Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials and for modeling next-generation nonlinear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.
Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials and for modeling next-generation nonlinear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.
Abstract Light-matter interactions are an established field that is experiencing a renaissance in recent years due to the introduction of exotic coupling regimes. These include the ultrastrong and deep-strong coupling regimes, where the coupling constant is smaller and of the order of the frequency of the light mode, or larger than this frequency, respectively. In the past few years, quantum simulations of light-matter interactions in all possible coupling regimes have been proposed and experimentally realized, in quantum platforms such as trapped ions, superconducting circuits, cold atoms, and quantum photonics. We review this fledgling field, illustrating the benefits and challenges of the quantum simulations of light-matter interactions with quantum technologies.
In this Thesis we design radiation patterns capable of creating effective light-matter interactions suited to applications in quantum computing, quantum simulation and quantum sensing. On the one hand, we have used dynamical decoupling techniques to design quantum operations that are robust against errors in environmental and control fields, achieving high-fidelity quantum logic in trapped ions and energy-efficient nuclear magnetic resonance at the nanoscale with nitrogen-vacancy centers in diamond. On the other hand, we have studied generalised models of light-matter interaction, leading to the discovery of selective multi-photon interactions in the Rabi-Stark model and a proposal for preparing non-classical quantum states using the nonlinear quantum Rabi model. Finally, we have shown how the appropriate tailoring of interactions among ultracold atoms in optical lattices could lead to solve the boson sampling problem faster than the best supercomputers, thus demonstrating quantum supremacy. In this manner, we believe the results presented here significantly expand our knowledge on the control of light-matter interactions, and provide optimal scenarios for current quantum devices to generate the next-generation of quantum applications.
Engineering strong photon–photon interactions at the quantum level have been crucial in various areas of research, notably in quantum information processing and quantum simulation. It is often done by coupling matter strongly to light. A promising way to achieve this is via waveguide quantum electrodynamics (QED). Motivated by these advancements, we study few-photon transport in waveguide QED setups. First, we present a diagrammatic technique to systematically study multiphoton scattering based on the scattering formalism and Green’s function approach. We demonstrate our proposal through physically relevant examples involving scattering of few-photon states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators described by the Bose–Hubbard model. In the second part, we apply the diagrammatic technique that was developed to perform a comprehensive study on a Bose–Hubbard lattice with a quasi-periodic potential. This model exhibits many-body localisation. We compute the two-photon transmission probability and show that it carries signatures of the underlying localisation transition with close agreement to the participation ratio of the eigenstates. The systematic scattering approach provided in this paper provides a foundation for future works at the interface between quantum optics and condensed matter.
This thesis offers novel strategies for the measurement of quantum correlations present in controllable quantum systems, as well as for a full-fledged implementation of the models of light-matter interaction through which these correlations can be generated. We propose the use of an ancillary qubit to efficiently access both time-correlation functions and entanglement monotones, and we provide two experimental demonstrations of our methods, measuring time correlations in an NMR setup and entanglement monotones in a photonic system. Moreover, we explain how time-correlation functions could be exploited for the quantum simulation of open quantum dynamics, and we provide an experimental recipe for the measurement of entanglement monotones in trapped ion technologies. On the other hand, we explore the quantum simulation of quantum optical models of light-matter interaction for inaccessible coupling regimes, providing experimental proposals for their implementation, both in ions and superconducting circuits. Finally, we also provide an experimental proposal for the quantum simulation of spin models in trapped ions following a digital-analog simulation scheme.
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up ways for simulating complex dynamics of, e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.
We propose a quantum dynamics simulator for light-irradiated matter. As the coherent control of the quantum states of matter is an intriguing problem in realizing quantum technology, the quantum properties of light-matter complexes have attracted much attention. Theoretical calculations corresponding to individual experimental configurations are required to understand these properties, and simulation methods that flexibly adapt to various experimental configurations are required. In this paper, we propose a quantum dynamics simulation method that encompasses program modules corresponding to light sources, optical components, material systems, and the evaluation of physical properties. We demonstrate the entanglement generation dynamics between two spin-chains via irradiated photons and show that a flexible and expandable quantum dynamics simulator can be constructed.