Tunnel Ionization Dynamics of Bound Systems in Laser Fields: How Long Does It Take for a Bound Electron to Tunnel?

A numerical method is developed by which the tunnel ionization dynamics of bound systems in laser fields can be isolated from the total wave function, as given by the time-dependent Schrodinger equation. The analysis of the numerical data for a step function field reveals the following definition for the tunnel time. It is the time it takes the ground state to develop the underbarrier wave function components necessary for reaching the static field ionization rate. This definition is generalized to time varying laser fields. The tunnel time is found to scale with the Keldysh tunnel time. Our Letter establishes the physical meaning of the tunnel time, its relation to the Keldysh tunnel time, and suggests how it can be measured.