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.
Bibliographical noteFunding Information:
We (the authors, and our combatants Analycia and Numerio ) are deeply grateful to the organisers of the Quantum Battles in Attoscience conference as well as to the audience members for their active participation, and we are especially grateful to the Battle’s ‘referee’, Stefanie Gräfe, for her insightful and even-handed moderation during the panel discussion. We also thank S.D. Bartlett, T. Rudolph and R.W. Spekkens  as well as G. Galilei  for inspiration for the format of this paper. GSJA acknowledges funding from the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/T019530/1. MAK acknowledges funding from the Alexander von Humboldt Foundation. ASM acknowledges Grant EP/P510270/1 funded by the UK EPSRC. ASM and EP acknowledge support from ERC AdG NOQIA, Spanish Ministry of Economy and Competitiveness (“Severo Ochoa” program for Centres of Excellence in R&D (CEX2019-000910-S), Plan National FIDEUA PID2019-106901GB-I00/10.13039/501100011033, FPI), Fundació Privada Cellex, Fundació Mir-Puig, and from Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341, CERCA program, QuantumCAT _U16-011424, co-funded by the ERDF Operational Program of Catalonia 2014-2020), MINECO-EU QUANTERA MAQS (funded by State Research Agency (AEI) PCI2019-111828-2/10.13039/ 501100011033), Marie Sklodowska-Curie grant STRETCH No. 101029393, EU Horizon 2020 FET-OPEN OPTOLogic (Grant No 899794), and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. MR acknowledges funding from the EPSRC/DSTL MURI Grant EP/N018680/1.
© 2021, The Author(s).
Copyright 2021 Elsevier B.V., All rights reserved.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics