Ultrahigh-time-resolution coherent transient spectroscopy with incoherent light

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 ${\overrightarrow{\mathrm{k}}}_1$ and ${\overrightarrow{\mathrm{k}}}_2$ which are originated from a single beam at frequency $\omega$ but have mutual time delay $\tau$. 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 ${\overrightarrow{\mathrm{k}}}_3=2\mathrm{}{\overrightarrow{\mathrm{k}}}_2-{\overrightarrow{\mathrm{k}}}_1$ at $\omega$ is calculated as a function of $\tau$. Even with the light having a much longer duration than both $T_1$ (the longitudinal relaxation time) and $T_2$ (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\tau$, represents a decay profile determined mainly by $T_2$ for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\tau }_c$ 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 $T_1$ effect. However, it does not cause a significant error in the determination of $T_2$. Moreover, as $\frac{T_2}{T_1}\to 0$, the trace becomes a single-exponential decay curve determined only by $T_2$. 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 ${\tau }_c$ 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.