Resolving in time the dynamics of light absorption by atoms and molecules, and the electronic rearrangement this induces, is among the most challenging goals of attosecond spectroscopy. The attoclock is an elegant approach to this problem, which encodes ionization times in the strongfield regime. However, the accurate reconstruction of these times from experimental data presents a formidable theoretical challenge. Here, we solve this problem by combining analytical theory with ab-initio numerical simulations. We apply our theory to numerical attoclock experiments on the hydrogen atom to extract ionization time delays and analyse their nature. Strong field ionization is often viewed as optical tunnelling through the barrier created by the field and the core potential. We show that, in the hydrogen atom, optical tunnelling is instantaneous. By calibrating the attoclock using the hydrogen atom, our method opens the way to identify possible delays associated with multielectron dynamics during strong-field ionization.

We develop the recently proposed analytical R-matrix (ARM) method to encompass strong field ionization by circularly polarized fields, for atoms with arbitrary binding potentials. Through the ARM method, the effect of the core potential can now be included consistently both during and after ionization. We find that Coulomb effects modify the ionization dynamics in several ways, including modification of (i) the ionization times, (ii) the initial conditions for the electron continuum dynamics, (iii) the "tunneling angle," at which the electron "enters" the barrier, and (iv) the electron drift momentum. We derive analytical expressions for the Coulomb-corrected ionization times, initial velocities, momentum shifts, and ionization rates in circularly polarized fields, for arbitrary angular momentum of the initial state. We also analyze how nonadiabatic Coulomb effects modify (i) the calibration of the attoclock in the angular streaking method and (ii) the ratio of ionization rates from p − and p + orbitals, predicted by I. Barth and O. Smirnova [Phys. Rev. A 84, 063415 (2011)] for short-range potentials.

Electron-core interactions play a key role in strong-field ionization and the formation of photoelectron spectra. We analyse the temporal dynamics of strong field ionization associated with these interactions using the time-dependent analytical R-matrix (ARM) method, developed in our previous work [J. Kaushal and O. Smirnova, Phys. Rev. A 88, 013421 (2013)]. The approach is fully quantum but includes the concept of trajectories. However, the trajectories are not classical in the sense that they have both real and imaginary components all the way to the detector. We show that the imaginary parts of these trajectories, which are usually ignored, have a clear physical meaning and are crucial for the correct description of electron-core interactions after ionization.In particular, they give rise to electron deceleration, as well as dynamics associated with electron recapture and release. Our approach is analytical and time-dependent, and allows one to gain access to the electron energy distribution and ionization yield as a function of time. Thus we can also rigorously answer the question: when is ionization completed? 1 arXiv:1308.1348v1 [physics.atom-ph]

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Strong field ionization by circularly polarized laser fields from initial states with internal orbital momentum has interesting propensity rule: electrons counter-rotating with respect to the laser field can be liberated more easily than co-rotating electrons [Barth and Smirnova PRA 84, 063415, 2011]. Here we show that application of few-cycle IR pulses allows one to use this propensity rule to detect ring currents associated with such quantum states, by observing angular shifts of the ejected electrons. Such shifts present the main observable of the attoclock method. We use timedependent Analytical R-Matrix (ARM) theory to show that the attoclock measured angular shifts of an electron originating from two counter-rotating orbitals (p + and p − ) are noticeably different. Our work opens new opportunities for detecting ring currents excited in atoms and molecules, using the attoclock set-up.

Abstract. Photoionisation is a process where absorption of one or several photons liberates an electron and creates a hole in a quantum system, such as an atom or a molecule. Is it faster to remove an electron using one or many photons, and how to define this time? Here we introduce a clock that allows us to define ionisation time for both one-photon and many-photon ionisation regimes. The clock uses the interaction of the electron or hole spin with the magnetic field created by their orbital motion, known as the spin-orbit interaction. The angle of spin precession in the magnetic field records time. We use the combination of analytical theory and ab-initio calculations to show how ionisation delay depends on the number of absorbed photons, how it appears in the experiment and what electron dynamics it signifies. In particular, we apply our method to calculate the derived time delays in tunnelling regime of strongfield ionisation.

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Here and in the two companion papers we use time-dependent analytical R-Matrix (ARM) theory to consider the impact of electron-core interaction on (i) sensitivity of strong field ionisation to the sense of electron rotation in the initial state and (ii) electron spin polarisation. ARM is a rigorous approach to strong field ionisation that takes advantage of the semiclassical nature of electron dynamics in strong laser fields and naturally incorporates complex-valued classical trajectories in the timepropagation. While the appearance of complex time is associated with optical tunnelling, complex coordinates reflect non-adiabaticity of the electron response to the strong laser field. We focus on non-adiabatic electron-core interaction in the sub-barrier region and show how it affects ionisation from orbitals with high angular momentum ℓ=2, 3 in multiply charged atomic ions with strong electron-core interaction. In this paper we discuss sub-cycle ionisation yields, while in the companion papers we focus on the effects of the long-range core potential on the 'initial conditions' (from the ARM perspective, companion paper II) for the photo electron as it emerges from the classically forbidden region and on the spin polarisation of the ejected electron (companion paper III).