Temporal and spectral evolution of an interrupted virtual single-photon transition: creation of optical gain and loss

We examine the optical response of a virtual dipole transition of a quantum mechanical two-level system (TLS). In the case of off-resonant excitation the time-integrated dipole response (TIDR) is expected to be zero, which corresponds to transparency of the system with respect to the exciting pulse. Our new time-frequency representation reveals that even for a zero TIDR there are positive and negative contributions included in the response. Furthermore, we present a way to access these contributions by using a second electromagnetic field, which interrupts the temporal evolution of the dipole response. The theoretical results are confirmed by attosecond transient absorption spectroscopy in helium (He).