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.
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.
High harmonic generation (HHG) has emerged as a powerful probe of ultrafast electron dynamics in solids. However, in strongly correlated materials, where electronic excitations arise from many-body interactions rather than single-particle band dispersion, the field remains in its infancy. Here, we report HHG up to the 23rd order in the prototypical Mott insulator La2CuO4. We observe a robust 4 eV cutoff that is independent of driving field strength, revealing an intrinsic energy scale defined by the Hubbard bands. Using time-resolved high harmonic spectroscopy, we disentangle the distinct contributions of carrier creation, intraband acceleration, and interband recombination to the nonequilibrium radiation spectrum. We demonstrate that photo-doping triggers a fundamental reorganization of the many-body manifolds above a critical excitation density, a process that renormalizes the band curvature and suppresses nonlinear intraband currents, thereby directly imprinting the signature of many-body band reconstruction onto the harmonic emission. These results establish HHG as a sensitive probe of subtle correlation-driven electronic reconstructions and highlight that many-body interactions enable extreme nonlinear optical responses that are highly tunable in nonequilibrium states.
Controlling and stabilising collective phases of many-body quantum systems is a problem of deep fundamental and technological interest. In this thesis, we perform a theoretical investigation on how useful quantum phases may be engineered in strongly correlated fermionic lattice systems, especially through periodic driving. We first compute the phase diagram of the one-dimensional t–J model with the addition of non-standard pair hopping terms. We show that at dilute fillings these terms enhance superconductivity while, counter- intuitively, suppressing it at large fillings. We argue that this is due to dynamical constraints originating from the fact that local pairs cannot overlap. We conjecture that these constraints may play a more significant role in the physics of two-dimensional systems where the t–J model is studied as a candidate model of high-Tc superconductivity. We begin to investigate these dynamical constraints on a ladder geometry. We then study the fermionic Hubbard model under periodic driving. We show that the driving induces a strong and robust singlet-pairing effect consistent with a superconducting state. This could provide a new mechanism for light-induced superconductivity in some classes of strongly cor- related materials. We show using Floquet theory that the dynamics of the driven Hubbard model are described precisely by the t–J model studied in the previous section. As the driven Hubbard model is also implementable with ultracold fermions in an optical lattice, our results could lead to their use as a quantum simulator for a broad class of candidate models for high-Tc superconductivity.
Strongly correlated systems have rich and intriguing behaviors that have been at the focal point of modern condensed-matter physics. One promising research direction is the study of the Fermi-Hubbard model, which is thought to describe the essential physics of the cuprates and is naturally realized with ultracold atoms in optical lattices. The development of single-site control and readout on this platform has allowed for new methods in creating and studying states in the Fermi-Hubbard model. In this thesis, we discuss the engineering of low-entropy correlated states using a novel technique. By preparing a gapped band-insulator in the presence of an entropy reservoir, we create states with an entropy per particle of 0.016(3) k_B. We then demonstrate that the low-entropy band insulator can be used as a resource for creating strongly correlated states; by dynamically manipulating the on-site potentials we are able to convert the uncorrelated band insulator into a correlated Mott insulator. We also investigate if heating is responsible for the increase in entropy when creating the correlated phase and determine that it does not play a dominant role. In a separate experiment, we leverage the single-site manipulation capabilities in a different way by creating a single localized hole dopant in an antiferromagnetic state. We then allow the hole to delocalize by suddenly removing its pinning potential and study the resulting density and spin correlation evolution. As the hole delocalizes, we find that it displaces the surrounding spin correlations in a trajectory that is initially controlled by quantum interference. At later times, the hole delocalizes at a rate that scales with the spin exchange energy, revealing that the presence of magnetism fundamentally alters charge transport. These developments demonstrate continued progress in optical lattice quantum simulators and how they can play a role in unraveling the mysteries of the Fermi-Hubbard model.
In this paper we present a general theoretical framework to study interacting electrons under the influence of an external time-periodic driving, such as a homogeneous laser field. This is performed through a true many-body calculation and the use of Floquet theory. In particular, we consider a linear atomic chain using the Hubbard model to describe the short-ranged Coulomb interactions between electrons, plus Cluster Perturbation Theory to embed the many-body exact solution for a finite system into both an extended and an infinite lattice. Due to the presence of the external time-periodic perturbation, the electronic problem can be mapped into the study of photon-dressed quasiparticles thanks to Floquet theorem, keeping into account of all the virtual processes (absorption and emission of photons by electrons) with the laser field. This leads to an extension of the many-body static theories to out-of-equilibrium systems. This theoretical approach allowed us to show how the electronic properties of the system can be controlled and tuned varying the laser parameters. Above all, an inverse insulator-to-metal transition can be obtained for the one dimensional infinite lattice, and edge localized states appear as a finite size effect in an extended truncated chain.
This work explores the possibility of creating and controlling unconventional nonlinearities by periodic driving, in a broad class of systems described by the nonlinear Schrödinger equation (NLSE).By means of a parent quantum many-body description, we demonstrate that such driven systems are well captured by an effective NLSE with emergent nonlinearities, which can be finely controlled by tuning the driving sequence.We first consider a general class of two-mode nonlinear systems-relevant to optical Kerr cavities, waveguides, and Bose-Einstein condensates-where we find an emergent four-wave mixing nonlinearity, which originates from pair-hopping processes in the parent quantum picture.Tuning this drive-induced nonlinearity is shown to modify the phase-space topology, which can be detected through relative population and phase measurements, and also leads to enhanced quantum properties such as spin squeezing.We then couple individual (two-mode) dimers in view of designing extended lattice models with unconventional nonlinearities and controllable pair-hopping processes.Following this general dimerization construction, we obtain an effective lattice model with drive-induced interactions, whose ground state exhibits orbital order, chiral currents, and emergent magnetic fluxes through the spontaneous breaking of time-reversal symmetry.We analyze these intriguing properties both in the weakly interacting (mean-field) regime, captured by the effective NLSE, and in the strongly correlated quantum regime.Our general approach opens a route for the engineering of unconventional optical nonlinearities in photonic devices and controllable drive-induced interactions in ultracold quantum matter.
This thesis makes three contributions to the understanding, control, and design of strongly correlated quantum matter. First, motivated by recent experiments reporting light-induced superconductivity, magnetism, and charge order, this thesis develops a unified description of photoexcited quantum materials. We show that seemingly disparate nonequilibrium phenomena can often be interpreted in terms of emergent order parameters and their collective dynamical fluctuations, providing a framework for modeling complex driven many-body systems with competing equilibrium phases. We propose experimental tests of this framework, several of which have already been realized, and highlight the role of programmable quantum simulators as platforms for studying driven many-body physics and probing emergent nonequilibrium order. Second, the thesis investigates atomically thin materials, with a primary focus on transition metal dichalcogenides (TMDs), as a platform for exploring strongly interacting quantum matter and for designing electro-optical quantum devices. In addition to electrical tunability, TMDs are direct band-gap semiconductors exhibiting sharp excitonic resonances in the optical frequency range, enabling optical manipulation of these materials. At relevant carrier densities, interactions dominate, leading to rich and unconventional behavior. To this end, we report the observation of Wigner crystallization, interlayer electron coherence, magnon hydrodynamics, and excitonic superradiance. Finally, motivated by rapid progress in programmable neutral-atom quantum simulation and computation, this thesis introduces a general algorithmic framework for {\it inverse quantum simulation} aimed at quantum material design. Target material characteristics are encoded as a cost function, which is minimized on quantum hardware to prepare a many-body state with the desired properties in quantum memory. Hamiltonian learning is then used to reconstruct a low-energy Hamiltonian for which this state is an approximate ground state, yielding a physically interpretable model that can guide experimental realization. This framework extends the scope of quantum simulators from exploring quantum many-body systems to designing and discovering new quantum materials.