The discovery of quantum theory has led to explanations for nearly all physical phenomena from the smallest to largest length scales. In recent decades, as quantum theories have become better understood, scientists and engineers now seek to apply the unique advantages of quantum systems to solve practical problems. The purpose of this dissertation is to engineer quantum light-matter systems, or quantum optical matter, for practical applications by using theoretical and computational methods at the intersection of quantum chemistry and quantum optics. This dissertation consists of three parts. In the first, we design and control a class of quantum optical matter, defects in solid-state materials, that can be used as a nanoscale interface between quantum light and quantum matter degrees of freedom. In the second part, we click together simple and generic systems of quantum optical matter, where the particular features of specific systems like defects in solid-state materials have been abstracted away, to form more complex composite systems. We then show that certain composite systems can emit entangled photons and perform multi-qubit gates on photons with applications in photonic quantum computing. Finally, in the third part, we study another application of quantum optical matter: chemistry. In particular, we propose an explanation for experiments in the field of vibrational polariton chemistry where it has been observed that molecules packed into a cavity with fundamental modes resonant with molecular vibrational resonances exhibit altered chemical reactivity.
The discovery of quantum theory has led to explanations for nearly all physical phenomena from the smallest to largest length scales. In recent decades, as quantum theories have become better understood, scientists and engineers now seek to apply the unique advantages of quantum systems to solve practical problems. The purpose of this dissertation is to engineer quantum light-matter systems, or quantum optical matter, for practical applications by using theoretical and computational methods at the intersection of quantum chemistry and quantum optics. This dissertation consists of three parts. In the first, we design and control a class of quantum optical matter, defects in solid-state materials, that can be used as a nanoscale interface between quantum light and quantum matter degrees of freedom. In the second part, we click together simple and generic systems of quantum optical matter, where the particular features of specific systems like defects in solid-state materials have been abstracted away, to form more complex composite systems. We then show that certain composite systems can emit entangled photons and perform multi-qubit gates on photons with applications in photonic quantum computing. Finally, in the third part, we study another application of quantum optical matter: chemistry. In particular, we propose an explanation for experiments in the field of vibrational polariton chemistry where it has been observed that molecules packed into a cavity with fundamental modes resonant with molecular vibrational resonances exhibit altered chemical reactivity.
Abstract When atoms come together and bond, these new states are called molecules and their properties determine many aspects of our daily life. Strangely enough, it is conceivable for light and molecules to bond, creating new hybrid light–matter states with far‐reaching consequences for these strongly coupled materials. Even stranger, there is no “real” light needed to obtain the effects; it simply appears from the vacuum, creating “something from nothing.” Surprisingly, the setup required to create these materials has become moderately straightforward. In its simplest form, one only needs to put a strongly absorbing material at the appropriate place between two mirrors, and quantum magic can appear. Only recently has it been discovered that strong coupling can affect a host of significant effects at a material and molecular level, which were thought to be independent of the “light” environment: phase transitions, conductivity, chemical reactions, etc. This review addresses the fundamentals of this opportunity: the quantum mechanical foundations, the relevant plasmonic and photonic structures, and a description of the various applications, connecting material chemistry with quantum information, entanglement, nonlinear optics, and chemical reactivity. Ultimately, revealing the interplay between light and matter in this new regime opens attractive avenues for various new technologies.
When in a quantum optical system the coupling between matter and cavity mode becomes comparable to the bare excitation frequency, we enter a non-perturbative coupling regime, as perturbation theory fails describing the system’s dynamics. While recent advances in Cavity Quantum Electrodynamics allowed to achieve very high values of the coupling strength, thanks to the resonators properties optimization and the employment of solid-state devices, an ever growing interest has been shown about the possibility of significantly modify materials’ properties. It has been demonstrated that the chemical structure of molecules strongly coupled to a photon mode can be altered, which opens the possibility to manipulate and control chemical reactions. The aim of this thesis is to explore non-perturbative regimes on several quantum systems, and to investigate the effects of the coupling upon their properties, such as internal degrees of freedom or electronic states structure. I first developed a novel theory to determine the polariton spectrum of a dipolar ensamble in which a Ising-like dipole-dipole interaction in the 2 non-perturbative regime is considered. A further important focus is the investigation of the saturation effects due to the inclusion of the inter-dipole interaction, and the interplay between the latter and light-matter coupling strength. I also explored specifically the influence of the coupling on the rotational degrees of freedom of an ensemble of two-dimensional freely rotating dipoles, all coupled to a single cavity mode, finding that they are driven by the collective light-matter coupling to undergo a crossover between an isotropic and an aligned phase. I then investigated the case of cavity-embedded doped quantum wells, demonstrating that not only it is possible to couple a discrete cavity mode and bound-to-continuum transitions, but also that a novel bound exciton state appears, induced by the coupling strength. This results shows how light–matter coupling can be used to tune both optical and electronic properties of semiconductor heterostructures beyond those permitted by mere crystal properties. Finally, I explored the physics of an array of THz metamaterial resonators coupled to cyclotron resonances of a two-dimensional electron gas, developing a multiple-mode theory that takes in account the interaction between multiple photon modes mediated by the electrons. My results show that this cross-interaction, due to the strong two-dimensional geometry of the optically active medium, leads to the hybridization of different uncoupled photon modes, and manifests as a visible change of the distribution of the coupled electromagnetic field.
Theoretical chemistry uses the laws of physics to provide explanations for chemical observations, including molecular structure, bonding, and reactivity, in close connection with experiment. Although many answers in chemistry and materials science have been elucidated by accurate first-principles quantum-chemical calculations, their applicability is limited by high computational costs. This motivates the use of reduced descriptions of quantum many-body systems that retain core physical information at a lower computational cost. This thesis explores the development of reduced density matrix (RDM) techniques at the interface of chemistry, physics, and quantum information that address challenges in quantum technologies, including decoherence and scalability. The first part explores how minimal single-particle information can be used to detect environmental interactions in many-body quantum systems, aiding in the development of novel quantum sensing techniques and error mitigation strategies for quantum computation. The second part presents a framework for accelerating quantum state characterization for practical molecular simulation on quantum devices. The final part elucidates properties of entanglement in systems with mixed particle statistics, offering insight into quantum communication and the design of hybrid quantum platforms. Together, these results demonstrate how RDM-based approaches can improve the efficiency, interpretability, and robustness of quantum sensing, computation, and simulation.
In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter-photon problems. We analyze model systems in optical cavities, where the matter-photon interaction is considered from the weak- to the strong-coupling limit and for individual photon modes as well as for the multimode case. We identify fundamental changes in Born-Oppenheimer surfaces, spectroscopic quantities, conical intersections, and efficiency for quantum control. We conclude by applying our recently developed quantum-electrodynamical density-functional theory to spontaneous emission and show how a straightforward approximation accurately describes the correlated electron-photon dynamics. This work paves the way to describe matter-photon interactions from first principles and addresses the emergence of new states of matter in chemistry and material science.
Quantum communication and quantum computation are anticipated quantum technologies which enable us to tackle problems which are hard or even impossible to solve by classical means. A major challenge in implementing real life applications for quantum communication and quantum computation is to implement efficient interfaces between different kinds of quantum systems which serve as carriers of quantum information, such as single photons and single material quantum systems (i.e. atoms, ions ...). These different kinds of quantum systems have different advantages and disadvantages if it comes to practical applications. Single photons, which may serve as flying qubits, can be transmitted over larger distances without suffering from too much decoherence while single material quantum systems may be used as matter qubits to store and process quantum information locally. For many applications, the particular advantages of both kinds of systems are needed. Hence, we require interfaces between flying qubits and matter qubits. In the first part of this thesis, we develop suitable protocols for implementing interfaces between these flying qubits and matter qubits. The key challenge is to design the interactions to allow the efficient coupling of single photons to single material quantum systems, such as atoms and ions. This is not only of interest for possible practical applications of quantum mechanics but also drives fundamental research, as it is directly connected to a precise control and enhancement of matter-field interactions. The second part of this thesis is concerned with the applications of quantum technologies for simulating complex quantum systems, which cannot be treated by classical means. In many cases, the simulation of complex quantum systems turns out to be a difficult task due to the basic structure of quantum mechanics. The same aspects of quantum mechanics, which allow us to tackle computationally hard problems by using quantum algorithms, create difficulties in understanding the behavior of complex quantum systems. However, the understanding of complex quantum systems is not only of fundamental importance but might also enable us to give answers to problems of practical significance, such as an explanation for high-temperature superconductivity. Here, we develop protocols for implementing such quantum simulations based on ions trapped in state of the art ion traps. The applications of these kinds of quantum simulations are ranging from fundamental research to process design, control, and optimization.
This dissertation develops quantum computing methods for two fundamental aspects of nature: electronic structure in molecules and materials, and the dynamics of open quantum systems. Framed by the theme of moving from structure to dynamics, the work explores how quantum computers can be utilized to compute both the stationary properties of many-body systems and their evolution in realistic environments. Throughout, the emphasis is on physically grounded algorithms that are compatible with noisy intermediate-scale quantum hardware.On the electronic-structure side, this dissertation develops hybrid quantum-classical workflows for chemistry and condensed-matter problems. Sample-based quantum diagonalization and its extended variant are used to recover low-energy molecular states from quantum samples, with application to a reactive molecular system. For materials, a quantum computing workflow is constructed for defect-containing LixCoO2 by combining first-principles electronic-structure calculations, Wannier downfolding, and quantum many-body solvers, including variational and neural-network-based approaches.On the dynamics side, this dissertation presents several complementary methods for simulating open quantum systems on quantum computers. A dilation-based framework is introduced to embed non-unitary reduced dynamics into enlarged unitary evolutions, first for Kraus-map dynamics and then for dynamics generated by the generalized quantum master equation. Two additional near-term strategies are also developed: an adaptive variational method for dissipative many-body dynamics, demonstrated for Dicke superradiance, and a stochastic Schr\"odinger equation approach based on quantum trajectories, applied to excitation transport in the Fenna-Matthews-Olson complex.Taken together, these results establish a set of quantum algorithmic tools that traverse scales and descriptions, from electronic structure to dynamical processes, and from molecular chemistry to complex quantum environments. In this way, the dissertation advances the use of quantum computers as a framework for probing the interconnected fabric of nature.