Hubbard-like Hamiltonian for ultracold atoms in a one-dimensional optical lattice

Francesco Massel and Vittorio Penna
Phys. Rev. A 72, 053619 – Published 17 November 2005

Abstract

Based on the standard many-fermion field theory, we construct models describing ultracold fermions in a one-dimensional optical lattice by implementing a mode expansion of the fermionic field operator where modes, in addition to space localization, take into account the quantum numbers inherent in local fermion interactions. The resulting models are generalized Hubbard Hamiltonians whose interaction parameters are derived by a fully analytical calculation. The special interest for this derivation resides in its model-generating capability and in the flexibility of the trapping techniques that allow the tuning of the Hamiltonian interaction parameters over a wide range of values. While the Hubbard Hamiltonian is recovered in the very low-density regime, in general, far more complicated Hamiltonians characterize high-density regimes, revealing a rich scenario for both the phenomenology of interacting trapped fermions and the experimental realization of devices for quantum-information processing. As a first example of the different situations that may arise beyond the models well known in the literature (the unpolarized-spin fermion model and the noninteracting spin-polarized fermion model), we derive a rotational Hubbard Hamiltonian describing the local rotational activity of spin-polarized fermions. Based on standard techniques we obtain the mean-field version of our model Hamiltonian and show how different dynamical algebras characterize the cases of attractive and repulsive two-body potentials.

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  • Received 1 April 2005

DOI:https://doi.org/10.1103/PhysRevA.72.053619

©2005 American Physical Society

Authors & Affiliations

Francesco Massel and Vittorio Penna

  • Dipartimento di Fisica and UdR INFM, Torino Politecnico, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy

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Issue

Vol. 72, Iss. 5 — November 2005

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