Symmetry and Quantum Entanglement in the Rotational Dynamics of a Molecular Dimer under an External Electric Field

Ultracold polar diatomic molecules coupled via dipole–dipole interaction have been proposed as promising candidates for implementing quantum logic gates and for controlling chemical reactions in ultracold gases. In particular, the interplay between intermolecular interactions and external fields provides a versatile framework for manipulating rotational dynamics and entanglement.

In this work, we investigate the rotational dynamics and entanglement properties of a dimer formed by two identical linear polar molecules coupled via dipole–dipole interaction and subjected to an external electric field. A linearly switched-on electric field is considered, and a general prototype of linear polar molecule is assumed. The molecules are allowed to rotate in three dimensions and are described within the Born–Oppenheimer and rigid-rotor approximations.

We analyze the symmetry properties of the system, which allow us both to simplify the problem and to identify a set of general relations governing the rotational dynamics. We explore the dependence of the rotational motion and entanglement on the switching time of the field and on the spatial configuration of the molecular dimer. Finally, we discuss the coupling mechanisms associated with dipole–dipole and field–molecule interactions, and analyze the time-dependent wave function to provide a physical interpretation of the different dynamical regimes arising from various molecular arrangements.