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arXiv:1208.0170 · Physical Review A

Dipolar dynamics for interacting ultracold fermions in a trapped optical lattice

Jia-Wei Huo, Wei-Qiang Chen, Ulrich Schollwöck, Matthias Troyer, Fu‐Chun Zhang

Published Sep 11, 2012• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.86.033611

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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.
We study the dynamics of a nonintegrable system comprising interacting cold bosons trapped in an optical lattice in one dimension by means of exact time-dependent numerical density-matrix renormalization group techniques. Particles are confined by a parabolic potential, and dipole oscillations are induced by displacing the trap center of a few lattice sites. Depending on the system parameters this motion can vary from undamped to overdamped. We study the dipole oscillations as a function of the lattice displacement, the particle density, and the strength of interparticle interactions. These results explain the recent experiment [C. D. Fertig et al., Phys. Rev. Lett. 94, 120403 (2005)].
We examine spectral properties on one-dimensional (1D) trapped ultracold Fermi atoms loaded on optical lattices by using the dynamical density-matrix renormalization group (DDMRG) method. We find that spectra are very rich due to the interplay of free or repulsive interaction and the harmonic-trap potential. One of the rich examples is that a 1D Tomonaga-Luttinger (TL) liquid spectrum emerges beneath multiple bound-state flat levels in the Mott-plateau phase and the TL spectrum gradually disappears with a partial breakdown of the central Mott plateau by increasing the trap strength. A more striking example is the growth of a distinct low-energy broadened band from the bound-state flat levels together with the breakdown. It demonstrates a carrier doping effect into the Mott phase in optical lattice systems.
We analyze the dynamics of ultracold atoms in optical lattices induced by a sudden shift of the underlying harmonic trapping potential. In order to study the effect of strong interactions, dimensionality, and lattice topology on transport properties, we consider bosonic atoms with arbitrarily strong repulsive interactions on a two-dimensional square lattice and a hexagonal lattice. On the square lattice we find insulating behavior for weakly interacting atoms and slow relaxation for strong interactions, even when a Mott plateau is present, which in one dimension blocks the dynamics. On the hexagonal lattice the center of mass relaxes to the new equilibrium for any interaction strength.
We investigate the properties of fermions trapped in a one-dimensional (1D) optical lattice by using the density-matrix renormalization (DMRG) group method. Owing to a harmonic confinement potential inherent in real experiments, system becomes inhomogeneous structure. Under certain conditions for weak-repulsive interaction, we find that the single-particle excitation spectrum structure changes to band branching and discrete bound-state states as increasing the trap strength. Additionally, we consider the case of strong-repulsive interacting regimes which local density profile show coexist with central Mott-plateau phase with surrounded by metallic regions. As increasing the trap strength, we find the breakdown of 1D Tomonaga-Luttinger (TL) liquid which is alternative to an effective doping into the Mott phase. We will present the various kinds of striking spectra, show the comparison of repulsive interaction case with attractive interaction one.
We investigate the transport properties in out-of-equilibrium dynamics of strongly correlated dipolar fermions initially localized in one-dimensional inhomogeneous optical lattice. The dynamics is studied by experimentally measurable dynamical variables such as one-body density, pair-correlation function and size of the expanding cloud. In the noninteracting limit, we trace the usual fingerprints of ballistic expansion in the short time dynamics. However, dynamics is strongly affected by system size due to Pauli principle. The dynamics also exhibits significant dependence on the sign of the interactions. We observe that strong repulsive dipolar interaction gives rise to many-body features in the dynamics, while strong attractive dipolar interaction leads to stabilized cluster states. Intermediate dipolar interaction are found to hinder expansion of correlations, while very strong dipolar interaction favors expansion of the cloud. Our work show the effect of dipolar interaction in the transport properties of interacting fermions, that can be studied in on-going experiments with ultracold dipolar fermions.