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.

Here we present an expanded analysis of a model for the manipulation and control of observables in a strongly correlated, many-body system, which was first presented by McCaul et al. [G. McCaul et al., Phys. Rev. Lett. 124, 183201 (2020)]. A field-free, nonlinear equation of motion for controlling the expectation value of an essentially arbitrary observable is derived, together with rigorous constraints that determine the limits of controllability. We show that these constraints arise from the physically reasonable assumptions that the system will undergo unitary time evolution, and has enough degrees of freedom for the electrons to be mobile. Furthermore, we give examples of multiple solutions to generating target observable trajectories when the constraints are violated. Ehrenfest theorems are used to further refine the model and provide a check on the validity of numerical simulations. Finally, the experimental feasibility of implementing the control fields generated by this model is discussed.

We introduce a new technique for the simulation of dissipative quantum systems. This method is composed of an approximate decomposition of the Lindblad equation into a Kraus map, from which one can define an ensemble of wave functions. Using principal component analysis, this ensemble can be truncated to a manageable size without sacrificing numerical accuracy. We term this method ensemble rank truncation (ERT), and find that in the regime of weak coupling, this method is able to outperform existing wave-function Monte Carlo methods by an order of magnitude in both accuracy and speed. We also explore the possibility of combining ERT with approximate techniques for simulating large systems [such as matrix product states (MPS)], and show that in many cases this approach will be more efficient than directly expressing the density matrix in its MPS form. We expect the ERT technique to be of practical interest when simulating dissipative systems for quantum information, metrology, and thermodynamics.

Erik Verlinde's theory of entropic gravity [E. Verlinde, J. High Energy Phys. 04 (2011) 029], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultracold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless free parameter $\sigma$ goes to infinity, the entropic master equation recovers conservative gravity. We show that the proposed master equation is fully compatible with the $q$Bounce experiment for ultracold neutrons as long as $\sigma \gtrsim 250$ at $90\%$ confidence. Furthermore, the entropic master equation predicts energy increase and decoherence on long time scales and for large masses, phenomena that tabletop experiments could test. In addition, comparing entropic gravity's energy increase to that of the Diósi-Penrose model for gravity-induced decoherence indicates that the two theories are incompatible. These findings support the theory of entropic gravity, motivating future experimental and theoretical research.

Here we introduce the concept of the twinning field—a driving electromagnetic pulse that induces an identical optical response from two distinct materials. We show that for a large class of pairs of generic many-body systems, a twinning field which renders the systems optically indistinguishable exists. The conditions under which this field exists are derived, and this analysis is supplemented by numerical calculations of twinning fields for both the 1D Fermi-Hubbard model, and tight-binding models of graphene and hexagonal boron nitride. The existence of twinning fields may lead to new research directions in nonlinear optics, materials science, and quantum technologies.