Inherent contradictions in the tunneling-multiphoton dichotomy

Abstract

Strong-field phenomena are currently described as being multiphoton or tunneling, based on whether the Keldysh parameter $\gamma$ is greater than or less than unity. There are disqualifying features in this categorization. It is specific to the length gauge, dependent on only one intensity parameter, and backward in the sense that ionization with $\gamma ⪢1$ can occur only by tunneling, and ionization with $\gamma ⪡1$ must be over the barrier, and hence is not achieved by tunneling. As $\gamma$ becomes smaller, ionization becomes increasingly distant from tunneling, and eventually reaches conditions where the dipole approximation fails and there is no meaningful scalar-potential diagram at all.