Instantaneous ionization rate as a functional derivative. Issue 1 (December 2018) - Ivanov, I.; Hofmann, C.; Ortmann, L.; Landsman, A.; Nam, Chang; Kim, Kyung
Abstract The notion of the instantaneous ionization rate (IIR) is often employed in the literature for understanding the process of strong field ionization of atoms and molecules. This notion is based on the idea of the ionization event occurring at a given moment of time, which is difficult to reconcile with the conventional quantum mechanics. We describe an approach defining instantaneous ionization rate as a functional derivative of the total ionization probability. The definition is based on physical quantities, such as the total ionization probability and the waveform of an ionizing pulse, which are directly measurable. The definition is, therefore, unambiguous and does not suffer from gauge non-invariance. We compute IIR by numerically solving the time-dependent Schrödinger equation for the hydrogen atom in a strong laser field. In agreement with some previous results using attoclock methodology, the IIR we define does not show measurable delay in strong field tunnel ionization. There has been much recent experimental and theoretical interest in the physics of ionization, in particular the question of tunneling time. In this work, the authors derive a gauge invariant definition of the instantaneous ionization rate as a functional derivative of the total ionization probability.