Delayed double ionization as a signature of Hamiltonian chaos

Abstract

We analyze the dynamical processes behind delayed double ionization of atoms subjected to strong laser pulses. Using reduced models, we show that these processes are a signature of Hamiltonian chaos which results from the competition between the laser field and the Coulomb attraction to the nucleus. In particular, we exhibit the paramount role of the unstable manifold of selected periodic orbits which lead to a delay in these double ionizations. Among delayed double ionizations, we consider the case of "Recollision Excitation with Subsequent Ionization" (RESI) and, as a hallmark of this mechanism, we predict oscillations in the ratio of RESI to double ionization yields versus laser intensity. We discuss the significance of the dimensionality of the reduced models for the analysis of the dynamical processes behind delayed double ionization.

Attoscience in phase space

“…Subsequently, the role of multiple recollisions on the efficient energy transfer in NSDI has been investigated using symplectic maps and similar approaches to those used in kicked Rydberg atoms, and a road map has been provided for identifying different NSDI mechanisms in [99,100]. Further work by the same group has focused on an in-depth analysis of recollision excitation with subsequent ionisation (RESI) in terms of resonances and their proximity to periodic orbits [103,104]. In particular, a sticky region in phase space arises due to the interplay of the external field and the binding potential.…”

“…This region traps trajectories before ionisation, leading to time delays for the second electron. A detailed analysis of the types of periodic orbits, resonance conditions and distinct sources of chaos is provided in [104]. Interestingly, if reduceddimensionality models are used, oscillations in the RESI yield as functions of the laser intensity are reported and attributed to resonances.…”

“…Still, some groups have explored phase space dynamics in a strong-field context. This includes stabilisation [69][70][71][72], strong-field ionisation [73][74][75][76][77][78], high-order harmonic generation [79][80][81][82][83], laser-induced core dynamics [84,85], rescattering [79,80,[86][87][88][89], nonsequential double ionisation [90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106], or in connection with initial-value representations in strong fields [76,[107][108][109][110]. Furthermore, the growing interest in free-electron lasers (FELs) means that the tools employed in quantum optics are being explored in the X-ray and extreme ultraviolet (XUV) regime [111,112].…”

Triggering recollisions with XUV pulses: Imprint of recolliding periodic orbits

“…For ω = 0.0584, the energy of the periodic orbit of period T is E ≈ −0.12 and its maximum distance from the core is x m (E) ≈ 8.19 (see Ref. [35] for an approximation of the energy of the electron in the field-free atom as a function of its period). This periodic orbit corresponds to the RPO O 1 .…”

Dynamical Organization of Recollisions by a Family of Invariant Tori

“…Here we study the nonlinear dynamics of the electron by identifying specific invariant objects as guides for recollisions. We focus on two families of periodic orbits: recolliding periodic orbits [31,30,35,1] (RPOs) and saddle periodic orbits [37,36,4,39,38] (SPOs) as relevant for the recollision process. We show that the RPOs lead to a fast escape in the transverse direction, i.e., they do not favor recollisions by themselves.…”