Degenerate Fermi gas in a combined harmonic-lattice potential

Abstract

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favourable conditions for realizing degenerate Fermi gases in optical lattices.

Fermi-Hubbard Physics with Atoms in an Optical Lattice

“…The interplay between t and U, the filling, and the underlying confining potential e i determines the physics of the system. high-energy eigenstates, which are localized in the outer regions of the trap, can be identified (68)(69)(70)(71)(72). A very convenient measure in a harmonic trap with a geometric mean trapping frequency o is the characteristic atom number (70,71).…”

Thermodynamic properties of a rotating Bose--Einstein condensation in a deep optical lattice

“…Properties of the single particle energy eigenvalues have been discussed for the combined harmonic optical trap [19], as well as rotating harmonic potential [20,24]. Here we use the results of these studies to suggest an approximated single particle spectrum for the rotating harmonic oscillator in an optical lattice.…”

“…Since the rate of decreasing is rapid in small depth due to rotation and it slows down for high depth, we have to conclude that for the rotating boson in optical lattice, the compensate of the critical temperature can be balanced by the localization of the atoms at the optical trap lattice sites due to the centrifugal force. The increase or decrease in the critical temperature as a function of V 0 is considered by Blakie and Wang [19] for optically trapped nonrotating Bose gas.…”

“…Separately, fast rotation or the deepness of the optical potential is affected significantly by the thermodynamic properties of the system [19,20] compared to the pure harmonically BEC. Consequently, study of the thermodynamic properties of a rotating Bose gas in an optical lattice under a realistic experimental condition is quite interesting.…”

Preparing a highly degenerate Fermi gas in an optical lattice

“…However, temperatures low enough to observe exotic phases such as these are difficult to achieve when optical lattices are loaded with a harmonic external confining potential. It has been theoretically predicted [9] and experimentally observed [3] that fermions adiabatically loaded into an optical lattice with harmonic external confinement experience heating for all but very high initial temperatures and filling factors (number of atoms per lattice site) [10].…”