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

Journal Article · Tue Nov 15 00:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.72.0· OSTI ID:20786565

Massel, Francesco; Penna, Vittorio ^[1]

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1. Dipartimento di Fisica and UdR INFM, Torino Politecnico, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy)

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.

• OSTI ID: 20786565
• Journal Information: Physical Review. A, Vol. 72, Issue 5; Other Information: DOI: 10.1103/PhysRevA.72.053619; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
ATOMS
DENSITY
FERMIONS
FIELD OPERATORS
FIELD THEORIES
HAMILTONIANS
HUBBARD MODEL
MEAN-FIELD THEORY
ONE-DIMENSIONAL CALCULATIONS
POTENTIALS
QUANTUM INFORMATION
QUANTUM NUMBERS
RADIATION PRESSURE
SPIN
SPIN ORIENTATION
TRAPPING
TWO-BODY PROBLEM