Tunnel ionization
In an intense electric field, the potential barrier of an atom (molecule) is distorted drastically.
Tunneling ionization is a quantum mechanical phenomenon since in the classical picture an electron does not have sufficient energy to overcome the potential barrier of the atom.
The electron may recombine with the nucleus (nuclei) and its kinetic energy is released as light (high harmonic generation).
If the recombination does not occur, further ionization may proceed by collision between high-energy electrons and a parent atom (molecule).
[1] Tunneling ionization from the ground state of a hydrogen atom in an electrostatic (DC) field was solved schematically by Lev Landau,[2] using parabolic coordinates.
This provides a simplified physical system that given it proper exponential dependence of the ionization rate on the applied external field.
In SI units the previous parameters can be expressed as: The ionization rate is the total probability current through the outer classical turning point.
This rate is found using the WKB approximation to match the ground state hydrogen wavefunction through the suppressed coulomb potential barrier.
Thus, atoms with low ionization energy (such as alkali metals) with electrons occupying orbitals with high principal quantum number
The ionization rate of a hydrogen atom in an alternating electric field, like that of a laser, can be treated, in the appropriate limit, as the DC ionization rate averaged over a single period of the electric field's oscillation.
Multiphoton and tunnel ionization of an atom or a molecule describes the same process by which a bounded electron, through the absorption of more than one photon from the laser field, is ionized.
When the intensity of the laser is strong, the lowest-order perturbation theory is not sufficient to describe the MPI process.
In this model, the perturbation of the ground state by the laser field is neglected and the details of atomic structure in determining the ionization probability are not taken into account.
The major difficulty with Keldysh's model was its neglect of the effects of Coulomb interaction on the final state of the electron.
As is observed from the figure, the Coulomb field is not very small in magnitude compared to the potential of the laser at larger distances from the nucleus.
A. M. Perelomov, V. S. Popov and M. V. Terent'ev [6][7] included the Coulomb interaction at larger internuclear distances.
[8] Many experiments have been carried out on the MPI of rare gas atoms using strong laser pulses, through measuring both the total ion yield and the kinetic energy of the electrons.
These findings weakened the suspicion on the applicability of models basically founded on the assumption of a structureless atom.
S. Larochelle et al.[12] have compared the theoretically predicted ion versus intensity curves of rare gas atoms interacting with a Ti:sapphire laser with experimental measurement.
They have shown that the total ionization rate predicted by the PPT model fits very well the experimental ion yields for all rare gases in the intermediate regime of Keldysh parameter.
is the charge of atomic or ionic core) at a long distance from the nucleus, is calculated through first order correction on the semi-classical action.
Walsh et al.[14] have measured the MPI rate of some diatomic molecules interacting with a 10.6 μm CO2 laser.
They found that these molecules are tunnel-ionized as if they were structureless atoms with an ionization potential equivalent to that of the molecular ground state.
A. Talebpour et al.[15][16] were able to quantitatively fit the ionization yield of diatomic molecules interacting with a Ti:sapphire laser pulse.
The conclusion of the work was that the MPI rate of a diatomic molecule can be predicted from the PPT model by assuming that the electron tunnels through a barrier given by
[18] The question of how long a tunneling particle spends inside the barrier region has remained unresolved since the early days of quantum mechanics.
In a recent publication[20] the main competing theories of tunneling time are compared against experimental measurements using the attoclock in strong laser field ionization of helium atoms.
Refined attoclock measurements reveal a real and not instantaneous tunneling delay time over a large intensity regime.
It is found that the experimental results are compatible with the probability distribution of tunneling times constructed using a Feynman path integral (FPI) formulation.
[21][22] However, later work in atomic hydrogen has demonstrated that most of the tunneling time measured in the experiment is purely from the long-range Coulomb force exerted by the ion core on the outgoing electron.
