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arXiv:cond-mat/0403429 · New Journal of Physics

Quantum transport of non-interacting Fermi gas in an optical lattice combined with harmonic trapping

V Ruuska, Päivi Törmä

Published Jun 11, 2004• 15 citations
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Abstract

We have considered non-interacting Fermi gas in a combined harmonic and periodic potential. We calculate the energy spectrum and simulate the motion of the gas after sudden replacement of the trap centre. For different parameter regimes, the system presents dipole oscillations, damped oscillations around the replaced centre as well as localization. The behaviour can be explained by a change in the energy spectrum from linear to quadratic.

DOI
10.1088/1367-2630/6/1/059

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We have considered non-interacting Fermi gas in a combined harmonic and periodic potential. We calculate the energy spectrum and simulate the motion of the gas after sudden replacement of the trap centre. For different parameter regimes, the system presents dipole oscillations, damped oscillations around the replaced centre as well as localization. The behaviour can be explained by a change in the energy spectrum from linear to quadratic.
Using the time-dependent density-matrix renormalization-group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass when the interaction strength is increased. This unique feature can be considered as a dynamical signature for the emergence of a Mott plateau for an interacting trapped Fermi gas in an optical lattice.
We explore the transport properties of an interacting Fermi gas in a three-dimensional optical lattice. The center of mass dynamics of the atoms after a sudden displacement of the trap minimum is monitored for different interaction strengths and lattice fillings. With increasingly strong attractive interactions the weakly damped oscillation, observed for the noninteracting case, turns into a slow relaxational drift. Tuning the interaction strength during the evolution allows us to dynamically control the transport behavior. Strong attraction between the atoms leads to the formation of local pairs with a reduced tunneling rate. The interpretation in terms of pair formation is supported by a measurement of the number of doubly occupied lattice sites. This quantity also allows us to determine the temperature of the noninteracting gas in the lattice to be as low as (27+/-2)% of the Fermi temperature.
Abstract This chapter discusses some features exhibited by quantum gases in the presence of periodic optical potentials (optical lattices). The behaviour of the single-particle excitation spectrum exhibiting the typical Bloch band structure is briefly summarized. The equilibrium properties of a Bose–Einstein condensate and of the ideal Fermi gas are discussed, with special focus on the behaviour of the momentum distribution. It also considers the effects of localization in one-dimensional quasiperiodic potentials and the nature of Bloch oscillations. The chapter discusses the structure of the elementary excitations in an optical potential, including the motion of the centre of mass in the presence of an additional harmonic potential. Finally, the chapter mentions the problem of quantum fluctuations, and it introduces the physics of the Bose–Hubbard and Fermi–Hubbard models, whose systematic investigation lies outside the scope of this book.
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 favorable conditions for realizing degenerate Fermi gases in optical lattices.