Attoscience in phase space

Abstract

We provide a brief review of how phase space techniques are explored within strong-field and attosecond science. This includes a broad overview of the existing landscape, with focus on strong-field ionisation and rescattering, high-order harmonic generation, stabilisation and free-electron lasers. Furthermore, using our work on the subject, which deals with ionisation dynamics in atoms and diatomic molecules as well as high-order harmonic generation in inhomogeneous fields, we exemplify how such tools can be employed. One may for instance determine qualitatively different phase space dynamics, explore how bifurcations influence ionisation and high-harmonic generation, establish for which regimes classical and quantum correspondence works or fails, and what role different timescales play. Finally, we conclude the review highlighting the importance of the tools available in quantum optics, quantum information and physical chemistry to strong-field laser–matter interaction. Graphic Abstract

Controlling quantum effects in enhanced strong-field ionisation with machine-learning techniques

“…The final time is chosen to be T = 150 a.u. as it has been used in previous publications [49,35,58]. Throughout, Γ will be written in arbitrary units.…”

“…• Obtain an in depth understanding of how certain parameters influence the system, and expand on the conclusions drawn in [49,35].…”

“…Although the phenomenon is widely known, phase-space tools, such as the Wigner quasi-probability distributions [38] have shed new light on its behaviour [39,40,35]. Phase-space quasiprobability distributions have found enormous success in many research areas such as quantum optics [41,42,43], quantum information [44,45], chemical physics [46,47] and cold gases [48], but are hitherto underused in attoscience (for a recent review on the overall landscape within this research field see our article [49]). Nevertheless, they provide valuable insight into the dynamics of these systems of interest and have been used to study phenomena such as strong-field ionisation [50,39,40,51], rescattering [52,53] and entanglement [54].…”

Quantum aspects of attoscience

“…This stance is more radical than that of the first battle, and the very title, ‘no light at the end of the tunnel,’ highlights that a transverse field, such as light, does not produce a quantum tunnel. In [ 6 ], Chomet and Faria provide an overview of phase-space methods in a wide range of strong-field phenomena. These are powerful tools widely used in myriad areas, such as quantum optics, quantum information, physical chemistry and semiclassical theory, but underused in attoscience.…”

Phase space propagation of waves in nonhomogeneous media: corrections beyond the optical geometry limit

“…The Wigner representation of optical rays has various applications in signal processing [19][20][21][22][23][24], tomography [25,26], optics [27][28][29][30], transmission electron microscopy [31], radiophysics [32,33], acoustics [34], analysis of short pulses [35]. Corrections beyond the ray tracking method have been considered by the WKB approach and by the stationary phase approximation technique [48][49][50][51][52].…”