Theory of resonance secondary emission in femtosecond laser excitation: On the connection with wave packet dynamics

The resonance secondary emission (RSE) in femtosecond laser excitation is discussed in reference to the motion of the created wave packet moving on the excited state potential surface. The density matrix of emitted light for the multi-intermediate-level system is outlined, from which the emission correlation function is derived. The correlation function is put into the theoretical expression of the time-dependent "physical spectrum" for the Fabry-Perot interferometer (which is used in order to consider temporal and energetic resolution inherent in detection). The compact and practical expressions obtained connect the time- and frequency-resolved spectrum with the time evolution of the wave packet. Numerical results for a displaced harmonic oscillator model indicate that the time- and frequency-resolved spectrum can reveal how the wave packet created by a fs laser pulse travels on the excited potential surface if the response time 1/Γ_d of the photodetector satisfies the relation that Ω<Γ_d <∼ the Stokes shift (where Ω is the vibrational frequency). It is shown that the excited state wave function can be split into two terms, the one that adiabatically follows the temporal change in incident light (the adiabatic term) and the one that represents the effect of spectral broadening of light (the Fourier broadening term). It is only the Fourier broadening term that survives after the termination of incident light and reflects the motion of the created wave packet on the excited potential surface. In off-resonance excitation, the adiabatic term produces Raman-like emission and the Fourier broadening one produces fluorescence-like emission. In resonance excitation, these two terms are indistinguishable from each other with respect to emission frequency: for the duration of incident light, the adiabatic term offsets the Fourier broadening one, leading to a slow buildup of intensity in the time- and frequency-resolved spectrum (which is slower than the initial rise of the incident pulse profile).