Nonlinear Tight-Binding Approximation for Bose-Einstein Condensates in a Lattice
arXiv:cond-mat/0309285 · doi:10.1103/PhysRevA.68.023613
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.
References in corpus (18)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Theory of Bose-Einstein condensation in trapped gases
- Cold bosonic atoms in optical lattices
- Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
- Josephson Junction Arrays with Bose-Einstein Condensates
- Ground-State Properties of Magnetically Trapped Bose-Condensed Rubidium Gas
- Exploring phase coherence in a 2D lattice of Bose-Einstein condensates
- Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1-D optical lattices
- Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
- Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates
- Nonlinear excitations in arrays of Bose-Einstein condensates
- Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
- Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential
- Expansion of a coherent array of Bose-Einstein condensates
- Macroscopic dynamics of a trapped Bose-Einstein condensate in the presence of 1D and 2D optical lattices
- Collective excitations of a trapped Bose-Einstein condensate in the presence of a 1D optical lattice
- Output from Bose condensates in tunnel arrays: the role of mean-field interactions and of transverse confinement
- Free expansion of a Bose-Einstein condensate in a 1D optical lattice
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- Stability of Bose-Einstein condensates in a Kronig-Penney potential
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- Avalanches of Bose-Einstein Condensates in Leaking Optical Lattices
- Self-Trapping of Bose-Einstein Condensates in an Optical Lattice: the Effect of the System Dimension
- Stable periodic density waves in dipolar Bose-Einstein condensates trapped in optical lattices
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- Modulational instability of two-component Bose-Einstein condensates in an optical lattice
- Propagation of sound in a Bose Einstein condensate in an optical lattice
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- Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement
- Phase-slips and vortex dynamics in Josephson oscillations between Bose-Einstein condensates
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- Optical lattice influenced geometry of quasi-2D binary condensates and quasiparticle spectra
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- Stability and decay of Bloch oscillations in presence of time-dependent nonlinearity
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