Dialogue on analytical and ab initio methods in attoscience

Eur. Phys. J. D (2021) 75 :209 https://doi.org/10.1140/epjd/s10053-021-00207-3 THE EUROPEAN PHYSICAL JOURNAL D Regular Article - Atomic Physics Dialogue on analytical and ab initio methods in attoscience Gregory S. J. Armstrong1,a , Margarita A. Khokhlova2,3 , Marie Labeye4 , Andrew S. Maxwell5,6 , Emilio Pisanty2,5 , and Marco Ruberti3 1 Centre for Theoretical Atomic, Molecular, and Optical Physics, Queen’s University Belfast, Belfast BT7 1NN, UK Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Straße 2A, 12489 Berlin, Germany 3 Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK 4 CNRS, PASTEUR, Département de chimie, Ecole Normale Supérieure, PSL University, Sorbonne Université, 75005 Paris, France 5 Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain 6 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK 2 Received 21 January 2021 / Accepted 18 June 2021 / Published online 20 July 2021 © The Author(s) 2021 Abstract. The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the ‘Quantum Battles in Attoscience’ cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience—covering both analytical and numerical methods—and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in ‘analytical’ techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community. Introduction Modern developments in laser technologies have kickstarted the attosecond revolution, which formed the field of attoscience, dealing with dynamics on the attosecond (10−18 s) timescale [1–3]. Attosecond science was born with the study of above-threshold ionisation (ATI) and high-order harmonic generation (HHG) driven by strong laser pulses. As it has matured over the past three decades, attoscience has given us access to phenomena which were previously thought to be inaccessible—including the motion of valence electrons in atoms [4], charge oscillations in molecules [5], as well as the direct observation of the electric-field oscillations of a laser pulse [6]—and it has also spurred advances in ultrafast pulse generation which have opened a completely new window into the dynamics of matter. The meteoric progress of attoscience has been fuelled, on the one hand, by formidable experimental efforts, and, on the other hand, it has been supported by a matching leap in our theoretical capabilities. These theoretical advances have come in a wide variety, forming two opposing families of analytical and numerical approaches. While these two families generally work together, the dichotomy between analytical and numerical methods is sometimes perceived as a source of tension within the attoscience community. In this Topical Review, we present an exploration of this dichotomy, which collects the arguments presented in the panel discussion ‘Quantum Battle 3— Numerical versus Analytical Methods’ held during the online conference ‘Quantum Battles in Attoscience’ [7]. Our main purpose is to resolve the tension caused by this dichotomy, by identifying the critical tension points, developing the different viewpoints involved, and finding a common ground between them. This process forms a natural dialogue between the analytical and numerical perspectives. We delegate this dialogue to two hypothetical ‘combatants’— a e-mail: (corresponding author) 123 209 Page 2 of 31 Analycia Hi, I’m Analycia Formuloff, and I am an attoscience theorist working with analytical approaches. Numerio Hello, my name is Numerio Codeman, and I’m a computational scientist working on ab initio methods. —who will voice the different views expressed during the panel discussion. We follow the dialogue between Analycia and Numerio through three main questions. First, in Sect. 1, we explore the scope and nature of analytical and numerical methods, including the interchangeability of the terms ‘numerical’ and ‘ab initio’. We then analyse, in Sect. 2, the relative advantages and disadvantages of the two approaches, using non-sequential double ionisation (NSDI) as a case study. Finally, in Sect. 3, we examine their roles in scientific discovery, via the case study of resonant HHG. In addition, in Sect. 4, we present some extra discussion points, as well as our combatants’ responses to the questions raised by audience members, and a summary of the responses to several polls taken during the live session. 1 ‘Ab initio’ and analytical methods A constructive discussion is always based on a good knowledge of the subject. To this end, in this section we tackle the subtleties in the definitions of ‘ab initio’, ‘numerical’ and ‘analytical’ methods: we detail their differences, and we present a rough classification of the various theoretical methods used in attosecond science. We first concentrate on Numerio’s speciality, ab initio methods, then we move to Analycia’s forte, analytical theories. For each combatant, we first introduce their theoretical approach and then list the main methods in the corresponding toolset. After these presentations, Numerio and Analycia discuss the friction points they have with each other’s methods. 1.1 Ab initio and numerical methods In its dictionary sense, ab initio is Latin for ‘from the beginning’. Thus, a theoretical method can be defined to be ab initio when it tackles the description of a certain physical process starting from first principles, i.e. using the most fundamental laws of nature that—according to our best understanding—govern the physics of the phenomena that we aim to describe. Within an ab initio framework, the inputs of the theoretical calculation should be limited to only well-known physical constants, with any interactions kept as fundamental as possible. This means that no additional simplifications or assumptions may be made on top of what we believe are the established laws of nature. In other words, the specific aspects of the physical process of interest need to be approached without using specially tailored models. We now bring our combatants to the stage, to discuss the consequences of this defi (...truncated)