Mapping atomic trapping in an optical superlattice onto the libration of a planar rotor in electric fields

Abstract We show that two seemingly unrelated problems—the trapping of an atom in optical superlattice (OSL) and the libration a planar rigid rotor combined electric fields (PR) – have isomorphic Hamiltonians. Formed by interference lattices whose spatial periods differ factor two, OSL gives rise to periodic potential acts on atomic translation via AC Stark effect. The PR system, also known as generalized pendulum, is realized subjecting orienting aligning interactions due coupling rotor’s permanent induced dipole moments fields. system belongs class conditionally quasi-exactly solvable problems exhibits intriguing spectral properties been established our previous work Becker et al (2017 Eur. Phys. J. D 71 149). Herein, we make use both ↦ mapping quasi-exact solvability treat ultracold atoms semifinite-gap system. band structure this follows from eigenenergies their genuine avoided crossings obtained previously for solutions Whittaker-Hill equation. These characterize squeezing tunneling trapped pave way unraveling dynamics analytic form. Furthermore, makes it possible establish correspondence between concepts developed eigenproblems individually, such localization one hand orientation/alignment other.