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 wavepackets. We calculate the ground-state atomic distribution in the presence of an harmonic confining potential, and the frequencies of small amplitude dipole and quadrupole oscillations. We finally quantize the DNL, recovering an extended Bose-Hubbard model.

Nonlinear tight-binding approximation for Bose-Einstein condensates in a lattice / Smerzi, A; Trombettoni, A. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - 68:2(2003), pp. 1-8. [10.1103/PhysRevA.68.023613]

Nonlinear tight-binding approximation for Bose-Einstein condensates in a lattice

Trombettoni, A
2003-01-01

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 wavepackets. We calculate the ground-state atomic distribution in the presence of an harmonic confining potential, and the frequencies of small amplitude dipole and quadrupole oscillations. We finally quantize the DNL, recovering an extended Bose-Hubbard model.
2003
68
2
1
8
023613
https://arxiv.org/abs/cond-mat/0309285
Smerzi, A; Trombettoni, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32200
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