Waveguide quantum electrodynamic (waveguide QED) systems (arrays of qubits coupled to a waveguide) can exhibit a vast array of phenomena from collective effects, non-trivial topology to novel localisation effects. This thesis is the first study of a long-range coupled topological waveguide QED system. The existence of topological edge states for when one photon is incident on a spatially modulated qubit array is numerically verified and the results are analogous to a photonic crystal set-up in Ref. [1]. This thesis then goes beyond the single photon regime to consider the effect of interactions for when two photons are incident in the qubit array. Bound photon pairs and bound pair edge states are readily observed. Numerical results suggest that the bound pair edge states are topologically non-trivial, however, a topological invariant should be calculated before making stronger conclusive statements. Even more interestingly, the two-photon qubit array can also exhibit a self-induced localised state. This appears to be a completely unexplored effect that can connect many body physics, collective effects as well as topological properties. The exotic topological properties of these waveguide QED systems are promising developments in the growing field of quantum topological photonics which is said to have large potential for quantum computing technologies. The novel localised states also reveals that the physics of waveguide QED systems are richer than expected with many unexplored phenomena.
Waveguide quantum electrodynamic (waveguide QED) systems (arrays of qubits coupled to a waveguide) can exhibit a vast array of phenomena from collective effects, non-trivial topology to novel localisation effects. This thesis is the first study of a long-range coupled topological waveguide QED system. The existence of topological edge states for when one photon is incident on a spatially modulated qubit array is numerically verified and the results are analogous to a photonic crystal set-up in Ref. [1]. This thesis then goes beyond the single photon regime to consider the effect of interactions for when two photons are incident in the qubit array. Bound photon pairs and bound pair edge states are readily observed. Numerical results suggest that the bound pair edge states are topologically non-trivial, however, a topological invariant should be calculated before making stronger conclusive statements. Even more interestingly, the two-photon qubit array can also exhibit a self-induced localised state. This appears to be a completely unexplored effect that can connect many body physics, collective effects as well as topological properties. The exotic topological properties of these waveguide QED systems are promising developments in the growing field of quantum topological photonics which is said to have large potential for quantum computing technologies. The novel localised states also reveals that the physics of waveguide QED systems are richer than expected with many unexplored phenomena.
While designing the energy-momentum relation of photons is key to many linear, nonlinear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself.In this work we experimentally investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model.We explore topologically induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects.Addition of qubits to this waveguide system also enables direct quantum control over topological edge states that form in finite waveguide systems, useful for instance in constructing a topologically protected quantum communication channel.More broadly, our work demonstrates the opportunity that topological waveguide-QED systems offer in the synthesis and study of many-body states with exotic long-range quantum correlations.
Strong coupling between light and matter has been demonstrated both in classical cavity quantum electrodynamics (QED) systems and in more recent circuit-QED experiments. This enables the generation of strong nonlinear photon-photon interactions at the single-photon level, which is of great interest for the observation of quantum nonlinear optical phenomena, the control of light quanta in quantum information protocols such as quantum networking, as well as the study of strongly correlated quantum many-body systems using light. Recently, strong coupling has also been realized in a variety of one-dimensional (1D) waveguide- QED experimental systems, which in turn makes them promising candidates for quantum information processing. Compared to cavity-QED systems, there are two new features in waveguide-QED: the existence of a continuum of states and the restricted 1D phase space, which together bring in new physical effects, such as the bound-state effects. This thesis consists of two parts: 1) understanding the fundamental interaction between local quantum objects, such as two-level systems and four-level systems, and photons confined in the waveguide; 2) exploring its implications in quantum information processing, in particular photonic quantum computation and quantum key distribution. First, we demonstrate that by coupling a two-level system (TLS) or three/fourlevel system to a 1D continuum, strongly-correlated photons can be generated inside the waveguide. Photon-photon bound states, which decay exponentially as a function of the relative coordinates of photons, appear in multiphoton scattering processes. As a result, photon bunching and antibunching can be observed in the photon-photon correlation function, and nonclassical light source can be generated on demand. In the case of an N-type four-level system, we show that the effective photon-photon interaction mediated by the four-level system, gives rise to a variety of nonlinear optical phenomena, including photon blockade, photon-induced tunneling, and creation of single-photon states and photon pairs with a high degree of spectral entanglement, all in the absence of a cavity. However, to enable greater quantum networking potential using waveguide- QED, it is important to study systems having more than just one TLS/qubit. We develop a numerical Green function method to study cooperative effects in a system of two qubits coupled to a 1D waveguide. Quantum beats emerge in photon-photon correlations, and persist to much longer time scales because of non-Markovian processes. In addition, this system can be used to generate a high-degree of long-distance entanglement when one of the two qubits is driven by an on-resonance laser, further paving the way toward waveguide-QED-based quantum networks. Furthermore, based on our study of light-matter interactions in waveguide- QED, we investigate its implications in quantum information processing. First, we study quantum key distribution using the sub-Possonian single photon source obtained by scattering a coherent state off a two-level system. The rate for key generation is found to be twice as large as for other sources. Second, we propose a new scheme for scalable quantum computation using flying qubits--propagating photons in a one-dimensional waveguide--interacting with matter qubits. Photonphoton interactions are mediated by the coupling to a three- or four-level system, based on which photon-photon -phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
Light-matter interaction at the single-quantum level is the heart of many regimes of high fundamental importance to modern quantum technologies. Strong interaction of a qubit with a single photon of an electromagnetic field mode is described by the cavity/circuit electrodynamics (QED) regime which is one of the most advanced platforms for quantum computing. The opposite regime of the waveguide QED, where qubits interact with a continuum of modes in an infinite one-dimensional space, is also at the focus of recent research revealing novel quantum phenomena. Despite the demonstration of several key features of waveguide QED, the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size is neither rigorously justified nor fully understood. In this paper, we formulate a unifying theory which under a minimal set of standard approximations accounts for physical boundaries of a system in all parameter domains. Considering two qubits in a rectangular waveguide which naturally exhibits a low frequency cutoff we are able to account for infinite number of modes and obtain an accurate description of the waveguide transmission, a life-time of a qubit-photon bound state and the exchange interaction between two qubit-photon bounds states. For verification, we compare our theory to experimental data obtained for two superconducting qubits in a rectangular waveguide demonstrating how the infinite size limit of waveguide QED emerges in a finite-size system. Our theory can be straightforwardly extended to other waveguides such as the photonic crystal and coupled cavity arrays.
Waveguide quantum electrodynamics (waveguide QED) describes the interaction between an electromagnetic field confined to a one-dimensional waveguide with atom-like quantum emitters close by. The characteristics of these kinds of systems are the possibility for strong and even ultrastrong interactions between the photonic and atom-like systems, and practically infinite range interactions between the emitters. These properties are valuable for a wide range of quantum optical applications, like quantum communication, quantum networks and quantum metrology. In this thesis we focus on two challenges in quantum optics, namely the generation and scattering of multiphoton states. In the first part of this thesis we demonstrate how waveguide QED systems can be exploited for the generation of multiphoton states, in particular of single-mode Fock states and superpositions thereof as well as multi-mode photonic states with metrological applications. The basic setup for this goal is an ensemble of quantum emitters coupled to a waveguide. In the so-called atomic mirror configuration symmetric Dicke states (or a superposition thereof) decay superradiantly to the ground state and emit the desired multiphoton state, which can be efficiently collected at the ends of the waveguide. We propose various protocols for the preparation of these Dicke states in waveguide QED systems and characterize the emitted photonic state. It turns out that in the low excitation regime, that is, if the number of photons is much lower than the ensemble size, the photonic state is emitted into a single mode. This single-mode structure is fundamental to current proposals for applications in quantum metrology with optical interferometers. Outside the low excitation regime, a multi-mode photonic state is generated, for which the metrological capabilities were unknown. We were able to show that these states still lead to quantum-enhanced optical interferometry. In the second part of this thesis we demonstrate how the scattering of multiphoton states on a single quantum emitter coupled to the waveguide can be used for testing the limits of the light-matter interaction strength. In particular, we investigate systems in the so-called ultrastrong coupling regime, where the coupling strength between the photonic and atom-like system is of the order of the emitter's transition energy. In this regime, many methods and approximations used in quantum optics, especially the Rotating Wave Approximation, break down and one needs to develop new analytical and numerical methods to study these systems. One approach is the so-called polaron Transformation. We show how this transformation can be applied for predicting the scattering amplitude of few photons scattering on the emitter. The comparison of these results with numerical simulations using matrix product states shows a good agreement for moderate coupling strengths. Both parts together show that waveguide QED systems are promising candidates for the generation of multiphoton states as well as for the investigation of fundamental limits probed through the scattering of multiphoton states. The latter also finds application in the implementation of photon-photon nonlinearities induced by the interaction with the quantum emitters. Apart from these and many other theoretical predictions, waveguide QED systems are also undergoing rapid progress in experiments. Therefore, we expect these kinds of systems to bring forth several advances in the field of quantum optics.
The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics that take place in low dimensional topological systems, specifically 1D and 2D lattices that are instances of topological insulators. First, we study the dynamics of doublons, bound states of two fermions that appear in systems with strong Hubbard-like interactions. We also include the effect of periodic drivings and investigate how the interplay between interaction and driving produces novel phenomena. Prominent among these are the disappearance of topological edge states in the SSH-Hubbard model, the sublattice confinement of doublons in certain 2D lattices, and the long-range transfer of doublons between the edges of any finite lattice. Then, we apply our insights about topological insulators to a rather different setup: quantum emitters coupled to the photonic analogue of the SSH model. In this setup we compute the dynamics of the emitters, regarding the photonic SSH model as a collective structured bath. We find that the topological nature of the bath reflects itself in the photon bound states and the effective dipolar interactions between the emitters. Also, the topology of the bath affects the single-photon scattering properties. Finally, we peek into the possibility of using these kind of setups for the simulation of spin Hamiltonians and discuss the different ground states that the system supports.
Quantum light-matter interactions, described by the theory of quantum electrodynamics (QED), have motivated numerous scientific discoveries and technological developments over the past few decades. Considerable effort has been made to develop different QED platforms, e.g., free space, waveguides, cavities, and photonic crystals, for engineering quantum light-matter interactions. This thesis explores a new frontier, deep microscopic QED, which leverages the deep microscopic response of materials to reveal new topological, quantum, and thermal photonic phenomena with applications to quantum sensing and information processing. In the first part of this thesis, we investigate unique topological photonic effects arising in the deep microscopic QED regime. Previous efforts focused on topological photonic phases and edge states arising from artificial spatial structures of materials (e.g., photonic crystals or metamaterials). One fundamental question is whether topological photonic states can also arise from the intrinsic response of many-body systems and do not rely on materials' macroscopic structures. Here, we first discuss a new topological electromagnetic phase - ‘optical N-phase’ arising in two-dimensional (2D) viscous hydrodynamic electrons in graphene, which originates from the microscopic response of 2D materials and does not rely on materials' macroscopic structures. We then introduce the associated edge states, optical N-plasmons, which are topologically protected ultra-subwavelength edge magneto-plasmons. We further show how these topological plasmons can be harnessed to design chiral radio-frequency nonreciprocal circuit components, topological hydrodynamic circulators, that interface quantum and classical hardware.In the second part of this thesis, we focus on collective atom-photon interactions in the deep microscopic QED regime. In atom interactions with photonic environments, there exist two non-unitary processes -- pure dephasing and spontaneous emission. Despite considerable interest in collective effects in spontaneous emission since the 1950s, one long-standing problem is whether collective effects in pure dephasing can arise in atom-photon interactions. This question is particularly important in the quantum information era since pure dephasing is the main obstacle in current quantum information technologies. Here, we first introduce a new collective quantum phenomenon, ‘nanophotonic superdephasing,’ occurring in atom/spin ensembles in nanoscale photonic environments. This nanophotonic superdephasing phenomenon originates from low-frequency photonic environment correlations, and leads to collectively accelerated disentanglement without photon emission, in stark contrast to conventional collective spontaneous emission/superradiance effects. We further reveal the effects of nanophotonic environment mediated correlated dynamics on quantum computing and sensing. We demonstrate that correlations of nanoscale EM environments in spin qubit quantum computing devices can induce correlated errors and limit quantum gate fidelity. Meanwhile, based on nanophotonic collective dephasing, we also propose a multiqubit quantum sensing protocol that exploits spatially correlated noise near materials to enable order parameter symmetry characterization of materials beyond single-qubit methods.In the final part, we explore thermal photonic phenomena in the deep microscopic regime. Conventional techniques in engineering near-field radiative heat transfer typically rely on phonons, plasmons, and electromagnetic modes in structured materials. Here, we reveal a new approach to enhance near-field thermal radiation: leveraging intrinsic quantum coherence in superconducting materials. We reveal the quantum fingerprint of superconductivity in thermal photonics, ‘superconducting coherence peak’ in near-field thermal radiation, which originates from quantum coherence of Bogoliubov quasiparticles, with potential applications in thermal engineering in superconducting circuits.Overall, the thesis establishes a deep microscopic QED platform for new quantum, topological, and thermal photonic phenomena in many-body systems, with applications in quantum sensors and devices.