We theoretically study the excitation spectrum of confined macroscopic optical lattices in the Mott-insulating limit. For large systems, a fast numerical method is proposed to calculate the ground state filling and excitation energies. We introduce many-particle on-site energies capturing multi-band effects and discuss tunnelling on a perturbative level using an effectively restricted Hilbert space. Results for small one-dimensional lattices obtained by this method are in good agreement with the exact multi-band diagonalization of the Hamiltonian. Spectral properties associated with the formation of regions with constant filling, so-called Mott shells, are investigated and interfaces between the shells with strong particle fluctuations are characterized by gapless local excitations.We theoretically study the excitation spectrum of confined macroscopic optical lattices in the Mott-insulating limit. For large systems, a fast numerical method is proposed to calculate the ground state filling and excitation energies. We introduce many-particle on-site energies capturing multi-band effects and discuss tunnelling on a perturbative level using an effectively restricted Hilbert space. Results for small one-dimensional lattices obtained by this method are in good agreement with the exact multi-band diagonalization of the Hamiltonian. Spectral properties associated with the formation of regions with constant filling, so-called Mott shells, are investigated and interfaces between the shells with strong particle fluctuations are characterized by gapless local excitations.

arXiv:0906.5229Journal of Physics B Atomic Molecular and Optical PhysicsJun 24, 20096 citations

Microscopic derivation of the low-lying excitation spectrum of an interacting bose system

Willy Bierter, Harry L. Morrison

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoMay 1, 19696 citations

Perturbative spectrum of trapped weakly interacting bosons in two dimensions

Velimir Bardek, Larisa Jonke, Stjepan Meljanac

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large- $N$ expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-$N$ expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.

arXiv:cond-mat/0012438Physical Review AJun 11, 20013 citations

Excitation spectrum of a condensed bose system

P. D�rre

The European Physical Journal BMar 1, 19801 citation

Microscopic computational model of a superfluid

M. Ovchinnikov, Alexey Novikov

A finite one-dimensional microscopic model of a superfluid is presented. The model consists of interacting Bose particles with an additional impurity particle confined to a ring. Both semiclassical and exact quantum calculations reveal dissipationless motion of impurity with increased effective mass due to its interaction with the excitations of Bose fluid. It is shown that both the excitation spectrum of Bose fluid and the excitation spectrum of impurity can be analyzed using the structure of the ground state of the system.A finite one-dimensional microscopic model of a superfluid is presented. The model consists of interacting Bose particles with an additional impurity particle confined to a ring. Both semiclassical and exact quantum calculations reveal dissipationless motion of impurity with increased effective mass due to its interaction with the excitations of Bose fluid. It is shown that both the excitation spectrum of Bose fluid and the excitation spectrum of impurity can be analyzed using the structure of the ground state of the system.

arXiv:0911.2216The Journal of Chemical PhysicsJun 2, 20103 citations

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-

N

expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.