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In the dilute limit, the properties of fermionic lattice models with short-range attractive interactions converge to those of a dilute Fermi gas in continuum space. We investigate this connection using mean-field and we show that the existence of a finite lattice spacing has consequences down to very small densities. In particular we show that the reduced translational invariance associated to the lattice periodicity has a pivotal role in the finite-density corrections to the universal zero-density limit. For a parabolic dispersion with a sharp cut-off, we provide an analytical expression for the leading-order corrections in the whole BCS-BEC crossover. These corrections, which stem only from the unavoidable cut-off, contribute to the leading-order corrections to the relevant observables. In a generic lattice we find a universal power-law behavior $n^{1/3}$ which leads to significant corrections already for small densities. Our results pose strong constraints on lattice extrapolations of dilute Fermi gas properties.
In this work we analyze the dynamical behavior of the collision between two clouds of fermionic atoms with opposite spin polarization. By means of the time-evolving block decimation (TEBD) numerical method, we simulate the collision of two one-dimens
We review the status of cooling techniques aimed at achieving the deepest quantum degeneracy for atomic Fermi gases. We first discuss some physical motivations, providing a quantitative assessment of the need for deep quantum degeneracy in relevant p
The Hartree energy shift is calculated for a unitary Fermi gas. By including the momentum dependence of the scattering amplitude explicitly, the Hartree energy shift remains finite even at unitarity. Extending the theory also for spin-imbalanced syst
We present in detail two variants of the lattice Monte Carlo method aimed at tackling systems in external trapping potentials: a uniform-lattice approach with hard-wall boundary conditions, and a non-uniform Gauss-Hermite lattice approach. Using thos
We investigate a species selective cooling process of a trapped $mathrm{SU}(N)$ Fermi gas using entropy redistribution during adiabatic loading of an optical lattice. Using high-temperature expansion of the Hubbard model, we show that when a subset $