Front Matter

Published:2022
Lampros A. A. Nikolopoulos, "Front Matter", Computing Atomic Quantum Dynamics in Laser Fields, Lampros A. A. Nikolopoulos
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Computing Atomic Quantum Dynamics in Laser Fields introduces theory in tandem with practical methods to calculate end numbers—teaching typically separate subjects together. The topics covered are at the core of several contemporary areas of theoretical atomic, molecular, and optical physics (AMO) including ultrashort laser fields, quantum dynamics and control, quantum imaging, and computational physics. High performance algorithms, numerical analysis, and differential and matrix calculus are presented in the context of the theory of laser atom dynamics.
Computing Atomic Quantum Dynamics in Laser Fields:
Combines practical numerical methods in computing atomic processes in ultrashort laser fields in a systematic and coherent manner
Shortens learning time for mastering computational techniques in atomic, molecular, and optical research
Presents theoretical formulations in a manner that fits naturally with the discrete nature of computational algorithms
Postgraduate students and practitioners in the field of AMO and computational physics will find this an invaluable resource.
To Andriana, Thano, and Foteini
Preface
In its general form, the problem of an atomic or molecular system in an electromagnetic field is computationally intractable without physically justified approximations, and part of the art is finding suitable approximations for the problem at hand, guided by physical intuition as well as experience. Of course, the ultimate criterion for using any particular approach is comparison with experimental observations.
Regarding such computations, it is natural to discuss their physical context and to provide at a fundamental level a reasonable account of the approximations that are used. Over the years, most of the underlying physics has become well established, and most of the processes that take place have been studied thoroughly both theoretically and experimentally. Nowadays, the ongoing effort is mostly in developing sophisticated technology to exploit the current state of knowledge, and this is not a trivial task, especially given the new types of intense and shortduration radiation delivered by freeelectron lasers or the high harmonics of Tisapphire lasers, both at extreme ultraviolet wavelengths. From a theoretical perspective, much of the effort looks more like a struggle to tackle a computational grandchallenge problem rather than develop a theoretical formulation of a physical problem. Although this situation might not yet be the norm, it is certainly a reality that cannot be ignored.
That said, it is also natural to provide an account of the computational aspects of the problemtogether with its associated numericalmethods, given that in practice they come to the foremore often than not. Although experienced researchers may not struggle to identify qualitatively the important processes that take place in a particular situation, theywill undoubtedly face severe problems in quantifying these for experimental or technological use. Worse still, for neophytes, especially those just after undergraduate level and therefore inexperienced, there is a rather steep learning curve to climb. Also, the current state of research is that younger researchers tend to implement computational codes (either from scratch or as updates of existing ones) based on various numerical algorithms, and of course the high specialization of modern research means that those numerical algorithms might also need to be designed inhouse. Given that onus and the equivalent one of studying and absorbing the associated theoretical formulation, fastpaced progress is not to be expected.
It was in the above spirit that this book was written. Rather than being a thorough treatment, it presents in some detail the relevant theory for some frequently encountered processes, alongside a limited presentation of the numerical methods that have proven useful over the years and are still used widely. I have assumed that the reader has a good background in quantum mechanics and classical electrodynamics, both ofwhich are indispensable if onewants to delve into the heart of laser–matter interactions. Also, familiarity with basic numerical methods can only help.
Given the vast research literature on the subject together with its rapid progress, it is also appropriate to mention here the following textbooks that deal with strong laser–atom processes that are not mentioned in the references because they focus on other aspects:
Attosecond and StrongField Physics: Principles and Applications, C. D. Lin, AnhThu Le, Cheng Jin, and Hui Wei, Cambridge University Press (2018)
Attosecond and XUV Physics: Ultrafast Dynamics and Spectroscopy, Thomas Schultz and Marc Vrakking (eds.), WileyVCH (2013)
Quantum Control of Molecular Processes, Moshe Shapiro and Paul Brumer, WileyVCH (2012)
Atoms in Intense Laser Fields, C. J. Joachain, N. J. Kylstra, and R.M. Potvliege, Cambridge University Press (2011)
RMatrix Theory of Atomic Collisions, P. Burke, Springer (2011)
Also of note are the pioneering articles in the special issue of the journal Computer Physics Communication entitled Timedependent Methods for Quantum Dynamics (ed. Kenneth Kulander), and the textbook entitled Introduction to Quantum Mechanics: A Timedependent Perspective by David J. Tannor (University Science Books, 2006) should be of particular help to the novice reader.
My aim was to be detailed and descriptive to minimize any leaps that would prevent understanding; the reader should be unhappy if they are left with a feeling of semiunderstanding.However, Imade no attempt to present an exhaustive reference list, that being outside the present scope; current technology offers the reader instant virtual access to any reference required.
The content starts with simpler problems and thenmoves tomorecomplex ones: a treatment of weakfield excitation/ionization, the basic theoretical methods, the (timedependent) perturbation method, and the direct solution of timedependent Schrödinger equation. Also included are the basics of how to turn differential equations into amatrix (eigenvalue or linear algebraic) problemthat can be tackled directly by computation; some other important numerical methods are discussed, such as numerical quadrature and polynomial expansions. To place all the above in context, atomic structure and laser theories are covered to a decent depth.
To avoid overloading the text with myriads of definitions and variations, it deals with the simplest of systems, i.e., hydrogenic systems, while the electromagnetic field is treated classically and as simply as possible as being fully coherent, intense, linearly polarized, pulsed (of femtosecond scale), and with infrared and soft xray wavelengths. In all cases, I made a conscious effort to keep the level of presentation as simple as possible, even if that was not always the appropriate approach. For the formulas, I have used atomic units, but in places the text contains other more appropriate units.
With some regret, I have either omitted or undertreated some important numerical methods and approaches, including elements of the trigonometric basis expansion, the Lanczos method, the fast Fourier transform, the Davidsonmethod, blockdiagonalmethods, the splitoperator scheme, nonuniform finitedifference schemes, some basics on finiteprecision arithmetic, and some moreadvanced matrix propagation schemes. Also, I have omitted some laserdynamics approaches, such as tunneling theory and Floquet approximation, and the inclusion of morecomplex pulses (elliptically polarized, attosecond, chirp, and the theory of freeelectron pulses, etc.).
L. Nikolopoulos
Dublin, 6 June 2022