Exact decoupling of two dipole-dipole interacting dimers

Abstract

It is today possible to test many quantum mechanical predictions, even the most puzzling ones, setting up sophisticated experiments on exemplary "textbook" physical systems like a single atom or molecule or a single material quantum harmonic oscillator. It is therefore conceptually highly exciting to conceive simple but not trivial physical situations representable by exactly solvable hamiltonian models, in the grasp of the experimentalists. In this paper we study a physical system consisting of two coupled identical dimers. Each molecule possesses both fermionic and bosonic degrees of freedom and its internal non adiabatic dynamics is governed by a bilinear term conserving the total excitation number. The two molecules are assumed to interact by a dipole like term. Our main result is that the hamiltonian model representing such a composite system may be unitarily put in a form describing two fictitious uncoupled JC dimers provided the initial excitation number is less than two. The advantage of these canonical transformations is that it makes the restricted dynamical problem exactly tractable. In this way we may successfully study the time evolution of quantum correlation effects get established in the dimer-dimer system due to dipolar like coupling.