# Strong-field ionization

Our studies in strong-field ionization encompass many subareas, such as tunneling dynamics in phase space, above-threshold ionization, and, in recent years, ultrafast photoelectron holography. Earlier studies deals with the importance of pulse shapes in stabilization.

## Ultrafast photoelectron holography

with Dr Andy Maxwell, Ahmed Al Jawahiry, Toni Das, Abbie Bray, Tom Rooke, Dr Cornelia Hofmann, Gyeonghun Kim and several groups, e.g., Wuhan and Frankfurt.

Ultrafast photoelectron holography is a powerful tool to trace changes in matter in the subfs regime. It uses two qualitatively different quantum pathways that an electronic wave packet may take to the detector, one of which acts as a probe and the other as a reference. From the correspondent interference pattern, one may reconstruct the target by exploring different patterns and their phase differences. Our work focuses on using a novel approach developed at UCL, the Coulomb Quantum Orbit Strong-Field Approximation (CQSFA) to understand the physics of holographic interference patterns. Key questions are: How do the patterns form? What is the role of the residual Coulomb tail? Can we derive analytic conditions for different types of interference? Because the CQSFA incorporates tunneling and quantum interference, considers the binding potential and the external field on equal footing, is semi-analytical and allows one to switch different pathways on and off at will, it is the ideal tool to address such questions.

In our work, we have performed an in-depth study of well-known interference patterns, such as the fan and the spider [1,2], have predicted the existence of a myriad patterns that have been overlooked by previous studies [3], and developed analytical approximations for several types of quantum interference, which led to an excellent description of the structures encountered [4]. We have also extended out theory to complex trajectories, with the help of Prof Sergey Popruzhenko [5]. Recent applications involve the measurement of bound-state parity using isoelectronic atomic and molecular pairs [6], together with Prof Reinhard Doerner's group, and the measurement of a novel spiral-like structure by Prof Xiaojun Liu's group in Wuhan [7].

Further work involves tailored fields and is being taken up by Dr Cornelia Hofmann, Tom Rooke and Gyeonghun Kim, and the study of the influence of different bound states and hybrid types of orbits ("the inbetweeners"), taken up by Abbie Bray. We have also written the first comprehensive review on the topic [8].

[1] A. S. Maxwell, A. Al-Jawahiry, T. Das, and C. Figueira de Morisson Faria, Phys. Rev. A 96, 023420 (2017)

[2] XuanYang Lai, ShaoGang Yu, YiYi Huang, LinQiang Hua, Cheng Gong, Wei Quan, C. Figueira de Morisson Faria, and XiaoJun Liu, Phys. Rev. A 96, 01341 (2017)

[3] A. S. Maxwell and C. Figueira de Morisson Faria, J. Phys. B 51, 124001 (2018)

[4] A. S. Maxwell, A. Al-Jawahiry, X.Y. Lai and C. Figueira de Morisson Faria, J. Phys. B 51, 044004 (2018)

[5] A. S. Maxwell, S. V. Popruzhenko and C. Figueira de Morisson Faria, Phys. Rev. A 98, 063423 (2018)

[6] HuiPeng Kang, Andrew S. Maxwell, Daniel Trabert, XuanYang Lai, Sebastian Eckart, Maksim Kunitski, Markus Schöffler, Till Jahnke, XueBin Bian, Reinhard Dörner, and Carla Figueira de Morisson Faria, Phys. Rev. A 102, 013109 (2020)

[7] Andrew S. Maxwell, Carla Figueira de Morisson Faria, XuanYang Lai, RenPing Sun, and XiaoJun Liu, , Phys. Rev. A 102, 033111 (2020)

[8]C Figueira de Morisson Faria, AS Maxwell, Rep. Prog. Phys. 83 (3), 034401 (2020)

## Exploring nonclassicality in strong-field ionization

with Heloise Chomet, Druva Sarkar, Dominik Kufel

Tunnel ionization plays a huge role in the dynamics of an electronic wave packet in an intense, near or mid-IR laser field. The tunnel ionization dynamics are however poorly understood, and often explained using ad-hoc arguments. Thereby, a great resource is phase-space analysis. This is often employed in quantum optics and quantum information, but underused in strong-field and attosecond science. We have shown that quantum-interference effects play an important role in molecular strong-field enhanced tunnel ionization by providing a ‘quantum bridge’ for the electron to reach the continuum. This pathway is highly nonclassical, and this has been demonstrated using the Quantum Liouville equation. The quantum bridges exist and perform a peridodic clockwise phase-space rotation even for a static field or even in the absence of an external field altogether (H Chomet et al, New J. Phys. 21, 123004 (2019)) This called into question the existing interpretation, based on non-adiabatic response to a time-dependent field.

Further work has focused on computing the the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width. Our approach has led to a quantisation condition and to eigenfrequencies that cold be used to determine the time dependence of the quantum bridges in phase space analytically (D Kufel et al, J. Phys. A: Math. Theor. 54, 035304 (2021))

## Analytical treatment of stabilization

with Prof Andreas Fring (city, University of London) and Prof Robert Schrader (FU Berlin)

In the high-intensity regime, Fermi's golden rule is fully inadequate for calculating ionization yields. Therefore, several alternative methods are used, some of which (mainly numerical) predict the existence of ``atomic stabilization'' (i.e the decrease of the ionization probability with the field intensity) for atoms subject to short-pulsed laser radiation. The existence of stabilization and the conditions for its occurrence have led to a great deal of controversy. In this early work, I have applied theoretical approaches which are unusual in strong-field physics to atomic stabilization, in collaboration with leading mathematical physicists, and have established rigorous conditions for the existence of this phenomenon [1,2,3]. This highly controversial and original work had a large repercussion on how stabilization is viewed.

[1] C. Figueira de Morisson Faria, A. Fring and R. Schrader, J. Phys. B 31(3), 449-464 (1998)

[2] C. Figueira de Morisson Faria, A. Fring and R. Schrader, Laser Phys. 9(1), 379-387 (1999).

[3] C. Figueira de Morisson Faria, A. Fring and R. Schrader, , J. Phys. B. 33(8), 1675-1685 (2000),

## Above-threshold ionization

with Dr Xuanyang Lai (CAS Wuhan), Prof Maciej Lewenstein, (ICFO - Barcelona), Dr Wilhelm Becker (MBI Berlin) and Dr Pascal Salieres (CEA Saclay)

Above-threshold ionization (ATI) is a strong-field phenomenon in which an atom absorbs more photons than the necessary amount for it to ionize. Our studies on above-threshold ionization are mainly related to the quantum interference between the possible trajectories along which the electron returns to its parent ion. We have looked at tailored fields [1], additional attosecond pulses [2] and above-threshold ionization in molecules [1,3].

[1] Xuanyang Lai and C. Figueira de Morisson Faria, Phys. Rev. A 88, 013406 (2013)

[2] C. Figueira de Morisson Faria, P. Salieres, P.Villain and M. Lewenstein, Phys. Rev. A 74, 053416 (2006)

[3] H. Hetzteim, C. Figueira de Morisson Faria, and W. Becker, Phys. Rev. A 76, 023418 (2007)

Angular distributions for above-threshold ionization caused by an infrared field and an attosecond pulse train. From [2]