We consider a one-dimensional optical lattice of three-dimensional Harmonic Oscillators which are loaded with neutral fermionic atoms trapped into two hyperfine states. By means of a standard variational coherent-state procedure, we derive an effective Hamiltonian for this quantum model and the hamiltonian equations describing its evolution. To this end, we identify the algebra $\mathcal L$ of two-fermion operators --describing the relevant microscopic quantum processes of our model-- whereby the natural choice for the trial state appears to be a so(2r) coherent state. The coherent-state parameters, playing the role of dynamical variables for the effective Hamiltonian, are shown to identify with the $\mathcal L$ -operator expectation values thus providing a clear physical interpretation of this algebraic mean-field picture.We consider a one-dimensional optical lattice of three-dimensional Harmonic Oscillators which are loaded with neutral fermionic atoms trapped into two hyperfine states. By means of a standard variational coherent-state procedure, we derive an effective Hamiltonian for this quantum model and the hamiltonian equations describing its evolution. To this end, we identify the algebra $\mathcal L$ of two-fermion operators --describing the relevant microscopic quantum processes of our model-- whereby the natural choice for the trial state appears to be a so(2r) coherent state. The coherent-state parameters, playing the role of dynamical variables for the effective Hamiltonian, are shown to identify with the $\mathcal L$-operator expectation values thus providing a clear physical interpretation of this algebraic mean-field picture.

arXiv:cond-mat/0512605Journal of Physics B Atomic Molecular and Optical PhysicsMay 2, 20061 citation

Fermionic atoms in an optical lattice

Michael Köhl, Henning Moritz, Thilo Stöferle +2 more

Conference on Lasers and Electro-OpticsJan 1, 20050 citations

Optical lattice emulators

Eric Duchon, Yen Lee Loh, N. Trivedi

Abstract The equilibrium thermodynamics of bosons and fermions in optical lattices are considered in the single-band Hubbard regime, with an emphasis on interesting magnetic, superfluid, and spin liquid ground states. The parameters of the Hubbard model—the tunneling and interaction parameters—can be obtained quantitatively in terms of the strength and periodicity of the optical lattice potential, tuned by the laser intensity and wavelength. This direct link between the parameters of a theoretical model and the actual experimental optical lattice gives rise to the phase diagram of the Bose–Hubbard model. The definition of the order parameter as an expectation value of the annihilation operator in a coherent state is discussed. This phase-coherent superfluid state is contrasted with the phase-incoherent Mott state naturally defined in terms of number states. Following the repulsive Bose–Hubbard model, the phase diagram of the Fermi–Hubbard model is considered with both attractive and repulsive interactions.Abstract The equilibrium thermodynamics of bosons and fermions in optical lattices are considered in the single-band Hubbard regime, with an emphasis on interesting magnetic, superfluid, and spin liquid ground states. The parameters of the Hubbard model—the tunneling and interaction parameters—can be obtained quantitatively in terms of the strength and periodicity of the optical lattice potential, tuned by the laser intensity and wavelength. This direct link between the parameters of a theoretical model and the actual experimental optical lattice gives rise to the phase diagram of the Bose–Hubbard model. The definition of the order parameter as an expectation value of the annihilation operator in a coherent state is discussed. This phase-coherent superfluid state is contrasted with the phase-incoherent Mott state naturally defined in terms of number states. Following the repulsive Bose–Hubbard model, the phase diagram of the Fermi–Hubbard model is considered with both attractive and repulsive interactions.

Nov 27, 20141 citation

Interacting Fermions in Optical Lattices

Tilman Esslinger

Bulletin of the American Physical SocietyMay 19, 20050 citations

Fermionic Coherent States

Monique Combescure, Didier Robert

Theoretical and mathematical physicsJan 1, 20122 citations

\mathcal L

of two-fermion operators --describing the relevant microscopic quantum processes of our model-- whereby the natural choice for the trial state appears to be a so(2r) coherent state. The coherent-state parameters, playing the role of dynamical variables for the effective Hamiltonian, are shown to identify with the

\mathcal L

-operator expectation values thus providing a clear physical interpretation of this algebraic mean-field picture.