Ultrafast propagation of Schrödinger waves in absorbing media

We show that the temporal peak of a quantum wave may arrive at different locations simultaneously in an absorbing medium. The arrival occurs at the lifetime of the particle in the medium from the instant when a point source with a sharp onset is turned on. We also identify other characteristic times. In particular, the “traversal” or “Büttiker-Landauer” time (which grows linearly with the distance to the source) for the Hermitian, non-absorbing case is substituted by several characteristic quantities in the absorbing case. The simultaneous arrival due to absorption, unlike the Hartman effect, occurs for carrier frequencies under or above the cutoff, and for arbitrarily large distances. It holds also in a relativistic generalization but limited by causality. A possible physical realization is proposed by illuminating a two-level atom with a detuned laser.