Tunneling Ionization Rates from Arbitrary Potential Wells

We present a practical numerical technique for calculating tunneling ionization rates from arbitrary 1-D potential wells in the presence of a linear external potential by determining the widths of the resonances in the spectral density, ρ(E), adiabatically connected to the field-free bound states. While this technique applies to more general external potentials, we focus on the ionization of electrons from atoms and molecules by DC electric fields, as this has an important and immediate impact on the understanding of the multiphoton ionization of molecules in strong laser fields. While the behavior of atoms and molecules in strong laser fields has been studied for almost two decades, new phenomena continue to arise and a unified picture for either does not yet exist [1, 2, 3]. However, simple models for tunneling ionization [4, 5] have provided a crucial baseline for understanding atoms in strong fields, as deviations from this basic process in ion yields and electron energy spectra have pointed to new physics [1, 2, 6]. Conversely, the lack of a general tunneling model for molecules has seriously impeded the interpretation of molecular data which clearly hints at even richer phenomena [3, 7] than for atoms due to the extra degrees of freedom present in a molecule. Ionization from even diatomic potential wells are more difficult to treat than atoms because the barrier to ionization can shift between the barrier separating the two wells and the outer barrier as a function of field strength and internuclear separation [8] (see Fig. 1). These situations are quite distinct and, indeed, this competition between barriers leads to interesting and complex behavior. Thus, it is critical for any tunneling ionization model to work for arbitrary potential wells so as to treat these different situations uniformly. Furthermore, a useful model for molecules in strong laser fields must be non-perturbative in both the rates and the Stark shifts. In this Letter we introduce a practical non-perturbative technique for computing tunneling ionization rates from an arbitrary 1-D potential well. After outlining the general method, we apply it to a single-well (‘atomic’) potential, yielding