We consider a generic model for interacting waveguide QED systems, where photons in a coupled-cavity array localize around atomic impurities while simultaneously interacting through local Kerr nonlinearities. This scenario appears naturally in nanophotonic crystals, circuit QED lattices, and ultracold atomic systems and is governed by the competition between attractive Jaynes-Cummings-mediated binding and intrinsic photon-photon repulsion. We analyze how this interplay affects the formation of localized few-photon bound states and determine the resulting many-body ground states for large periodic arrays of impurities and different filling factors. With the help of large-scale numerical simulations and approximate analytical models, we identify a rich phase diagram featuring Mott-like insulating states as well as superfluid phases with long-range correlations, which are mediated by an unbound, but strongly interacting photonic fluid.
We consider a generic model for interacting waveguide QED systems, where photons in a coupled-cavity array localize around atomic impurities while simultaneously interacting through local Kerr nonlinearities. This scenario appears naturally in nanophotonic crystals, circuit QED lattices, and ultracold atomic systems and is governed by the competition between attractive Jaynes-Cummings-mediated binding and intrinsic photon-photon repulsion. We analyze how this interplay affects the formation of localized few-photon bound states and determine the resulting many-body ground states for large periodic arrays of impurities and different filling factors. With the help of large-scale numerical simulations and approximate analytical models, we identify a rich phase diagram featuring Mott-like insulating states as well as superfluid phases with long-range correlations, which are mediated by an unbound, but strongly interacting photonic fluid.
Waveguide quantum electrodynamics (QED) studies the interaction between quantum emitters and guided photons in one dimension. When the waveguide hosts interacting photons, it becomes a platform to explore many-body quantum optics. However, the influence of photonic correlations on emitter dynamics remains poorly understood. In this work, we study the collective decay and coherent interactions of quantum emitters coupled to a one-dimensional Bose-Hubbard waveguide, an array of coupled photonic modes with repulsive on-site interactions that supports superfluid and Mott insulating phases. We show that photon-photon interactions alone can trigger a superradiant burst, independent of emitter spacing and transition frequency. In the off-resonant regime, emitters exhibit two distinct types of mediated interactions. Delocalized superfluid excitations yield persistent, long-range couplings, challenging the noninteracting paradigm, where long-range (dissipative) couplings occur in band, whereas short-range and coherent interactions occur in a bandgap. In the Mott limit, quasiparticles generate short-range interactions mediated by doublons and holons. Our work bridges many-body physics and waveguide QED, revealing how photonic many-body states shape emitter dynamics.
We discuss the properties of atom-photon bound states in waveguide QED systems consisting of single or multiple atoms coupled strongly to a finite-bandwidth photonic channel. Such bound states are formed by an atom and a localized photonic excitation and represent the continuum analog of the familiar dressed states in single-mode cavity QED. Here we present a detailed analysis of the linear and nonlinear spectral features associated with single- and multiphoton dressed states and show how the formation of bound states affects the waveguide-mediated dipole-dipole interactions between separated atoms. Our results provide both a qualitative and quantitative description of the essential strong-coupling processes in waveguide QED systems, which are currently being developed in the optical and microwave regimes.
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.
The scattering between light and individual saturable quantum emitters can induce strong optical nonlinearities and correlations between individual light quanta. Typically, this leads to an effective attraction that can generate exotic bound states of photons, which form quantum mechanical precursors of optical solitons, as found in many optical media. Here, we study the propagation of light through an optical waveguide that is chirally coupled to three-level quantum emitters. We show that the additional laser coupling to a third emitter state not only enables control of the properties of the bound state but can even eliminate it entirely. This makes it possible to turn an otherwise focusing nonlinearity into a repulsive photon-photon interaction. We demonstrate this emerging photon-photon repulsion by analyzing the quantum dynamics of multiple photons in large emitter arrays and reveal a dynamical fragmentation of incident uncorrelated light fields and self-ordering into regular trains of single photons. These striking effects expand the rich physics of waveguide quantum electrodynamics into the domain of repulsive photons and establish a conceptually simple platform to explore optical self-organization phenomena at the quantum level. We discuss implementations of this setting in cold-atom experiments and propose an approach based on arrays of mesoscopic Rydberg-atom ensembles.
An exciting frontier in quantum information science is the realization and control of complex quantum many-body systems. Hybrid nanophotonic system with cold atoms has emerged as the paradigmatic platform for engineering long-range spin models from the bottom up, exploiting their modal geometry and group dispersion for tailored interactions. An important challenge is the physical limitation imposed by the photonic bath, constraining the types of local Hamiltonians that decompose the available physical models and restricting the spatial dimensions to that of the dielectric media. However, at the nanoscopic scale, atom-field interaction inherently accompanies significant driven-dissipative quantum forces that may be tamed as a new form of a mediator for controlling the atomic internal states. Here, we formulate a quantum optics toolbox for constructing a universal quantum matter with individual atoms in the vicinity of 1D photonic crystal waveguides. The enabling platform synthesizes analog quantum materials of universal 2-local Hamiltonian graphs mediated by phononic superfluids of the trapped atoms. We generalize our microscopic theory of analog universal quantum simulator to the development of dynamical gauge fields. In the spirit of gauge theories, we investigate emergent lattice models for strongly coupled SU(n)-constrained excitations driven by an underlying multi-body interaction. As a minimal model in the infrared, we explore the realization of an archetypical strong coupling quantum field theory, SU(n) Wess-Zumino-Witten model, and discuss a diagnostic tool to extract the entire conformal data of the field theory by the static and dynamical correlators of the fluctuating photons in the guided mode.
An exciting frontier in quantum information science is the realization and control of complex quantum many-body systems. The hybrid nanophotonic system with cold atoms has emerged as a paradigmatic platform for realizing long-range spin models from the bottom up, exploiting their modal geometry and group dispersion for tailored interactions. An important challenge is the physical limitation imposed by the photonic bath, constraining the types of local Hamiltonians that decompose the available physical models and restricting the spatial dimensions to that of the dielectric media. However, at the nanoscopic scale, atom-field interaction inherently accompanies significant driven-dissipative quantum forces that may be tamed as a new form of a mediator for controlling the atomic internal states. Here we formulate a quantum optics toolbox for constructing universal quantum matter with individual atoms in the vicinity of one-dimensional photonic crystal waveguides. The enabling platform synthesizes analog quantum materials of universal 2-local Hamiltonian graphs mediated by phononic superfluids of the trapped atoms. We generalize our microscopic theory of an analog universal quantum simulator to the development of dynamical gauge fields. In the spirit of gauge theories, we investigate emergent lattice models of arbitrary graphs, for which strongly coupled SU(n) excitations are driven by an underlying multibody interaction. As a minimal model in the infrared, we explore the realization of an archetypical strong-coupling quantum field theory, the SU(n) Wess-Zumino-Witten model, and discuss a diagnostic tool to map the conformal data of the field theory to the static and dynamical correlators of the fluctuating photons in the guided mode.