Quantum signature of breathers in 1D ultracold bosons in optical lattices involving next-nearest neighbor interactions

The dynamics and the energy spectrum of an ultracold gas of bosonic atoms in an optical lattice can be described by a Bose–Hubbard model for which the system parameters can be controlled by laser light. We study by means of the perturbation theory in addition to the numerical diagonalization, the energy spectrum and the related features of the band structures of the ultracold bosons in optical lattices containing a few number of quanta interacting with next-nearest neighbor interactions (NNNI) modeled by the Bose–Hubbard Hamiltonian. The energy spectra of such system display the bound states signature, which are analyzed in the first Brillouin zone for different wave numbers. The finding, i.e., quantum breathers, shows that their probabilities’ weight depends on the wave vector. The influence of NNNI on both the probabilities’ amplitude and the correlation function is also realized in case of a system with a small number of sites, respectively.

Quantum breathers in XXZ ferromagnetic chains with on-site easy-plane anisotropy

The existence and properties of quantum breathers in a one-dimensional XXZ ferromagnetic Heisenberg spin chain with single-ion easy-plane anisotropy are investigated analytically in the Hartree approximation. We show that the system can support the appearance of quantum breathers, and discuss their existence conditions and properties. In addition, our results show that, for quantum breathers in this system, both the corresponding energy and magnetic moment are quantized.