Multiphoton ionization by a very short pulse

The detachment of a bound electron by an electric field pulse whose duration ranges from a fraction of to a few times the optical cycle but is long compared to $\hbar /I$ ($\hbar$ — Planck constant, $I$ — binding energy) is studied theoretically, simulating the ionization of atoms by extremely short laser pulses. Because of the strong nonlinearity, the solution to the problem does not reduce to the sum of monochromatic harmonic contributions and depends significantly on the pulse shape features. A general analysis is carried out for an analytical pulse shape, and exact formulas are given for standard pulse shapes such as solitonlike, gaussian, lorenzian, etc., one or a half optical cycle in duration. The intensity and pulse length dependences of the ionization probability are of a near-universal tunneling type at high intensities. However, at moderate intensities in the multiphoton regime, these dependences differ widely for different pulse shapes, with ionization probabilities always a few orders of magnitude higher than for ionization by a monochromatic wave of the same intensity and mean frequency.