Hopping Modulation in a One-Dimensional Fermi-Hubbard Hamiltonian

Abstract

We consider a strongly repulsive two-component Fermi gas in a one-dimensional optical lattice described in terms of a Hubbard Hamiltonian. We analyze the response of the system to a periodic modulation of the hopping amplitude in the presence of a large two-body interaction. By (essentially) the exact simulations of the time evolution, we find a nontrivial double occupancy frequency dependence. We show how the dependence relates to the spectral features of the system given by the Bethe ansatz. The discrete nature of the spectrum is clearly reflected in the double occupancy after a long enough modulation time. We also discuss the implications of the 1D results to experiments in higher dimensional systems.

Spin correlations and doublon production rate for fermionic atoms in modulated optical lattices

“…For fermions the energy absorption rate (EAR) cannot be implemented accurately enough and a variant of this probe measuring the doublon production rate (DPR) has been proposed [19]. This DPR measurement in the linear response regime could be successfully implemented [20], and thus stimulates further studies of theoretical calculation of DPR spectra [21][22][23][24][25][26] and doublon dynamics [27][28][29].In addition, it was shown [19] by a direct comparison of the two quantities, that the integrated intensity of the modulation does directly give access to the nearestneighbor AFM correlations. Intuitively, for fermionic atoms, spin configurations of neighboring atoms are relevant to the spectra because of the Pauli exclusive principle: while the hopping is allowed for neighboring atom spins pointing in anti-parallel, it is blocked for ferromagnetically aligned spin configuration.…”

Collision of one dimensional (1D) spin polarized Fermi gases in an optical lattice

“…[5]), while its dynamical behavior has been explored to a much lesser extent. Nevetheless, in the recent past, the versatility of ultracold atomic systems has led, from a numerical and theoretical point of view, to approach the analysis of the dynamics in such systems [6,7,8,9,10,11,12,13,14], leading to a revived interest in the unitary evolution of closed quantum systems [15]. Recently, an interesting experimental investigation of spin dynamics in a system of colliding Fermi gas clouds was reported [16], closely related to the topic of this article.…”

Dynamics of an impurity in a one-dimensional lattice

“…To obtain the ground state of this Hamiltonian and simulate the full many-body dynamics after the impurity has received a kick with a defined quasi-momentum, we use a code based on the TEBD algorithm, more details of which can be found in e.g. [46][47][48][49]. In our simulations, we have considered a lattice size of L = 200 sites (L = 400 in one case), N ↓ = 1, N ↑ = [1, 10, 20, .…”