  Ultrafast pump-probe spectroscopy with high temporal and spectral resolutions
provides new insight into ultrafast nonequilibrium phenomena. We propose that
transient interference between pump and probe pulses is realized in pump-probe
spectroscopy of band and Mott insulators, which can be observed only after
recent developments of ultrafast spectroscopic techniques. A continuum
structure in the excitation spectrum of band insulators is found to act as a
medium for storing the spectral information of the pump pulse, and the spectrum
detected by the probe pulse is interfered with by the medium, generating the
transient interference in the energy domain. We also demonstrate the transient
interference in the presence of electron correlations in a one-dimensional
half-filled Hubbard model. Furthermore, bosons coupled to electrons additively
contribute to the interference. Our finding will provide an interpretation of
probe-energy-dependent oscillations recently observed in the pump-probe
spectrum for a two-dimensional Mott insulator.
