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We calculate the fully retarded one-photon exchange interaction potential between electrically neutral, identical atoms, one of which is assumed to be in an excited state, by matching the scattering matrix (S matrix) element with the effective Hamiltonian. Based on the Feynman prescription, we obtain the imaginary part of the interaction energy. Our results lead to precise formulas for the distance-dependent enhancement and suppression of the decay rates of entangled superradiant and subradiant Dicke states (Bell states), as a function of the interatomic distance. The formulas include a long-range tail due to entanglement. We apply the result to an example calculation involving two hydrogen atoms, one of which is in an excited P state. 

We present a theoretical study on the energy dispersion of an ultrathin film of periodically-aligned single-walled carbon nanotubes (SWCNTs) with the help of the Bogoliubov–Valatin transformation. The Hamiltonian of the film was derived using the many-particle green function technique in the Matsubara frequency formalism. The periodic array of SWCNTs was embedded in a dielectric with comparatively higher permittivity than the substrate and the superstrate such that the SWCNT film became independent with the axis of quantization but keeps the thickness as the variable parameter, making the film neither two-dimensional nor three-dimensional, but transdimensional. It was revealed that the energy dispersion of the SWCNT film is thickness dependent. 

Pressure shifts inside an atomic beam are among the more theoretically challenging effects in high-precision measurements of atomic transitions. A crucial element in their theoretical analysis is the understanding of long-range interatomic interactions inside the beam. For excited reference states, the presence of quasi-degenerate states leads to additional challenges, due to the necessity to diagonalize large matrices in the quasi-degenerate hyperfine manifolds. Here, we focus on the interactions of hydrogen atoms in reference states composed of an excited nD state (atom A), and in the metastable 2S state (atom B). We devote special attention to the cases n=3 and n=8. For n=3, the main effect is generated by quasi-degenerate virtual P states from both atoms A and B and leads to experimentally relevant second-order long-range (van-der-Waals) interactions proportional to the sixth inverse power of the interatomic distance. For n=8, in addition to virtual states with two states of P symmetry, one needs to take into account combined virtual P and F states from atoms A and B. The numerical value of the so-called C6 coefficients multiplying the interaction energy was found to grow with the principal quantum number of the reference D state; it was found to be of the order of 1011 in atomic units. The result allows for the calculation of the pressure shift inside atomic beams while driving transitions to nD states. 

We study the magic wavelength for two-photon 1S–nS transitions in a hydrogen and deuterium atom, as well as 2S–nS transitions, where the lower level is the metastable 2S state. At the magic wavelength, the dynamic Stark shifts of the ground and the excited state of the transition coincide, so that the transition frequency is independent of the intensity of the trapping laser field. Experimentally feasible magic wavelengths of transitions with small slopes in the atomic polarizabilities are determined; these are the most stable magic wavelengths against variations of the laser frequency. We provide data for the magic wavelengths for the 1S–nS and 2S–nS transitions in hydrogen and deuterium, with n=2,⋯,8. We also analyze the stability of the elimination of the ac Stark shift at the magic wavelength against tiny variations of the trapping laser frequency from the magic value. 

We present a semi-analytical expression for the dielectric response function of quasi-2D ultrathin films of periodically aligned single-walled carbon nanotubes. We derive the response function in terms of the individual nanotube conductivity, plasma frequency, and the volume fraction of carbon nanotubes in the film. The real part of the dielectric response function is negative for a sufficiently wide range of the incident photon energy, indicating that the film behaves as a hyperbolic metamaterial. Inhomogeneous broadening increases the effect.