We review the development of the time-dependent close-coupling method to study atomic and molecular few body dynamics. Applications include electron and photon collisions with atoms, molecules, and their ions.

We address an efficient scheme to generate a broadband extreme-ultraviolet (xuv) continuum from high-order harmonic generation emerging from the concept of plasmonic field enhancement in the vicinity of metallic nanostructures [Kim et al., Nature (London) 453, 757 (2008)]. Based on the numerical solution of a timedependent Schrödinger equation, for moderate field intensities and depending on the inhomogeneity of the field, we are able to increase the plateau region roughly by a factor of two and generate a broadband xuv continuum. The underlying physics of the plasmon enhancement in harmonic generation is investigated in terms of the semiclassical trajectories of strong field-electron dynamics, and perfect consistency is found between quantum mechanical simulations. It is found that the field inhomogeneity plays a critical role in quantum path selection. After a critical value, we observe a systematic suppression in the long trajectories, suggesting the generation of a single isolated attosecond pulse. Finally, we investigate the dependence of cutoff position on the order of field inhomogeneity and find a β 2.3∓0.2 scaling.

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Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of large extent of Ry electron wave function on trapping potentials. We find that when the Ry orbit lies outside inflection points in laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron AC polarizability of Ry electron is modulated by intensity landscape and can accept both positive and negative values. We apply these insights to determining magic wavelengths for Ry-ground-state transitions for alkali atoms trapped in infrared optical lattices. We find magic wavelengths to be around 10 µm, with exact values that depend on Ry state quantum numbers.Magic trapping [1] of cold atoms and molecules is a powerful technique that has recently enabled ultrastable optical lattice clocks [2-4], long-lived quantum memory [5], and precision manipulation of ultracold molecules [6]. When neutral atoms are trapped, their internal energy levels are necessarily perturbed by spatially inhomogeneous trapping fields. For a cold atomic cloud, typical mK temperatures translates into the 10 MHz trap depths. In other words, as the atom travels about the trap, its energies are modulated at the 10 MHz level with associated coherence times of just 100 ns. If it were not for magic trapping techniques, such decoherences would be prohibitive for the enumerated cold-atom applications. The key idea of magic trapping is the realization that one is interested in differential properties of two levels, such as the clock frequency or a differential phase accumulated by two qubit states. Then if the trapping field affects both levels in the very same way, the differential perturbations vanish. Such engineered traps are commonly referred to as "magic". These ideas enabled precision clock spectroscopy at the sub-100 mHz level [3] and second-long coherence times [5], orders of magnitude better than the quoted "non-magic" values.Application of magic trapping techniques to Rydberg (Ry) states of alkali atoms has turned out to be challenging. Generic quantum-information protocols involve qubits encoded in hyperfine manifolds of the ground state (GS) and conditional multiqubit dynamics mediated by interactions of Ry states [7][8][9][10]. Therefore,the trapping field must be magic both for the GS hyperfine manifolds and also for the GS-Ry transition [11]. The first part by itself is a non-trivial problem and has been a subject of several studies [5,[12][13][14][15]. The GS-Ry transition presents another challenge [11,[16][17][18].To appreciate the problem, let us first review commonly invoked arguments. In optical fields, the trapping potential is proportional to the AC polarizability α(ω), leading to trapping potential U (R) = −α(ω)F 2 (R)/4, where F is the local value of the electric field [32]. The GS polarizability α g (ω) > 0 when red-detuned from atomic resonances, and the atoms are attracted to intensity max-ima. On the other hand, loosely-bound Ry electron is nearly "free"; therefo...