Non-classical and non-Hermitian aspects of electron-electron correlation in strong-field physics

The quintessential example of electron-electron correlation in strong-field physics is laser-induced nonsequential double ionization (NSDI) (for a review, see [l]). Thereby, a key question is whether this correlation is quantum or classical. For over two decades, NSDI has been viewed as an essentially classical phenomenon, well described by the laser-assisted collision of an electron with its parent ion. This has been due to the success of classical models reproducing electron-momentum distributions in direct, electron-impact NSDI, for which the returning electron provides enough energy for the second to overcome the ionization potential of the parent ion. Without much evidence, this line of thinking has been extrapolated to below-threshold NSDI. In this case, the first electron promotes the second to an excited state, from which it subsequently tunnels. This mechanism is known as recollision-excitation with subsequent ionization (RESI). Recently, however, it was found that quantum interference in the below-threshold regime, for which RESI occurs, is more robust than previously thought, and may survive (a) focal averaging; (b) integration over transverse electron momenta [2]. Experimental evidence for quantum interference has been found in [3]. Discrepancies between experiment and theory do exist, however. This is due to the fact that the computations in [2] have been performed using the Strong-Field Approximation (SFA), which neglects the residual Coulomb potential when the electron is in the continuum.
In this project, we intend to identify and quantify entanglement in below-threshold NSDI. This is a cutting edge problem as most groups across the globe still regard NSDI as classical. The first step to be undertaken is to develop a Coulomb corrected semi-analytic approach for RESI, building up on existing one-electron approaches [4], which will be com-pared with ab-initio two electron models. Subsequently, the student will calculate the covariant matrix for position and momentum within the developed model [5]. This will provide a lower bound for separable states, which hopefully will help distinguish classi-cal and quantum correlation. Other entanglement criteria will also be explored. We will seek optimal conditions to observe quantum effects in RESI, together with the experimen-tal groups of Prof. Jens Biegert (Institute for Photonic Sciences, Barcelona), and Prof. Xiaojun Liu (Chinese Academy of Sciences, Wuhan).
Having identified laser-induced nonsequential double ionization as being of a truely quantum orgin we also plan to explore whether this effect also occurs in non-Hermitian quantum system. I will focus my investigations mainly on PT-symmetric or pseudo/quasi Hermitian quantum mechanics. The latter systems are distinct from 11 conventional11 non-Hermitian system by having real eigenvalue spectra and unitary time-evolution, i.e. they are not considered as open systems. Only recently [6, 7,8] the full-timedependent treatment of these systems has been fully understood, which opens up the possibility to investigate effects such as the one mentioned above.
[1] C. Faria and X. Liu, J. Mod. Opt. 58, 1076 (2011).
[2] A. S. Maxwell and C. Faria, Phys. Rev. Lett. 116, 143001 (2016).
[3] Wei Quan, et al, Phys. Rev. A 96, 032511 (2017).
[4] A: S. Maxwell, A. Al-Jawahiry, T. Das and C. Faria, Phys. Rev. A 96, 023420 (2017).
[5] A. Serafini, Quantum Continuous Variables ( CRC Press, Taylor and Francis, 2017).
[6] C. Faria and A. Fring, J. of Physics A39 (2006) 9269.
[7] A. Fring and M.H.Y. Moussa, Phys .. Rev. A 93, 042114 (2016)
[8] A. Fring and T. Frith, J. of Physics A: Math. and Theor. 51 (2018) 265301