Driven Imposters: Controlling Expectations in Many-Body Systems

We present a framework for controlling the observables of a general correlated electron system driven by an incident laser field. The approach provides a prescription for the driving required to generate an arbitrary predetermined evolution for the expectation value of a chosen observable, together with a constraint on the maximum size of this expectation. To demonstrate this, we determine the laser fields required to exactly control the current in a Fermi-Hubbard system under a range of model parameters, fully controlling the nonlinear high-harmonic generation and optically observed electron dynamics in the system. This is achieved for both the uncorrelated metalliclike state and deep in the strongly correlated Mott insulating regime, flipping the optical responses of the two systems so as to mimic the other, creating “driven imposters.” We also present a general framework for the control of other dynamical variables, opening a new route for the design of driven materials with customized properties.

Figure 1

Doublon occupation for increasing correlation strengths of $U/t_0$ under the action of the laser. Simulations are distinguished by unit increments in $U/t_0$, from $U=0$ to $U=10t_0$. Black points indicate the time when dielectric breakdown is predicted to occur, and $U=7t_0$ is the first plotted value for which the laser field has an insufficient amplitude for causing a breakdown.

Figure 2

Using tracking, it is possible to make the HHG spectra of one system mimic the other. Here tracking has been implemented to swap the optical characteristics of two systems, i.e., $J_T^{(0)}(t)=J^{(7)}(t)$ and $J_T^{(7)}(t)=J^{(0)}(t)$. The top section shows the original and tracked control fields and currents in the time domain, while the bottom section demonstrates the strategy’s success in mimicking spectra.

Figure 3

The doublon density of the $U=0$ (upper plot) and $U=7t_0$ (lower plot) systems under the reference HHG field $D(t)$, or the tracking field to mimic the current of the other system $D_T(t)$. In the $U=0$ model, the doublon density is largely insensitive to the tracking field and resulting change in current, i.e., $D_T^{(0)}(t)\approx D^{(0)}(t)$. Conversely, at high $U/t_0$, the peak amplitude of the tracking control field needed to mimic the spectrum of the $U=0$ conducting system is large enough to cause a dielectric breakdown. This breakdown time for $D_T^{(7)}(t)$ is calculated via Eq. (15), and demonstrates that tracking the spectrum of a conductor from the Mott state necessitates a breakdown of the insulating state as measured by the doublon occupation.

Figure 4

Using tracking, it is possible to boost the yield of a higher (ninth) harmonic by tracking a synthetic spectrum. The upper panel shows the necessary control-field needed to reproduce this current is sensitive to the correlation strength.