Expansion dynamics of interacting fermions in a lattice are simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and non-paired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.PACS numbers: 71.10. Fd , 03.75.Ss, 73.20.Mf Important physical phenomena such as magnetism and high-temperature superconductivity are often approached by theories based on the Hubbard model [2, 3] which describes interacting particles in a lattice. Within ultracold gas systems [3, 4], the Hubbard model can be efficiently realized and studied in experiments with bosonic [5] and recently with fermionic atoms [6,7]. Intriguingly, the dimension can be easily controlled. Low-dimensional systems such as nanowires, iron pnictides and graphene are currently highlighted topics of research. Models for the quantum many-body physics of 2D and 1D systems can explored with ultracold gases, c.f. recent experiments on fermions in one dimension [8] and expanding fermions in a 2D lattice [5]. For one-dimensional systems, an advantage is that the experiments can be compared to exact theoretical descriptions. However, although the ground state and static properties of one-dimensional systems are known to an impressive degree [2, 3], dynamics is largely unexplored. Work on theory and simulation of dynamical properties of interacting fermions in 1D has recently been emerging [12].In this Letter, we study with exact numerical methods the expansion of fermions within the one-dimensional Hubbard model. We show that the resulting complex dynamics can be efficiently described by a two-fluid model in which we deduce the dynamics of the fluids from the dynamics of a Hubbard dimer. Our results explain several main features of the experiment [5] performed in 2D, and give exact predictions for future experiments in 1D. The simple Hubbard-dimer two-fluid model that we have developed provides a basis for the description of various types of expansion, collision and oscillation dynamics for fermions in lattices.We use the time-evolving block decimation (TEBD) algorithm [13] to describe the time evolution generated by the Hubbard Hamiltonian wheren i,σ = c † i σ c i σ with c † i σ and c i σ representing the creation and annihilation of a fermion with spin σ at the site i = 1 . . . L. Moreover, the initial state is given by |φ(0) = |∅ 1 . . . Fig. 1). The initial state consists thus of a band insulator occupying the central O L − O R sites of an oth...

We consider a two-component Fermi gas in the presence of spin imbalance, modeling the system in terms of a one-dimensional attractive Hubbard Hamiltonian initially in the presence of a confining trap potential. With the aid of the time-evolving block decimation method, we investigate the dynamics of the initial state when the trap is switched off. We show that the dynamics of a gas initially in the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is decomposed into the independent expansion of two fluids, namely the paired and the unpaired particles. In particular, the expansion velocity of the unpaired cloud is shown to be directly related to the FFLO momentum. This provides an unambiguous signature of the FFLO state in a remarkably simple way.Comment: Supplementary material include

We propose that with ultracold Fermi gases one can realize a spin-asymmetric Josephson effect in which the two spin components of a Cooper pair are driven asymmetrically--corresponding to driving a Josephson junction of two superconductors with different voltages V(↑) and V(↓) for spin up and down electrons, respectively. We predict that the spin up and down components oscillate at the same frequency but with different amplitudes. Furthermore our results reveal that the standard interpretation of the Josephson supercurrent in terms of coherent bosonic pair tunneling is insufficient. We provide an intuitive interpretation of the Josephson supercurrent as interference in Rabi oscillations of pairs and single particles, the latter causing the asymmetry.

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-dimensional clouds in a lattice. There is a symmetry in the collision behaviour between the attractive and repulsive interactions. We analyze the pair formation dynamics in the collision region, providing a quantitative analysis of the pair formation mechanism in terms of a simple two-site model.

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