Nonequilibrium steady states and resonant tunneling in time-periodically driven systems with interactions

Time-periodically driven systems are a versatile toolbox for realizing interesting effective Hamiltonians. Heating, caused by excitations to high-energy states, is a challenge for experiments. While most setups so far address the relatively weakly interacting regime, it is of general interest to study heating in strongly correlated systems. Using Floquet dynamical mean-field theory, we study nonequilibrium steady states (NESS) in the Falicov-Kimball model, with time-periodically driven kinetic energy or interaction. We systematically investigate the nonequilibrium properties of the NESS. For a driven kinetic energy, we show that resonant tunneling, where the interaction is an integer multiple of the driving frequency, plays an important role in the heating. In the strongly correlated regime, we show that this can be well understood using Fermi's golden rule and the Schrieffer-Wolff transformation for a time-periodically driven system. We furthermore demonstrate that resonant tunneling can be used to control the population of Floquet states to achieve “photodoping.” For driven interactions introduced by an oscillating magnetic field near a widely adopted Feshbach resonance, we find that the double occupancy is strongly modulated. Our calculations apply to shaken ultracold-atom systems and to solid-state systems in a spatially uniform but time-dependent electric field. They are also closely related to lattice modulation spectroscopy. Our calculations are helpful to understand the latest experiments on strongly correlated Floquet systems.

Figure 1

Double occupancy for the Falicov-Kimball model with ac-driven kinetic energy.

Figure 2

For the Falicov-Kimball model with ac-driven kinetic energy, we show the fraction of atoms excited to the upper band $n_{\mathrm{up}}$, double occupancy $D$, work $W$ (symbols), energy dissipation $I$ (lines), and Bessel function of the first kind ${\mathcal{J}}_l\left(\frac{E}{\mathrm{\Omega }}\right)$. At the one-photon resonance (top panel), the oscillation is qualitatively described by $\left|{\mathcal{J}}_1\left(\frac{E}{\mathrm{\Omega }}\right)\right|$, while the oscillation at the two-photon resonance qualitatively coincides with $\left|{\mathcal{J}}_2\left(\frac{E}{\mathrm{\Omega }}\right)\right|$.

Figure 3

For the Falicov-Kimball model with ac-driven kinetic energy, the fraction of atoms excited to the upper band $n_{\mathrm{up}}$, double occupancy $D$, work $W$ (symbols), energy dissipation $I$ (lines), and Bessel function of the first kind ${\mathcal{J}}_l\left(\frac{E}{\mathrm{\Omega }}\right)$ are shown in the weakly interacting regime.

Figure 4

Double occupancy versus driving amplitude $\delta U$ for different values of $U$ and the driving frequency $\mathrm{\Omega }$.

Figure 5

Spectral function $A\left(\omega \right)$ and occupied density of states $N\left(\omega \right)$ for points with the same color indicated in Fig. 4. The olive lines correspond to $U=0$.

Figure 6

Double occupancy versus $U$ for different driving amplitudes with driving frequency $\mathrm{\Omega }=7$.

Figure 7

Work done by the driving field $W$ (symbols) and energy dissipation to the bath $I$ (lines) as a function of $U$ for different driving amplitudes with driving frequency $\mathrm{\Omega }=7$.