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arXiv:1607.06352 · Physical Review A

Density redistribution effects in fermionic optical lattices

Medha Soni, Michele Dolfi, Matthias Troyer

Published Dec 6, 2016• 1 citation
arXivHTMLPDF

Abstract

We simulate a one-dimensional fermionic optical lattice to analyze heating due to nonadiabatic lattice loading. Our simulations reveal that, similar to the bosonic case, density redistribution effects are the major cause of heating in harmonic traps. We suggest protocols to modulate the local-density distribution during the process of lattice loading in order to reduce the excess energy. Our numerical results confirm that linear interpolation of the trapping potential and/or the interaction strength is an efficient method of doing so, bearing practical applications relevant to experiments.

DOI
10.1103/physreva.94.063404

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We simulate a one-dimensional fermionic optical lattice to analyze heating due to nonadiabatic lattice loading. Our simulations reveal that, similar to the bosonic case, density redistribution effects are the major cause of heating in harmonic traps. We suggest protocols to modulate the local-density distribution during the process of lattice loading in order to reduce the excess energy. Our numerical results confirm that linear interpolation of the trapping potential and/or the interaction strength is an efficient method of doing so, bearing practical applications relevant to experiments.
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Abstract Experiments with ultracold gases on the lattice give the opportunity to realize superfluid fermionic mixtures in a trapping potential. The external trap modifies the chemical potential locally. Moreover, this trap also introduces non-homogeneity in the superconducting order parameter. There are, among other approaches, two methods which can be used to describe the system of two-component mixtures loaded into an optical lattice: the Local Density Approximation (LDA) and the self-consistent Bogoliubov–de Gennes equations. Here, we compare results obtained within these two methods. We conclude that the results can be distinguishable only in the case of a small value of the pairing interaction.
The entropy-temperature curves are calculated for noninteracting bosons in a three-dimensional (3D) optical lattice and a 2D lattice with transverse harmonic confinement for ranges of depths and filling factors relevant to current experiments. We demonstrate regimes where the atomic sample can be significantly heated or cooled by adiabatically changing the lattice depth. We indicate the critical points for condensation in the presence of a lattice and show that the system can be reversibly condensed by changing the lattice depth. We discuss the effects of interactions on our results and consider nonadiabatic processes.
The dynamics of a Bose-Einstein condensate in a harmonic trap with a nonadiabatically loaded optical lattice is studied analytically. As the global effect of the optical potential can be described in terms of a renormalized interaction coupling constant and of an effective mass in the laser direction, a fast loading can be understood as a sudden change of those characteristic parameters. In this approach, a standard scaling transformation is applied to study the resulting dynamics, in particular, the generation of collective modes. The relevance of the excited modes to the interference patterns obtained after free expansion is analyzed. The applicability of trap-frequency adjustments as a strategy for suppressing the loading induced excitations is discussed.
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes.