Slalom in complex time: emergence of low-energy structures in tunnel ionization via complex time contours

The ionization of atoms by strong, low-frequency fields can generally be described well by assuming that the photoelectron is, after the ionization step, completely at the mercy of the laser field. However, certain phenomena, like the recent discovery of low-energy structures in the long-wavelength regime, require the inclusion of the Coulomb interaction with the ion once the electron is in the continuum. We explore the first-principles inclusion of this interaction, known as analytical R-matrix theory, and its consequences on the corresponding quantum orbits. We show that the trajectory must have an imaginary component, and that this causes branch cuts in the complex time plane when the real trajectory revisits the neighbourhood of the ionic core. We provide a framework for consistently navigating these branch cuts based on closest-approach times, which satisfy the equation $\mathbf{r}(t) \cdot \mathbf{v}(t) = 0$ in the complex plane. We explore the geometry of these roots and describe the geometrical structures underlying the emergence of LES in both the classical and quantum domains.Comment: Supplementary information at http://episanty.github.io/Slalom-in-complex-time

Momentum transfers in correlation-assisted tunnelling

We consider correlation-assisted tunnel ionization of a small molecule by an intense low-frequency laser pulse. In this mechanism, the departing electron excites the state of the ion via a Coulomb interaction. We show that the angular distribution for this process has significant qualitative differences compared to direct tunnelling of an electron from a deeper orbital. These differences could be used to distinguish the two contributions, and give rise to interference effects when the contributions are comparable. The saddle-point approximation is also shown to require special attention in this geometric analysis.Comment: 6 pages, 4 figure

Electron dynamics in complex time and complex space

This thesis investigates the dynamics of electrons ionized by strong low frequency laser fields, from a semiclassical perspective, developing a trajectory-based formalism to describe the interactions of the outgoing electron with the remaining ion. Trajectory models for photoionization generally arise in the regime known as optical tunnelling, where the atom is subjected to a strong, slow field, which tilts the potential landscape around the ion, forming a potential energy barrier that electrons can then tunnel through. There are multiple approaches that enable the description of the ionized electron, but they are generally limited or models derived by analogy, and the status of the trajectories is unclear. This thesis analyses this trajectory language in the context of the Analytical R-Matrix theory of photoionization, deriving a trajectory model from the fundamentals, and showing that this requires both the time and the position of the trajectory to be complex. I analyse this complex component of the position and I show that it requires careful handling: of the potentials where it appears, and of the paths in the complex plane that the trajectory is taken through. In this connection, I show that the Coulomb potential of the ion induces branch cuts in the complex time plane that the integration path needs to avoid, and I show how to navigate these branch cuts. I then use this formalism to uncover a kinematic mechanism for the recently discovered (Near-)Zero Energy Structures of above-threshold ionization. In addition, I analyse the generation of high-order harmonics of the driving laser that are emitted when the photoelectron recollides with the ion, using a pair of counter-rotating circularly polarized pulses to drive the emission, both in the context of the conservation of spin angular momentum and as a probe of the long-wavelength breakdown of the dipole approximation.Open Acces

Kinematic origin for near-zero energy structures in mid-IR strong field ionization

We propose and discuss a kinematic mechanism underlying the recently discovered 'near-zero energy structure' in the photoionization of atoms in strong mid-infrared laser fields, based on trajectories which revisit the ion at low velocities exactly analogous to the series responsible for low-energy structures. The different scaling of the new series, as $E\sim {I}_{p}^{2}/{U}_{p}$, suggests that the near-zero energy structure can be lifted to higher energies, where it can be better resolved and studied, using harder targets with higher ionization potential

Quantum tunnelling without a barrier

Tunnelling is a renowned concept in modern physics that highlights the peculiarity of non-classical dynamics. Despite its ubiquity questions remain. We focus on tunnelling through the barrier created by a strong laser field that illuminates an atomic target, which is essential to the creation of attosecond pulses and ultimately all attosecond processes. Here, we present an optical tunnelling event that, unexpectedly, happens at a time when the instantaneous electric field is zero and there is no barrier. We discover this strong-field ionisation event by introducing the colour-switchover technique $-$ the gradual replacement of a laser field with its second harmonic $-$ within which the zero-field tunnelling appears when the two amplitudes are equal. This event is a topologically stable feature and it appears at all Keldysh parameters. The tunnelling without a barrier highlights the disconnect between the standard intuition built on the picture of a quasi-static barrier, and the nonadiabatic nature of the process. Our findings provide a key ingredient to the understanding of strong-field processes, such as high-harmonic generation and laser-induced electron diffraction, driven by the increasingly accessible class of strongly polychromatic light fields.Comment: 7 pages, 5 figure

The imaginary part of the high-harmonic cutoff

High-harmonic generation - the emission of high-frequency radiation by the ionization and subsequent recombination of an atomic electron driven by a strong laser field - is widely understood using a quasiclassical trajectory formalism, derived from a saddle-point approximation, where each saddle corresponds to a complex-valued trajectory whose recombination contributes to the harmonic emission. However, the classification of these saddle-points into individual quantum orbits remains a high-friction part of the formalism. Here we present a scheme to classify these trajectories, based on a natural identification of the (complex) time that corresponds to the harmonic cutoff. This identification also provides a natural complex value for the cutoff energy, whose imaginary part controls the strength of quantum-path interference between the quantum orbits that meet at the cutoff. Our construction gives an efficient method to evaluate the location and brightness of the cutoff for a wide class of driver waveforms by solving a single saddle-point equation. It also allows us to explore the intricate topologies of the Riemann surfaces formed by the quantum orbits induced by nontrivial waveforms.Comment: Supplementary Material is available at https://imaginary-harmonic-cutoff.github.io with a stable version at https://doi.org/10.5281/zenodo.369256

High-harmonic generation: taking control of polarization

The ability to control the polarization of short-wavelength radiation generated by high-harmonic generation is useful not only for applications but also for testing conservation laws in physics

Principal frequency of an ultrashort laser pulse

We introduce an alternative definition of the main frequency of an ultrashort laser pulse, the principal frequency $\omega_P$. This parameter is complementary to the most accepted and widely used carrier frequency $\omega_0$. Given the fact that these ultrashort pulses, also known as transients, have a temporal width comprising only few cycles of the carrier wave, corresponding to a spectral bandwidth $\Delta\omega$ covering several octaves, $\omega_P$ describes, in a more precise way, the dynamics driven by these sources. We present examples where, for instance, $\omega_P$ is able to correctly predict the high-order harmonic cutoff independently of the carrier envelope phase. This is confirmed by solving the time-dependent Schr\"odinger equation in reduced dimensions, supplemented with the time-analysis of the quantum spectra, where it is possible to observe how the sub-cycle electron dynamics is better described using $\omega_P$. The concept of $\omega_P$, however, can be applied to a large variety of scenarios, not only within the strong field physics domain.Comment: 11 pages, 6 figures, accepted in PR