We explore the similarity between dc-field ionization and low-frequency multiphoton ionization atoms. If the frequency ω of the light is below the characteristic atomic-orbital frequency ${\mathrm{\omega }}_{\mathrm{at}}$, ionization of the atom occurs by tunneling provided that the intensity I is sufficiently high that the ratio of the tunneling time to the cycle time—this is essentially the ‘‘Keldysh parameter’’ γ— is less than unity. However, if I exceeds a critical intensity ${\mathit{I}}_{\mathrm{cr}}$, the electron flows over the top of the potential barrier rather than tunneling through it. ${\mathit{I}}_{\mathrm{cr}}$ depends on the magnetic quantum number m of the initial bound state, and is proportional to, but significantly less than, the characteristic atomic intensity. We give a simple approximate expression for ${\mathit{I}}_{\mathrm{cr}}$ in terms of m, valid in the absence of an exceptional symmetry (such as exists for hydrogen). We find that ${\mathit{I}}_{\mathrm{cr}}$ increases as m does; consequently, electrons with m=0 are stripped first as the intensity rises, and the residual ion will be left in a state of alignment, in agreement with calculations of ionization rates for Xe [K. Kulander, Phys. Rev. A 38, 778 (1988)].

We present results of Floquet calculations of rates for ionization of H(1s) by circularly or linearly polarized light in the wavelength range 355 to 1064 nm, at intensities somewhat below ${\mathit{I}}_{\mathrm{cr}}$. At these wavelengths, the rates approach more or less the same value as I increases, in accord with the Keldysh tunneling theory. We show that, provided ω<${\mathrm{\omega }}_{\mathrm{at}}$, the ac shift and the ac width, respectively, tend to the dc shift and the dc width (cycle averaged over the instantaneous field) once I is sufficiently large when γ<1. On the other hand, we show that for ω>${\mathrm{\omega }}_{\mathrm{at}}$ there is no tunneling regime; rather, in the absence of strong intermediate resonances, the ionization rate reaches a peak when γ≊1, and decreases toward zero as γ does. Presumably the Floquet picture becomes inadequate when the ionization width Γ approaches the photon energy ħω, for then ionization takes place in less than a cycle. We speculate as to how the Floquet picture breaks down and, finally, we show that the statement Γ≊ħ${\mathrm{\omega }}_{\mathrm{at}}$ yields the correct Z scaling of ${\mathit{I}}_{\mathrm{cr}}$ for ionization in a Coulomb field.

• Received 11 April 1990

DOI:https://doi.org/10.1103/PhysRevA.42.1656