Direct experimental detection of anyonic exchange statistics in fractional quantum Hall systems by braiding the excitations and measuring the wave-function phase is an enormous challenge. Here, we use a small, noisy quantum computer to emulate direct braiding within the framework of a simplified model applicable to a thin cylinder geometry and measure the topological phase. Our algorithm first prepares the ground state with two quasiholes. It then applies a unitary operation controlled by an ancilla, corresponding to a sequence of adiabatic evolutions that takes one quasihole around the other. We finally extract the phase of the wave function from measuring the ancilla with a compound error mitigation strategy. Our results open a new avenue for studying braiding statistics in fractional Hall states.

We study the dissociation dynamics of a diatomic molecule, modeled as a Morse oscillator, coupled to an optical cavity. Surprisingly, we find that the reaction rate decreases for cavity frequencies significantly below the fundamental transition frequency of the molecule. This suppression in the reaction rate occurs when certain key nonlinear resonances in the classical phase space of the molecule disappear, possible only when the dipole function is nonlinear. Future studies should address what happens for multiple molecules in a cavity and molecules with more than one intramolecular vibrational degree of freedom, as well as understand why experiments observe modified reaction rates at the fundamental transition frequency.

Recent experiments of chemical reactions in optical cavities have shown great promise to alter and steer chemical reactions, but the origin of resonant effects between the cavity and certain vibrational modes in the collective limit is still poorly understood. Here, we study unimolecular dissociation reactions of many molecules collectively interacting with an infrared cavity mode through their vibrational dipole moment. We find that the reaction rate can slow down when the molecules are aligned but is unaffected when they are randomly aligned.

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.

While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution processes can be modified inside an infrared cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom. We show how energy-dependent anharmonic resonances emerge and that resonantly coupling the optical cavity to particular dynamical resonance traps can either significantly slow down or increase the intramolecular vibrational energy redistribution processes depending on the strength of vibrational momentum-momentum mode coupling, leading to altered unimolecular dissociation reaction rates. These results demonstrate that chemical reactivity can be modified inside a cavity and lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polariton chemistry.

Entangled photons are crucial for quantum technologies, but generating arbitrary entangled photon states deterministically, efficiently, and with high fidelity remains a challenge. Here, we demonstrate how hybridization and dipole-dipole interactions—potentially simultaneously available in colloidal quantum dots and molecular aggregates—leveraged in conjunction can couple simple, well understood emitters into composite emitters with flexible control over the level structure. We show that cascade decay through carefully designed level structures can result in emission of frequency-entangled photons with Bell states and three-photon GHZ states as example cases. These results pave the way toward rational design of quantum optical emitters of arbitrarily entangled photons.

The field of vibrational polariton chemistry was firmly established in 2016 when a chemical reaction rate at room temperature was modified within a resonantly tuned infrared cavity without externally driving the system. Despite intense efforts by scientists around the world to understand why the reaction rate changes, no convincing theoretical explanation exists. In this perspective, we briefly review this seminal experiment, analyze the relevance of leading theories, and construct a roadmap toward the theory of vibrational polariton chemistry.

Here, we offer our perspective on how defect centers can mediate the transfer of quantum information between many leading qubit platforms.

Precise control over the electronic and optical properties of defect centers in solid-state materials is necessary for their applications as quantum sensors, transducers, memories, and emitters. In this study, we show that the optical properties of defects change drastically when they are placed inside a cavity that concentrates the vacuum electric fields.

Efficiently driving magnons, or quantized spin waves, in magnetic materials is necessary for next-generation memory devices. Here, we show that magnons can be driven with lasers, either directly or indirectly by first driving phonons, or quantized lattice vibrations. This more energy-efficient mechanism may enable magnons to be driven in a wider range of materials.

Precise control over the flow of energy in matter, such as light-absorbing molecules in plants that absorb light, transmit it through the backbone of the molecule, and convert it to chemical energy, is crucial. Here, we show that the flow of energy blocked in a single electron spin in a molecule or defect can be unblocked by placing it near a small magnetic nanoaparticle.