On the relation between ultracold atoms in optical lattices and a rigid rotor in external fields

In the present work, we study the band structure of ultra-cold atoms in an optical superlattice and establish a relation between this system and a two-dimensional quantum rigid rotor interacting with external orienting and aligning fields [1,2]. Using this analogy, we present analytic expressions of band edge energies and wavefunctions and provide insight into the semi-finite band structure of the superlattice. Furthermore, we show that it is possible to translate essential concepts of the rigid rotor, such as orientation and alignment, into the localization of ultracold atoms along a superlattice. We believe our results bring some advances in the field of coherent control of rotational degrees into the realm of atoms in optical lattices.

[1] S. Becker, M. Mirahmadi, B. Schmidt, K. Schatz and B. Friedrich, Eur. Phys. J. D 71 149 (2017).

[2] M. Mirahmadi, B. Schmidt and B. Friedrich, New J. Phys. 23 063040 (2021).