Dynamic tunneling ionization of excited hydrogen atoms: A precise experiment versus theories

Abstract

New data for no=24, . . . , 32 H atoms ionized b' a linearly polarized, 9.908-6Hz electric field are compared with calculations.Being more precise than laser multiphoton ionization experiments with tightly bound atoms, our experiments distinguish between tunneling through and classical escape o[.er a slowly oscillating barrier and between oneand many-state dynamical processes. Formulas used to interpret low-frequency laser multiphoton ionization data poorly describe our results. Our data delineate ranges of validity of other partly successful models and are best reproduced by a new 30 semiclassical model. PACS numbers: 32.80.Rm, 03.65.Sq, 73.40.Gk While the realization that a "particle" could traverse a classically impenetrable, static potential barrier arose early in the development of quantum mechanics, there has been continuing interest in (and some controversy [I] over) quantum-mechanical tunneling. Questions being raised [I] include the definition of tunneling time(s) and how a nonstationary barrier is traversed. Several theories [2-4] address the tunneling ionization of atoms in an oscillatory electric field with amplitude F. Tunneling interpretations have been applied to some intense-laser multiphoton ionization (LMPI) experiments [5-8], often with noble gas atoms or their positive ions. However, given that tunneling rates increase exponentially with F and that absolute determination of relevant peak intensities & 10' W/cm in focused laser beam pulses is said [8,9] to be diNcult even to a factor of 2, LMPI experiments have not provided sensitive tests of' dynamic tunneling theory. Indeed, the term tunneling ionization was even ascribed to LMPI experiments that were analyzed with a model based on classical, over-the-barrier escape [6(a)].In this Letter we use tunneling to refer specifically to a transition through a barrier, where the transition connects two states having the same total energy; we also contrast this with mechanisms, such as MPI, involving transitions to states with other energies.Our dat I come from micro~ave ionization of excited H atoms. Micro~ave technology facilitates precise determinations [10] of the field amplitude and pulse shape, a major advantage over LMPI experiments. Moreover, the simplicity of the hydrogen atom allows us to model details of the ionization process and make a direct comparison between experiment and theories. We find that a theory [4] often used [6-8] to model laser tunneling ion-Ization experiments fails to describe the present data. lt is convenient to use classically scaled variables [11] (r)t, .FO) for the f'requency to and amplitude F (atomic units are used throughout) of the applied field, where t&o=njj'to and Fo=noF The classical dyn. amics [11,12] depends on only these and not separately on m, F, and the principal classical action 10, here set equal (in a.u. ) to no Using results from Ref. [13] for each parabolic substate n =(no, n~,~m~), the highest [lowest] critical field F, '. ("(n) for classical escape is F0=0.38 [Fo=0.13] for the extremal upward-g...

Polarization Dependence of Microwave "ionization" of Excited Hydrogen Atoms

“…When Ω0 gets low enough, one expects quantal penetration of the slowly oscillating Coulomb-Stark potential barrier to become the dominant ionization mechanism. Comparisons of 9.91 GHz data for n0 = 24-32 with 3d quantal and theoretical calculations [94], reviewed in [1], show this behavior: as n0 decreases with fixed ω, the experimental onset of ionization falls systematically bełow the classical onset. A id theoretical model [43,95,96] reproduces and explains this behavior when the coupling constant Cn0 = 1.5n0(n30ω)(n40F) between adjacent quantal adiabatic basis states is sufficiently small.…”

“…As is now being prepared for publication, we have observed [81,161] that at very low Ω0 the quasistatic tunneling of regime-I becomes the dominant ionization mechanism even more dramatically for CP than it does for LP. The LP case was studied earlier [1,94].…”

“…F(t) = λ(t)ZF sin(ωt + ψ), with ψ an initial phase; again, separability leads to conservation of m. The dynamics is quasistatic [1,94] if 90 is suffIciently small and away from exponentially sharp resonances discussed theoretically for 1d in [43]. The spatial reversal of F on each half-cycle interchanges n 1 and n2; therefore, as Fig.…”

“…The spatial reversal of F on each half-cycle interchanges n 1 and n2; therefore, as Fig. 1 of [94] shows, for a uniform mixture of substates of a given n0, classically a microcanonical ensemble, the ionization probability Pi on rises from 0 to 1 as the scaled amplitude F0 varies between about 0.115-0.17. This is just the beginning of the wider classical range, F0 = 0.13-0.38, lowered 10-15% by tunneling, discussed above for the static field case.…”

Carrier Phase Dependence in the Ionization of Rydberg Atoms by Short Radio-Frequency Pulses: A Model System for High Order Harmonic Generation

“…Note that although the characteristic time scales and length scales of ground-state and Rydberg atoms are very different, the electron makes many round-trips per cycle of the field; hence, the electron samples the slowly varying potential in many orbits. The photon energy is much smaller than the binding energy in both cases, such that many photons are involved in the ionization process [15].…”