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Mean-field algebraic approach to the dynamics of fermions in a 1D optical lattice

F. P. Massel·V. Penna
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Abstract

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.

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F. P. Massel, V. Penna. 2005-12-23. Mean-field algebraic approach to the dynamics of fermions in a 1D optical lattice. https://doi.org/10.1088/0953-4075%2F39%2F10%2Fs14

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