Superoscillations Deliver Superspectroscopy.

In ordinary circumstances the highest frequency present in a wave is the highest frequency in its Fourier decomposition. It is however possible for there to be a spatial or temporal region where the wave locally oscillates at a still greater frequency in a phenomenon known as superoscillation. Superoscillations find application in wide range of disciplines, but at present their generation is based upon constructive approaches that are difficult to implement. Here, we address this, exploiting the fact that superoscillations are a product of destructive interference to produce a prescription for generating superoscillations from the superposition of arbitrary waveforms. As a first test of the technique, we use it to combine four quasisinusoidal THz waveforms to produce THz optical superoscillations for the first time. The ability to generate superoscillations in this manner has potential application in a wide range of fields, which we demonstrate with a method we term "superspectroscopy." This employs the generated superoscillations to obtain an observed enhancement of almost an order of magnitude in the spectroscopic sensitivity to materials whose resonance lies outside the range of the component waveform frequencies.

Optical Indistinguishability via Twinning Fields.

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.

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.

Entropy nonconservation and boundary conditions for Hamiltonian dynamical systems.

Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dynamical phase associated with such a construction is identified. By choosing distributions not belonging to this class, we produce explicit examples of both free particles and harmonic systems evolving in a bounded phase-space in such a way that entropy is nonconserved. While these nonconserving states are classically forbidden, they may be interpreted as states of a quantum system tunneling through a potential barrier boundary. In this case, the allowed boundary conditions are the only distinction between classical and quantum systems. We show that the boundary conditions for a tunneling quantum system become the criteria for entropy preservation in the classical limit. These findings highlight how boundary effects drastically change the nature of a system.