It is found that a new kind of excitations,the energy-level-excitations,exist in a narrow-band crystal which strongly couples to the optical field. The energy spectrum and some other properties of the energy-level excitations are analyzed.
By using bosonization technique and quantum self-consistent theory, we study the low-energy excitations of a spin-Peierls system. The ground state, one-particle excited state, two-particle bound state are calculated, and it is shown, as the frustration increases, the energy of the ground state decreases while the energy gap of the one- and two-particle states increases. By analysing the asymototic behavior of the longitudinal spin correlation function, we obtain that the two-particle bound state has similar spin structures as those of the singlet ground state. Thus, we regard the bound state as a singlet state, which exists between the ground state and the two-particle continuous excited state. Our results are qualitatively in agreement with the experimental phenomena observed by Ain et al. It is shown that the existence of bound state is one of the spin-Peierls system's characteristic features.
Ultracold polar molecules trapped on an optical lattice is a many-body system that, under appropriate conditions, may support collective excitations reminiscent of excitons in solid state crystals. Here, we discuss the rotational excitations of molecules on an optical lattice leading to rotational Frenkel excitons. Apart from solid hydrogen, there is no other natural system that exhibits rotational excitons. The rotational excitons have unique properties that can be exploited for tuning non-linear exciton interactions and exciton-impurity scattering by applying an external electric field. We show that this can be used to explore the competing role of the dynamical and kinematic exciton-exciton interactions in excitonic energy transfer and to study quantum localization in a dynamically tunable disordered potential. The rotational excitons can also be used as a basis for quantum simulation of condensed matter models that cannot be realized with ultracold atoms. As an example, we discuss the possibility of engineering the Holstein model with polar molecules on an optical lattice.