Multiple Ionization in Strong Laser Fields

R. Dörner, *doerner@hsb.uni-frankfurt.de; Th. Weber; M. Weckenbrock; A. Staudte; M. Hattass; H. Schmidt-Böcking    Institut für Kernphysik, August Euler Sir. 6, 60486 Frankfurt, Germany

R. Moshammer; J. Ullrich    Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

I Introduction

70 years ago Maria Göppert-Mayer [1] showed that the energy of many photons can be combined to achieve ionization in cases where the energy of one photon is not sufficient to overcome the binding. Modern short-pulse Ti:Sa lasers (800 nm, 1.5 eV) routinely provide intensities of more than 1016 W/cm2 and pulses shorter than 100 femtoseconds. Under these conditions the ionization probability of most atoms is close to unity. 1016 W/cm2 corresponds to about 1010 coherent photons in a box of the size of the wavelength (800 nm). This extreme photon density allows highly nonlinear multiphoton processes such as multiple ionization, where typically more than 50 photons can be absorbed from the laser field.

Such densities of coherent photons in the laser pulse also suggests a change from the “photon perspective” to the “field perspective”: The laser field can be described as a classical electromagnetic field, neglecting the quantum nature of the photons. From this point of view the relevant quantities are the field strength and its frequency. 1016 W/cm2 at 800 nm corresponds to a field of 3×1011 V/m, comparable to the field experienced by the electron in a Bohr orbit in atomic hydrogen (5 × 1011 V/m).

Single ionization in such strong fields has been intensively studied for many years now. The experimental observables are the ionization rates as function of the laser intensity and wavelength, the electron energy and angular distribution as well as the emission of higher harmonic light. We refer the reader to several review articles covering this broad field [2–4]. Also the generation of femtosecond laser pulses has been described in a number of detailed reviews [5–8].

The present article focuses on some recent advances in unveiling the mechanism of double and multiple ionization in strong fields. Since more particles are involved, the number of observables and the challenge to the experimental as well as to the theoretical techniques increases. Early studies measured the rate of multiply charged ions as a function of laser intensity. The work reviewed here employs mainly COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) [9] to detect not only the charge state but also the momentum vector of the ion and of one of the electrons in coincidence. Today such highly differential measurements are standard in the fields of ion–atom, electron–atom and high-energy single-photon–atom collision studies.

The main question discussed in the context of strong fields as well as in the above-mentioned areas of current research is the role of electron correlation in the multiple ionization process. Do the electrons escape from the atom “sequentially” or “nonsequentially,” i.e. does each electron absorb the photons independently, or does one electron absorb the energy from the field and then share it with the second electron via electron–electron correlation?

Despite its long history the underlying question of the dynamics of electron correlation is still one of the fundamental puzzles in quantum physics. Its importance lies not only in the intellectual challenge of the few-body problem, but also in its wide-ranging impact to many fields of science and technology. It is the correlated motion of electrons that is responsible for the structure and the evolution of large parts of our macroscopic world. It drives chemical reactions, it is the ultimate reason for superconductivity and many other effects in the condensed phase. In atomic processes few-body correlation effects can be studied in a particularly clear manner. This, for example, was the motivation for studying theoretically and experimentally the question of double ionization by charged-particle (see ref. [10] for a review) or single-photon [11,12] impact in great detail. As soon as lasers became strong enough to eject two or more electrons from an atom, electron correlation in strong light fields became subject of increased attention, too. As we will show below, in comparison with some of the latest results on double ionization by ion and single-photon impact, the laser field generates new correlation mechanisms, thereby raising more exciting new questions than settling old ones.

II COLTRIMS – A Cloud Chamber for Atomic Physics

For a long time the experimental study of electron correlation in ionization processes of atoms, molecules and solids has suffered from the technical challenge to observe more than one electron emerging from a multiple ionization event. The main problem lies in performing coincidence studies employing conventional electron spectrometers, which usually cover only a small part of the total solid angle. COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) is an imaging technique that solves this fundamental problem in atomic and molecular coincidence experiments. Like the cloud chamber and its modern successors in nuclear and high-energy physics, it delivers complete images of the momentum vectors of all charged fragments from an atomic or molecular fragmentation process. The key feature of this technique is to provide a 4π collection solid angle for low-energy electrons (up to a few hundred eV) in combination with 4π solid angle and high resolution for the coincident imaging of the ion momenta.

As we will show below, the ion momenta in most atomic reactions with photons or charged particles are of the same order of magnitude as the electron momenta. Due to their mass, however, this corresponds to ion energies in the range of μeV to meV. These energies are below thermal motion at room temperature. Thus, the atoms have to be cooled substantially before the reaction. In the experiments discussed here this is achieved by using a supersonic gas jet as a target. More recently, atoms in magneto-optical traps have been used to further increase the resolution [13–16].

A typical setup as used for the experiments discussed here is shown in Fig. 1. The laser pulse is focused by a lens of 5 cm focal length or a parabolic mirror into a supersonic gas jet providing target atoms with very small initial momentum spread of under 0.1 au (atomic units are used throughout this chapter) in the direction of the laser polarization (along the z-axis in Fig. 1). For experiments in ion–atom collisions or with synchrotron radiation the ionization probability is very small: That is why one aims at a target density in the range of up to 10− 4 mbar local pressure in the gas jet. Accordingly, a background pressure in the chamber in the range of 10− 8 mbar is sufficient. In contrast, for multiple ionization by femtosecond laser pulses the single ionization probability easily reaches unity. Thus, within the reaction volume defined by the laser focus of typically (10 μm)2 × 100 μm all atoms are ionized. Since for coincidence experiments it is essential that much less than one atom is ionized per laser shot, a background pressure of less than 10− 10 mbar is required. The gas jet has to be adjusted accordingly to reach single-collision conditions at the desired laser peak power. With standard supersonic gas jets this can only be achieved by tightly skimming the atomic beam, since a lower driving pressure for the expansion would result in an increase of the internal temperature of the jet along its direction of propagation. Single ionization (see Sect. III) allows for an efficient monitoring of the resolution as well as on-line control of single-collision conditions.

The ions created in the laser focus are guided by a weak electric field towards a position-sensitive channel plate detector. From the position of impact and the time-of-flight (TOF) of the ion all three components of the momentum vector and the charge state are obtained. A typical ion TOF spectrum from the experiment reported in ref. [17] is shown in Fig. 2.

The electric field also guides the electrons towards a second position-sensitive channel plate detector. To collect electrons with large energies...