2003/08/29 by Augusto Smerzi, Andrea Trombettoni · 7 citations
Physics and Astronomy · #Amplitude #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Dipole #Excitation #Lattice (music) #Matter wave #Nonlinear Photonic Systems #Nonlinear system #Physics #Quadrupole #Quantum #Quantum electrodynamics #Quantum mechanics #Strong Light-Matter Interactions #cond-mat
paper · pdf · doi:10.1103/physreva.68.023613
published as Phys. Rev. A 68, 023613 (2003)
openalex publication_date 2003/08/29 · arxiv created 2003/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The dynamics of Bose-Einstein condensates trapped in a deep optical lattice is governed by a discrete nonlinear equation (DNL). Its degree of nonlinearity and the intersite hopping rates are retrieved from a nonlinear tight-binding approximation taking into account the effective dimensionality of each condensate. We derive analytically the Bloch and the Bogoliubov excitation spectra and the velocity of sound waves emitted by a traveling condensate. Within a Lagrangian formalism, we obtain Newtonian-like equations of motion of localized wave packets. We calculate the ground-state atomic distribution in the presence of a harmonic confining potential, the frequencies of small amplitude dipole, and quadrupole oscillations. We finally quantize the DNL, recovering an extended Bose-Hubbard model.