**Time-resolved Photoelectron Holography in Molecules**

Laser-induced holographic patterns that form in above-threshold ionization (ATI) photoelectron angular distributions (PADs) are a powerful tool for investigating ultrafast electron dynamics in real time (Huismans et al, Science 331, 61 (2011)). Indeed, there is experimental evidence of coupling between nuclear and electronic motion in PH (Meckel et al, Nat. Phys. 10, 594 (2014), Walt et al, Nat. Comm. 15, 651 (2017)). These patterns require a reference and probe signal, which are associated with different types of interfering electron orbits. Most theoretical models of photoelectron holography (PH), however, either treat the contributing orbits classically, or neglect the binding potential in the continuum. This allows for hard collisions, but excludes soft collisions and distortions/phase shifts caused by the residual potential. Using a novel approach developed at UCL in Dr Carla Faria's group, the Coulomb Quantum Orbit Strong Field Approximation (CQSFA) (Lai et al, Phys. Rev. A 92, 043407 (2015)), we have achieved a much better understanding of how the key holographic patterns form, and of the interplay between the Coulomb potential and external field (Maxwell et al, Phys. Rev. A 96, 023420 (2017)). Our studies have also uncovered a myriad of holographic patterns that are normally overlooked in the literature. In an experimental setting, these patterns are however obfuscated by more prominent features.

In this project, the student will seek particular pulse shapes, frequencies and polarizations, in order to enhance or suppress specific holographic patterns and to extend the model developed by us to molecular systems, which will first be considered as static. Subsequently, we will incorporate nuclear degrees of freedom, such as vibration, rotation and dissociation. We intend seek particular ways to prepare the system in order to couple nuclear and electronic degrees of freedom.

The prospective student should have an MSc in physics or a related area. This project will require analytical and numerical skills. It will involve path integral methods, complex analysis, Mathematica, Matlab, and c++.

For inquiries please contact Dr Carla Faria (c.faria@ucl.ac.uk)

**Strong-Field Dynamics with Initial Value Representations**

The concept of orbits is extremely important for strong-field physics. Not only have they allowed a myriad of applications, but they also have provided access to some of the shortest time scales in nature: attoseconds (10-18s). These time scales allow, in principle, to steer electron dynamics. Electrons have a huge influence in, e.g., making/breaking chemical bonds, and transporting energy in molecules and solids. Hence, such studies severely impact physics, chemistry, biology and more applied areas such as light harvesting or nanotechnology (Ferenc Krausz and Misha Ivanov, Rev. Mod. Phys. 81, 163 (2009). Traditionally, strong-field dynamics are either modelled with ab-initio, or semi-analytical approaches. The former are not applicable for large systems as the numerical effort increases exponentially with its degrees of freedom, while the latter require drastic approximations. Hence, one needs orbit-based methods that (a) are suited for systems with many degrees of freedom; (b) treat the binding potential and the external field on equal footing; (c) allow for quantum interference and tunnelling. Semiclassical initial-value representations (IVRs) are an ideal choice as they satisfy these requirements (D. V. Shalashilin and M. S. Child, Chem. Phys. **304,** 103 (2004)). They are extensively used in physical chemistry and non-linear dynamics.

This project aims at modelling correlated multielectron strong-field dynamics with IVRS. This will build upon Dr Carla Faria's previous studies, in which IVRs were applied to strong-field ionization and high-harmonic generation for reduced-dimensionality models (C Zagoya, et al, New J. Phys. **16** 103040 (2014); C. Symonds et al, Phys. Rev. A **91**, 023427 (2015). This was part of an interdisciplinary effort involving scientists of several areas, such as quantum chemistry and mathematical physics. First, the student will extend existing codes to one-electron systems in three dimensions, and applications to photoelectron holography will be sought. Throughout, comparisons with other methods and existing experiments will be made.

The prospective student should have an MSc in physics or a related area. This project will require analytical and numerical skills. It has a strong numerical component and will require a great deal of coding in c++.

For inquiries please contact Dr Carla Faria (c.faria@ucl.ac.uk)

**Controlling Quantum Interference in Below-Threshold Nonsequential Double Ionization**

Laser-induced nonsequential double ionization (NSDI) is a strong-field pheonomenon for which electron-electron correlation is huge (for a review see C. Faria and X. Liu, J. Mod. Opt. **58**, 1076)(2011)). In particular, this correlation can be observed in NSDI electron-momentum distributions, for which the main features are described by a physical mechanism in which the first electron releases the second by recolliding with its parent ion. For many years, it was widely believed that NSDI can be described classically. This is true for direct ionization, in which the returning electron has enough energy to remove a second electron instantaneously. For below-threshold nonsequential ionization, this is not clear cut, especially if the returning electron excites the second. In this regime, we have found that quantum-interference patterns associated with different excitation channels and electron exchange may survive integration over the transverse momentum components and focal averaging (A. S. Maxwell and C. Faria, Phys. Rev. A **92**, 023421 (2015) and Phys. Rev. Lett. **116**, 143001(2016)). Many features are however absent in the above-stated model such as (a) the residual Coulomb potential; (b) the Stark shifts of the excited states; (c) the sub-barrier corrections; (d) the pulse width and intensity distributions; (e) the core dynamics. These features are necessary to successfully explain existing experiments.

The aim of this project is to incorporate the features (a)--(d) in our model,. We will commence by making an assessment of how the Coulomb potential and Stark shifts will influence exchange-related interference for each relevant channel. This will be performed extending the newly developed Coulomb quantum orbit strong-field approximation ((Lai et al, Phys. Rev. A 92, 043407 (2015)) to two electron systems. Subsequently, we will incorporate sub-barrier corrections and assess how the geometry of each intermediate bound state will influence these features. Time permitting, optimal pulse shapes will be sought in order to manipulate the RESI distributions and the intermediate state of the second electron. Our results will be compared with the outcome of experiments performed by several groups worldwide.

The prospective student should have an MSc in physics or a related area. This project will require analytical and numerical skills. It will involve path integral methods, complex analysis, Mathematica, Matlab, and c++.

For inquiries please contact Dr Carla Faria (c.faria@ucl.ac.uk)