Transient phenomena of phase-modulated cutoff wave packets are explored by deriving an exact general solution to Schrödinger's equation for finite-range potentials involving arbitrary initial quantum states. We show that the dynamical features of the probability density are governed by a virtual self-induced two-level system with energies $E_{+}$ and $E_{-}$ due to the phase modulation of the initial state. The asymptotic probability density exhibits Rabi oscillations characterized by the frequency $\mathrm{\Omega }=(E_{+}-E_{-})/\hslash$, which are independent of the potential profile. It is also found that for a system with a bound state, the interplay between the virtual levels with the latter causes a quantum beat effect with a beating frequency, $\mathrm{\Omega }$. We also find a regime characterized by a time-diffraction phenomenon that allows us to measure unambiguously the delay time, which can be described by an exact analytical formula. It is found that the delay time agrees with the phase time only for the case of strictly monochromatic waves.

• Received 12 January 2020
• Accepted 11 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.042109