We consider the resonant interaction energy and force between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. The atoms, having the same orientation of their dipole moment, are supposed prepared in their symmetrical state and interact with the quantum electromagnetic field. We consider two specific models of photonic crystals: a one-dimensional model and an isotropic model. We show that in both cases the resonant interatomic force can be strongly enhanced by the presence of the photonic crystal, as a consequence of the modified dispersion relation and density of states, in particular if the transition frequency of the atoms is close to the edge of a photonic gap. Differences between the two models considered of photonic crystal are discussed in detail, as well as comparison with the analogous system of two impurity atoms in a quantum semiconductor wire. A numerical estimate of the effect in a realistic situation is also discussed.

A new aspect of understanding a Fano absorption spectrum is presented in terms of the complex spectral analysis. The absorption spectrum of an impurity embedded in semi-infinite superlattice is investigated. The boundary condition on the continuum causes a large energy dependence of the self-energy, enhances the nonlinearity of the eigenvalue problem of the effective Hamiltonian, yielding several nonanalytic resonance states. The overall spectral features is perfectly reproduced by the direct transitions to these discrete resonance states. Even with a single optical transition path the spectrum exhibits an asymmetric Fano profile, which is enhanced for the transition to the nonanalytic resonance states. Since this is the genuine eigenstates of the total Hamiltonian, there is no ambiguity in the interpretation of the absorption spectrum, avoiding the arbitrary interpretation based on the quantum interference. The spectral change around the exceptional point is well understood when we extract the resonant state component.

We present the electronic Casimir-Polder effect for a system consisting of two impurities on a one-dimensional\ud semiconductor quantum wire. Due to the charge transfer from the impurity to a one-dimensional conduction band, the impurity states are dressed by a virtual cloud of the electron field. The attractive electronic Casimir\ud force arises due to the overlap of the virtual clouds. The Van Hove singularity causes the persistent bound state (PBS) to appear below the band edge even when the bare impurity state energy is above the band edge. Since the\ud decay rate of the virtual cloud of the PBS in space is small, the Casimir force can be of a very long range. While\ud the overlap of the electronic virtual cloud is consistent with the idea of the radiation reaction, it is shown that\ud also vacuum fluctuations play a role in the electronic Casimir force as a result of the fermionic anticommutation\ud relations. We introduce an effective mass, different from the effective band mass of the conduction band, which\ud is associated with the distance of the energy of the PBS from the band edge where the Van Hove singularity is\ud located and determines the decay rate of the electronic Casimir-Polder force

No abstract