SAMOP 2023 – scientific programme
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QI: Fachverband Quanteninformation
QI 32: Quantum Optics and Quantum Information with Rigid Rotors (joint session MO/Q/QI)
QI 32.6: Talk
Thursday, March 9, 2023, 15:45–16:00, F102
From the rotation of a planar rigid rotor in electric fields to the semifinite-gap structure of an optical superlattice — •Marjan Mirahmadi1, Bretislav Friedrich1, Burkhard Schmidt2, and Jesús Pérez-Ríos1,3,4 — 1Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany — 2Weierstraß-Institut, Berlin, Germany — 3Department of Physics, Stony Brook University, NY , USA — 4Institute for Advanced Computational Science, Stony Brook University, NY, USA
We show that two seemingly unrelated problems − the trapping of an atom in a one-dimensional optical superlattice (OSL) formed by the interference of optical lattices whose spatial periods differ by a factor of two, and the libration of a polar polarizable planar rotor (PR) in combined electric and optical fields − have isomorphic Hamiltonians. It is possible to establish a map between the translations of atoms in the former system and the rotations of the rotor due to the coupling of its permanent and induced electric dipole moments to the external fields. The latter system belongs to the class of conditionally quasi-exactly solvable problems in quantum mechanics and exhibits intriguing spectral properties. We make use of our findings to explain the semifinite-gap band structure of the OSL. This band structure follows from the eigenenergies obtained as solutions of the Whittaker-Hill equation and their genuine and avoided crossings. Furthermore, the mapping makes it possible to establish correspondence between concepts, such as localization on the one hand and orientation/alignment on the other.