One-dimensional optical lattices and impenetrable bosons

Abstract

We study the limit of large onsite repulsion of the one-dimensional Bose-Hubbard model at low densities, and derive a strong-coupling effective Hamiltonian. By taking the lattice parameter to zero, the Hamiltonian becomes a continuum model of fermions with attractive interactions. The leading corrections to the internal energy of a hard-core-boson (Tonks) gas as well as the (finite temperature) pair correlations of a strongly interacting Bose gas are calculated. We explore the possibility of realizing, in an optical lattice, a Luttinger liquid with stronger density correlations than the Tonks gas. A quantum phase transition to a charge-density-wave Mott insulator is also discussed.

4 pages. Version accepted for publication in Phys. Rev. A; title changed

References in corpus (4)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Commensurate-incommensurate transition of cold atoms in an optical lattice
• Low-Energy Properties of a One-dimensional System of Interacting bosons with Boundaries
• Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap

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