VOLUME 70, NUMBER 4 PH YSICAL REVIEW LETTERS 25 JANUARY 1993 Atoms in Strong Optical Fields: Evolution from Multiphoton to Tunnel Ionization Eric Mevel, Pierre Breger, Rusty Trainham, Guillaume Petite, and Pierre Agostini Service de Recherches sur les Surfaces et I'Irradiation de la Matiere, Centre d'Etude de Sac!ay, 9l l 9I Gif Sur -Yvet-te, France Arnold Migus, Jean-Paul Chambaret, and Andre Antonetti I aboratoire O'Optique Appliquee, Ecole Nationale Superieure de Techniques Avancees, Ecole Polytechnique, 91120 Palaiseau, France (Received 24 August 1992) Electron energy spectra from ionization of the noble gases by 617-nm, 100-fs intense laser pulses show that the periodical double structure of narrow Stark-induced resonances and above-threshold ionization disappears gradually from xenon to helium. This implies that shifts and widths become of the order of the atomic-orbital frequencies, as expected at the onset of the tunneling regime. PACS numbers: 32.80. Fb, 32.80. Rm, 32.80.&r The behavior of atoms under strong irradiation has been a subject of constant interest ever since powerful laser sources became available. Although it is now rela- tively easy to produce extremely intense electromagnetic fields from compact, laboratory-sized laser systems, it is not possible to submit a given atom to an arbitrarily high intensity because it will be ionized before sensing the peak of the pulse. The maximum practical intensity, the saturation intensity, as defined by Lambropoulos [1], that can be applied to a neutral atom is determined by its ion- ization probability and the pulse characteristics. The upper limit for the saturation is reached by using state- of-the-art intense 70-fs pulses. The highest saturation in- tensities are obtained, under given laser conditions, with atoms having the highest ionization potential (e.g. , heli- um). However, the ionization rate is too small to allow a study of the interaction at low intensities. A qualitative idea of the atomic behavior over a large range of intensi- ties can nevertheless be obtained by studying similar atoms with increasing ionization potentials. The rare gases are well suited for this purpose and conveniently provide targets which span a factor of 2 in ionization po- tential and more than 10 in saturation intensities. Ionization is one of the possible outcomes of the light- atom interaction. In the regime of strong fields, multi- photon ionization (MPI) and tunnel ionization (TI) are the two limiting cases of the ionization process [2]. The ratio y of the tunneling time (i.e. , the width of the barrier divided by the electron velocity) to the optical period is known as the adiabaticity or Keldysh parameter and is generally used to separate the two regimes, ) =(IP/2U, ) '", where IP is the atom ionization potential and Uz the pon- deromotive potential of the laser, In the low frequency limit (y « I ), TI is a good description of the transition dynamics. This is typical of rare gases ionized by a CO2 laser, in which case the elec- tron tunnels out in a time less than half the field period while its energy and momentum are subsequently deter- mined by the Lorentz force [3]. In the other limit (y»1), the multiphoton character is evident in the pho- toelectron spectra as a structure repeated with the photon energy period [above-threshold ionization (ATI)] and whose rate scales as I, where I is the intensity and 1V the number of absorbed photons. This is typically the case for visible or uv excitation of an alkali atom. The ioniza- tion of rare gases by visible or near-infrared light spans a range of y's large enough to encompass both limits. Ac- cording to the definition above, y seems to be an increas- ing function of IP. However, y is an intensity-dependent parameter through U~. Therefore, the effective value of y depends on the intensity at which the ionization is actual- ly observed. It is qualitatively obvious that this intensity is an increasing function of the ionization potential. A quantitative estimate (known to be in good agreement with the experiment [4]) can be obtained by taking the threshold intensity for a (dc) field ionization, lych =IP /16Z (2) in the definition of U„ in (1). The result of this substitu- tion is that y actually scales as IP and therefore de- creases from xenon to helium. Furthermore, due to satu- ration, the effective y in an experiment depends also on the pulse rise time. For short pulses, good agreement with the tunnel ionization rate [S] was found [6,7]. To study ionization, one possible option is to measure the power law of the total yield as a function of the in- cident intensity. However, it is also well known that such measurements are difficult and may lead to inconclusive results. The energy spectra of the photoelectrons result- ing from the interaction between a laser pulse and an atom are known to carry somewhat more information than the ions. Many features that had remained hidden in total ion yield measurements have been uncovered by electron spectroscopy: the nonperturbative character of ATI, Stark-induced resonances (Freeman et al. [8]), etc. These were the two basic motivations of the current work, in which we try to reconstruct a typical atomic response to strong fields over a large intensity range from 406 1993 The American Physical Society