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

Abstract

We investigate the existence of quantum {\it 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 {\it 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 {\it quasi} phase transitions as a function of the depth of the external potential when the on-site mean-field 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 {\it 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.

arXiv comment7 pages, 7 figures; Revised version accepted for publication on Phys.Rev.A

References in corpus (7)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Mott Domains of Bosons Confined on Optical Lattices
• Revealing Superfluid--Mott-Insulator Transition in an Optical Lattice
• Superfluidity and Interference Pattern of Ultracold Bosons in Optical Lattices
• Bogoliubov approach to superfluidity of atoms in an optical lattice
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• Studies of bosons in optical lattices in a harmonic potential
• Dipole and monopole modes in the Bose-Hubbard model in a trap
• Scalable quantum computation in systems with Bose-Hubbard dynamics
• Collective modes of a strongly interacting Bose gas: probing the Mott transition
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• Correlated bosons in a one-dimensional optical lattice: Effects of the trapping potential and of quasiperiodic disorder
• Mott insulator dynamics