Singularities of Floquet scattering and tunneling

H. Landa 1, 2

Physical Review A, American Physical Society, 2018, 97 (4), 〈10.1103/PhysRevA.97.042705〉

We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known « spectral singularities » (or « exceptional points »). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.

  • 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. IPHT – Institut de Physique Théorique – UMR CNRS 3681

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