Measurements of the relaxation times T
1 and T
2 of a two-level system by nonlinear transient spectroscopic methods are discussed, where delayed incident pulses are assumed to have correlation times much shorter than T
1 or T
2 but varied widths. In particular, a delayed degenerate four-wave mixing (photon echoe) and apump-and-probe type transmission measurement with incoherent long pulses are considered in detail, and a principle of their use for ultrafast spectroscopy is clarified. If the field is steady and T
1>>T
2, the time resolutionof T
2measurement by the delayed four-wave mixlng is determined by the field correlation, therefore by the spectral width of the incident light irrespective of the pulse width. The time resoution of the T
1 measurement by the pump-and-probe method is determined by the intensity correlation of the incident light, whereasthe one by the delayed four-wave mixing by a higher order correlation.
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