Multiple particle-hole pair creation in the harmonically driven Fermi-Hubbard model

We study the Fermi-Hubbard model in the strongly correlated Mott phase under the influence of a harmonically oscillating hopping rate $J\left(t\right)=J_0+\mathrm{\Delta }Jcos\left(\omega t\right)$. Apart from the well-known fundamental resonance, where the frequency $\omega$ of this oscillation equals (or a little exceeds) the Mott gap, we also find higher-order resonances where multiple particle-hole pairs are created when $\omega$ is near an integer multiple of the gap. These findings should be relevant for experimental realizations such as ultracold fermionic atoms in optical lattices or pump-probe experiments using laser pulses incident on correlated electrons in solid-state materials.

Figure 1

Connectivity diagrams of the considered lattice geometries: a tetrahedron as 3D representation (top left) and as planar diagram (top middle); a square (top right); and fully permutationally invariant lattices with six sites (bottom left) and with eight sites as planar diagram (bottom middle) and as 3D representation (bottom right).

Figure 2

Ratio of the probabilities for double pair creation compared to single pair creation for a tetrahedron (solid black curve) as well as fully permutationally invariant lattices with six sites (dashed blue curve) and with eight sites (dotted red curve). The top plot displays these probabilities as a function of $\arctan (J/U)$ in order to show the full range from $J/U=0$ to $J/U\to \infty$ within the finite interval $[0,\pi /2]$. (Even though we are mostly interested in the strongly correlated Mott regime with $J\ll U$, we show full range from $J/U=0$ to $J/U\to \infty$ in order to study the overall behavior.) The bottom plot shows the same functions after the hopping rate $J$ is rescaled with the coordination number $Z$ of the lattice (i.e., the number of neighbors $\nu$ for a fixed lattice site $\mu$) via $J\to J/Z$. This suggests that the change in position and width of the peaks, when going from four to eight sites, can mainly be attributed to the increasing coordination number $Z$.

Figure 3

Ratio of the probabilities for triple pair creation (top) and quadruple pair creation (bottom), both compared to single pair creation, for fully permutationally invariant lattices with six sites (dashed blue curve) and with eight sites (dotted red curves), again plotted as a function of $\arctan (J/U)$.