ensemble of molecules, the question therefore arises: What quantum state should be used to describe the molecular ensemble following spontaneous Stokes scattering? We experimentally address this question by measuring time-resolved Stokes-anti-Stokes two-photon coincidences on a molecular liquid consisting of several sub-ensembles with slightly different vibrational frequencies. When spontaneously scattered Stokes photons and subsequent anti-Stokes photons are detected into a single spatiotemporal mode, the observed dynamics is inconsistent with a statistical mixture of individually excited molecules. Instead, we show that the data are reproduced if Stokes-anti-Stokes correlations are mediated by a collective vibrational quantum, i.e. a coherent superposition of all molecules interacting with light. Our results demonstrate that the degree of coherence in the vibrational state of the liquid is not an intrinsic property of the material system, but rather depends on the optical excitation and detection geometry.
A theory for selective-vibrational-dephasing experiments using transient stimulated Raman scattering in high laser depletion is presented. The transient stimulated Raman scattering equations are numerically solved including laser depletion for homogeneously and inhomogeneously broadened vibrational line shapes. A detailed account of the effects of low and high laser depletion on the vibrational amplitudes is given. An interpretation for excite-and-probe vibrational-dephasing experiments undertaken in the low- and high-laser-depletion regimes is developed. For a collinear laser probe pulse, high depletion of the excitation laser pulse leads to enhanced coherent Stokes probe scattering from one vibrational subgroup in the inhomogeneously broadened line shape. This selective scattering is greatly dependent upon the excitation laser pulse width and the off-resonance frequency of the vibrational subgroup. The enhanced selectivity in high laser depletion allows the homogeneous dephasing time
T2 to be measured to a high level of accuracy.