Time–frequency theory of pump-probe absorption spectroscopy

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Abstract
A variation of density matrix formulation based on the nature of field–matter interference in a mixed time–frequency domain is developed to study molecular pump-probe absorption spectra in condensed phases. Considered are both the integrated probe transmitant signals and the frequency-dispersed transient absorption coefficients for molecular systems with either two or three electronic surfaces involved. The present formulation is exact and applicable to any field with arbitrary timescale and shape, and it is valid when the pulses are overlapped as well as separated. The dual temporal-spectral effect of both the excitation and detection fields can be clearly elucidated via a transformation that preserves causality. The resulting field–matter interference picture of transient absorption in the correlated time-frequency domain is conceptually natural and physically transparent. The molecular dynamics, and the field–matter temporal/spectral coherence and interference phenomena can all be clearly demonstrated.