Interference effects in photodetachment of F - in a strong circularly polarized laser pulse S. Bivona, G. Bonanno, R. Burlon, * and C. Leone Dipartimento di Fisica e Tecnologie Relative, Universitá degli Studi di Palermo, Palermo, Italy and CNR-CNISM, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy Received 25 May 2007; published 30 August 2007 A numerical simulation of photodetachment of F - by a circularly polarized laser pulse has been accom- plished by using a Keldysh-type approach. The numerical results are in agreement with measurements of photoelectron energy spectra recently reported in the literature. The features exhibited by the spectra are traced back to quantum interference effects, in the same spirit as in a double-slit experiment in the time domain. DOI: 10.1103/PhysRevA.76.021401 PACS numbers: 32.80.Rm, 32.80.Gc Recent developments in laser technology have made it possible to produce short, high-power laser pulses with du- rations of a few optical cycles, which have become available as research tools 1. For not too short pulses, the electric field may be represented as a product of a monochromatic carrier wave and a positive-definite envelope function. One of the parameters characterizing this type of pulse is the so- called carrier-envelope relative phase. By varying this pa- rameter, the temporal shape of the pulse may vary signifi- cantly, allowing coherent control and study of elementary atomic processes. An instance of application of this source to the study of quantum fundamental processes was recently given in attosecond double-slit experiments in the time- energy domain 2. In these experiments, due to the highly nonlinear processes, the ionization occurs in time windows having a duration of attoseconds. By changing the relative carrier-envelope phase, the temporal shape of the field may be altered in such a way that the time windows may be “open” or “closed”, controlling the recorded photoelectron spectra modulations which can be described in terms of quantum interference. In order to describe the ionization of an atomic system irradiated by strong laser fields, different nonperturbative methods have been developed 3–10. The strong-field ap- proximation 3–5 is one of the most widely used models because of its analyticity. The main assumption of this ap- proximation is that the action of the ionic Coulomb field on the photoelectron may be be neglected with respect to the driving effect of the laser field, and, therefore, the final elec- tron state may be described by a Volkov wave function. This treatment is believed to describe more accurately the photo- detachment of negative ions, because of the short-range na- ture of the interaction between the photodetached electron and the parent atom. By using a saddle-point method, Gribakin and Kuchiev 6 have given an analytical solution to the problem of mul- tiphoton detachment by a monochromatic linearly polarized laser field, and have shown that the rapid oscillations in the angular distribution of the n-photon detachment rate may be described in terms of interference of two classical trajectories leading to the same final electron state. In Ref. 11, Beiser et al. extended the approach of Grib- akin and Kuchiev to the multiphoton detachment of a nega- tive ion by a monochromatic circularly polarized field. By a saddle-point analysis of the transition amplitude they in- ferred that quantum interference effects do not occur in the direct process of photodetachment by a circularly polarized laser field. Recently, an image technique has been used to measure the energy- and angle-resolved spectrum of elec- trons produced by the photodetachment of F - exposed to a circularly polarized infrared femtosecond laser field 12. The image processing involves a conventional Abel inver- sion routine, which requires that the electrons be emitted symmetrically with respect to the axis perpendicular to the static electric field that projects the photoelectrons in the x , z plane 13, z being the propagation pulse direction. We remark that, while electron emission caused by a monochro- matic circularly polarized laser field is expected to be sym- metrically distributed around the pulse propagation direction, the azimuthal symmetry breaks down when electrons are de- tached by short laser pulses. In fact, because during its rota- tion the electric field amplitude varies, the electron distribu- tion turns out to depend on the azimuthal angle  between the component of the electron momentum q parallel to the laser polarization plane and the axis along which the electric field reaches its maximum value. However, below we will show that the ejected electron distribution anisotropy is strongly reduced when the spatial distribution of the laser pulse intensity is taken into account, restoring the require- ment for using the above-mentioned experimental technique. Of course, in order to understand the features of the recorded electron energy spectra, it is of crucial importance to include the temporal and spatial laser intensity distribution in the simulation. The experimental results show that the angular distribution of the electrons ejected at a given energy, as a function of the angle  between the photoelectron emission direction and the laser pulse propagation direction, does not exhibit any structure that can be associated with quantum interference effects. Instead, the energy distribution of pho- toelectrons emitted in the polarization plane exhibits struc- tures whose origin has not yet been discussed. The aim of this Rapid Communication is to show that the experimental electron energy spectra exhibit features surviving the damp- ing effects of the laser spatial inhomogeneity that can be explained in terms of quantum interferences. The simulation of the experimental data will be performed by using the Keldysh theory modified to include the shape of the laser *burlon@unipa.it PHYSICAL REVIEW A 76, 021401R2007 RAPID COMMUNICATIONS 1050-2947/2007/762/0214014 ©2007 The American Physical Society 021401-1