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

强场物理中电子-电子关联的典型例子是激光诱导的非序列双电离（NSDI）（综述见[1]）。因此，一个关键问题是这种相关性是量子的还是经典的。二十多年来，NSDI一直被认为是一种经典现象，可以通过电子与其母离子的激光辅助碰撞来描述。这是由于经典模型成功地再现了直接电子碰撞NSDI中的电子动量分布，其中返回的电子为第二个提供了足够的能量来克服母离子的电离势。在没有太多证据的情况下，这一思路被外推到低于阈值的NSDI。在这种情况下，第一个电子将第二个电子提升到激发态，随后从激发态隧穿。这种机制被称为电离-激发-后续电离（RESI）。然而，最近，人们发现，在低于阈值的制度，RESI发生的量子干涉，是更强大的比以前认为的，并可能生存（a）焦点平均;（B）整合横向电子动量[2]。量子干涉的实验证据已在[3]中找到。然而，实验和理论之间确实存在着分歧。这是由于[2]中的计算是使用强场近似（SFA）进行的，当电子处于连续介质中时，该方法忽略了剩余库仑势。在这个项目中，我们打算识别和量化低于阈值的NSDI纠缠。这是一个前沿问题，因为地球仪上的大多数团体仍然认为NSDI是经典的。第一步是在现有的单电子方法[4]的基础上，开发一种用于RESI的库仑校正半分析方法，该方法将与从头算双电子模型相结合。随后，学生将在开发的模型中计算位置和动量的协变矩阵[5]。这将为可分离态提供一个下限，这有望有助于区分经典相关和量子相关。还将探索其他纠缠标准。我们将与Jens Biegert教授（巴塞罗那光子科学研究所）和刘晓军教授（中国科学院武汉）的实验小组一起寻找在RESI中观察量子效应的最佳条件。在确认了激光诱导的非序双电离是真正的量子起源之后，我们还计划探索这种效应是否也发生在非厄米量子系统中。我将集中我的研究主要是PT对称或伪/准厄米量子力学。后一类系统与传统的非厄米特系统的不同之处在于它们具有真实的本征值谱和幺正的时间演化，即它们不被认为是开放系统。直到最近[6，7，8]才完全理解了这些系统的全时依赖性治疗，这为研究上述效应提供了可能性。[1]C. Faria和X. Liu，J.Mod.Opt.58，1076（2011）. [2]A. S.麦克斯韦和C. Faria，Phys. Rev. Lett. 116，143001（2016）。[3]Wei Quan等人，Phys. Rev. A 96，032511（2017）。[4]答：S。麦克斯韦，A. Al-Jawahiri，T. Das和C. Faria，Phys. Rev. A 96，023420（2017）。[5]A. Serafini，Quantum Continuous Variables（CRC Press，Taylor和弗朗西斯，2017）。[6]C. Faria和A. Fring，J. of Physics A39（2006）9269. [7]A. Fring和M.H.Y. Moussa，Phys.. Rev. A 93，042114（2016）[8] A. Fring和T. Frith，J. of Physics A：Math. and Theor.粤ICP备16018888号-1

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