Nonlinear tight-binding approximation for Bose-Einstein condensates in a lattice
Year: 2003
Authors: Smerzi A., Trombettoni A.
Autors Affiliation: Univ Trent, Ist Nazl Fis Mat, BEC, CRS, I-38050 Povo, Italy; Univ Trent, Dipartimento Fis, I-38050 Povo, Italy; Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA; Univ Parma, Ist Nazl Fis Mat, I-43100 Parma, Italy; Univ Parma, Dipartimento Fis, I-43100 Parma, Italy.
Abstract: 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.
Journal/Review: PHYSICAL REVIEW A
Volume: 68 (2) Pages from: 23613-1 to: 23613-8
KeyWords: Instabilities; Superfluid; Insulator; ArraysDOI: 10.1103/PhysRevA.68.023613Citations: 131data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)