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Effects of Inhomogeneity on the Spectrum of the Mott-Insulator State



G Pupillo, Eite Tiesinga, Carl J. Williams


We investigate the existence of quantum quasi phase transitions for an ensemble of ultracold bosons in a one-dimensional optical lattice, performing exact diagonalizations of the Bose-Hubbard Hamiltonian. When an external parabolic potential is added to the system quasi phase transitions are induced by the competition of on-site mean-field energy, hopping energy, and energy offset among lattice sites due to the external potential and lead to the coexistence of regions of particle localization and delocalization in the lattice. We clarify the microscopic mechanisms responsible for these quasi energy is large compared to the hopping energy. In particular, we show that a model Hamiltonian involving a few Fock states can describe the behavior of energy gap, mean particle numbers per site, and number fluctuations per site almost quantitatively. The role of symmetry on the gap as a function of the depth of the external trapping potential is elucidated. We discuss possible experimental signatures of quasi phase transitions studying the single particle density matrix and explain microscopically the occurrence of local maxima in the momentum distribution. The role of a thermal population of the excited states on the momentum distribution is discussed.
Physical Review A (Atomic, Molecular and Optical Physics)
No. 6


Bose-Hubbard Hamiltonian, Optical lattice, phase transition, ultracold atoms


Pupillo, G. , Tiesinga, E. and Williams, C. (2003), Effects of Inhomogeneity on the Spectrum of the Mott-Insulator State, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed March 4, 2024)
Created November 30, 2003, Updated October 12, 2021