Coulomb asymmetry and sub-cycle electron dynamics in multiphoton multiple ionization of H2

We present a systematic study of the molecular-frame photo-electron angular distributions produced by multiphoton double ionization of H2 using circularly polarized 800 nm, femtosecond laser pulses. We compare experimental results to numerical results obtained from a reduced-dimensionality time-dependent Schrödinger equation (TDSE) model. In addition, we implement a TDSE-like version of the strong-field approximation to isolate the effect of the parent ion’s Coulomb potential on the continuum electron in our simulations. Thereby we identify the contributions of the parent ion potential, and light induced sub-optical cycle electron dynamics on the observable energy and angular distributions. (Some figures may appear in colour only in the online journal) The basic principles of attosecond science in intense laser fields are readily understood with a few simplifications, such as treating the optical field classically, neglecting the parent ion potential after ionization and ignoring the detailed electronic structure of the parent atom or molecule. The last two decades have provided ample opportunity to probe the validity of these basic assumptions. In particular, the importance of the parent ion’s Coulomb potential for the continuum electron wave packet has been widely recognized and studied in the ionization of atoms by linearly polarized light (e.g., [1–8]), where it has been named Coulomb focusing, and elliptically polarized light (e.g., [9–14]), where it is known as Coulomb asymmetry due to mainly a rotation of the photo-electron 6 Present address: Novaled AG, Tatzberg 49, D-01307 Dresden, Germany. 7 Present address: Carl Zeiss Microscopy GmbH, Rudolf-Eber-Str. 2, D-73447 Oberkochen, Germany. angular distributions. The recently introduced technique of attosecond angular streaking relies on a precise accounting of this rotation that accompanies ionization by circular fields [15, 16]. However, under some circumstances, the parent ion’s potential can be neglected. For example, experiments along the lines of laser scanning tunnelling microscopy (laser-STM) [17] with the goal of imaging static [17–22] and transient [23, 24] electronic structure have largely ignored Coulomb effects. The extension of laser-STM to more complex systems, such as the recently suggested charge migration processes in molecular ions [25, 26], require a careful understanding of its limitations. While the influence of the Coulomb potential in atomic ionization is now well understood (e.g., [5, 27–32] and references therein), only a few attempts [33–37] have been made to unravel the qualitative effects on the strongfield photo-electron spectrum due to higher charge states and 0953-4075/12/194011+10$33.00 1 © 2012 IOP Publishing Ltd Printed in the UK & the USA J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 194011 M Spanner et al non-isotropic Coulomb potentials, i.e. distributed charges, as they occur in molecules. Here, we study the effect of a doubly charged, twocentre Coulomb potential on the asymptotic momentum distribution of a tunnel-ionized photo-electron. For this purpose we recorded the strong-field-molecular-frame photoelectron angular distributions (SF-MFPADs) from doubly ionized H2 and D2 in circularly polarized, 800 nm laser pulses. The SF-MFPADs of the second ionization exhibit a very strong Coulomb asymmetry compared to the first ionization step. In addition they provide evidence for sub-cycle ionization bursts. We then compare the experiment to solutions of a reduceddimensionality time-dependent Schrödinger equation (TDSE). In order to clearly isolate the effect of the Coulomb potential on the photo-electrons, we couple the laser-dressed boundstate dynamics to a Coulomb-free continuum. We find that the molecular ion distorts and blurs the asymptotic momentum space of the photo-electron beyond a simple rotation of the SF-MFPADs. Much of the complexity of laser-molecule interaction is already manifest in the hydrogen molecule. Hence, studies of H2 in intense laser pulses provide understanding of how the electronic structure of a molecule can give rise to new phenomena, such as electron localization—a fundamental response of molecular systems driven by strong laser fields. Electron localization is the underlying mechanism of phenomena such as bondsoftening [38, 39], charge resonance enhanced ionization (CREI) (thereafter referred to as enhanced ionization (EI)) [40], and sub-cycle ionization bursts [41] (for a review see, e.g. [42]). The so-called EI [40] is a sequential double ionization mechanism where the second ionization step is preceded by bondsoftening, a non-ionizing, light induced breaking of the molecular bond [38, 39]. The ionization then occurs typically at two to four times the equilibrium internuclear separation. While predicted for the neutral H2 [43], the overwhelming majority of experiments has associated EI with H2 and other molecular ions as the precursor molecule (e.g., [44–52]). Molecular ions undergoing EI are therefore ideal candidates to study charge state and charge distribution effects on the ionized electron wave packet. The experiment was performed using cold target recoil ion momentum spectroscopy [53]. The details of the experiment have been published before [50]. We use relatively low electrostatic extraction fields of 20–30 V cm−1 in our spectrometer. A Ti:Sa based regenerative amplifier was used to produce 40 fs, 800 nm pulses, which were focussed to peak intensities of up to 3 × 1014 W cm−2. For a subset of the data presented here, we used laser pulses from a second Ti:Sa laser system, which were spectrally broadened in an argon filled hollow core fibre and subsequently compressed to 10 fs using chirped mirrors. Whereas in [50] we presented the ion energy spectra we now concentrate on the correlated electron spectra for circularly polarized light. Figure 1(a) shows the kinetic energy release (KER) spectrum of the detected protons in the bondsoftening (H + H+) and the EI channel (H+ + H+) as a white area and a grey area, respectively. Since the bondsoftening channel yields only one charged fragment, the KER is calculated from twice the momentum of the detected proton. For the EI channel two correlated protons are required and their relative momentum is used to calculate the KER. The two peaks in the bondsoftening channel arise from dissociation via the net-1 and net-2 photon channels [38, 39]. Their individual width is dictated by the width of the nonadiabatic curve crossings of the field-coupled 1sσg and 2pσu states in H2 . Since the dissociation occurs after the first ionization, both bondsoftening channels are integrated for studying electron spectra. The structure in the KER spectrum of EI has been shown to arise from the interference of the nuclear wave packets in the net-1 and net-2 photon channels [50, 54] and has a related origin as the subcycle ionization bursts identified recently [41]. In contrast to bondsoftening, the KER spread for EI can be related to an internuclear distance R at the instant of the second ionization step through the established relation R = (KER − 1 eV)−1 [55, 56]. Hence, we can compare the influence of singly and doubly charged Coulomb potentials as well as the effect of increasing anisotropy in the charge distribution. In the following we make the assumption that the photo-electron emitted in the single ionization channel with subsequent dissociation (SI+BS channel), is identical to the primary ionization step in CREI, the double ionization channel of H2. This assumption is based on the well established sequential nature of CREI [44–50]. Although we can detect more than one electron, we cannot distinguish between the photo-electrons from the first and second ionization step on an event-by-event basis. Thus, the momentum distribution of the detected photo-electron in the CREI channel is an incoherent sum of a primary ionization and the secondary ionization. With the above assumption we can isolate the distributions pertaining to the secondary ionization by subtracting the distribution measured in the SI+BS channel. In figure 1(b) we compare the electron energy spectra for the primary ionization step (white area) and the secondary ionization (grey area). The energy spectrum for the secondary ionization was obtained by subtracting the distribution for the primary ionization scaled to one half of the area in the EI channel. In circularly polarized light the asymptotic electron momentum describes a torus in the polarization plane, i.e. the electron energy will be proportional to the peak intensity [57, 58]. Furthermore, in the absence of the ion potential, the asymptotic electron momentum can be shown to point at an angle of 90◦ relative to the field at the time of ionization [19–21, 23]. Although we measure the electron distribution in the lab frame from an unaligned ensemble of H2 molecules, the detection of a proton fixes the molecular axis and allows the transformation ex post facto into the molecular frame. Thereby we implicitly assume that the dissociation occurs fast on the time scale of rotation and is known as the axialrecoil approximation. Figure 1(c) shows the molecular-frame photo-electron angular distribution from the first ionization step, followed by the breakup of H2 via bondsoftening (white area), and the second ionization step (grey area), followed by Coulomb explosion. In the latter SF-MFPAD we removed the contribution of the first ionization step by subtracting the SF-MFPAD of the bondsoftening channel.