While engineering long-range light-matter interactions is the principal aim in waveguide-QED, ironically most of the building blocks rest on local short-range couplings, such as nearest-neighbor-coupled cavity arrays employed in canonical models. Here, we propose a waveguide-QED system with native long-range interactions, comprising a single emitter coupled to a left-handed transmission line (LHTL). Interestingly, the LHTL emulates a synthetic photonic lattice with a slow logarithmic decay of hopping amplitudes over a distance set entirely by the ratio of UV and IR cutoffs of line dispersion. Its intrinsic long-range nature manifests both in the properties of atom-photon bound and scattering states, which exhibit algebraic localization and accelerated photon propagation respectively. Using a method of 'running exponents', we develop a unified picture connecting waveguide dispersion to bound state and light front profiles obtained in the strong long-range hopping regime. These results motivate how transmission lines can enable multi-qubit information processing with tunable-range interactions.
While engineering long-range light-matter interactions is the principal aim in waveguide-QED, ironically most of the building blocks rest on local short-range couplings, such as nearest-neighbor-coupled cavity arrays employed in canonical models. Here, we propose a waveguide-QED system with native long-range interactions, comprising a single emitter coupled to a left-handed transmission line (LHTL). Interestingly, the LHTL emulates a synthetic photonic lattice with a slow logarithmic decay of hopping amplitudes over a distance set entirely by the ratio of UV and IR cutoffs of line dispersion. Its intrinsic long-range nature manifests both in the properties of atom-photon bound and scattering states, which exhibit algebraic localization and accelerated photon propagation respectively. Using a method of 'running exponents', we develop a unified picture connecting waveguide dispersion to bound state and light front profiles obtained in the strong long-range hopping regime. These results motivate how transmission lines can enable multi-qubit information processing with tunable-range interactions.
Atom arrays are a new type of quantum light-matter interface.Here we propose to employ one-dimensional ordered arrays as atomic waveguides.These arrays support optical guided modes that do not decay into free space.We show that these modes can be harnessed to mediate tunable, long-range interactions between additional "impurity qubits" coupled to the chain, without need for photonic structures.The efficient coupling between qubits and atomic waveguides enables the realization of tunable qubit-qubit interactions, which can be short or long range, dissipative or coherent, as well as chiral.Moreover, owing to the two-level nature of atoms, these waveguides are intrinsically quantum.In contrast to classical waveguides, where photons do not interact with each other, atomic waveguides display strong nonlinearities, which create a tunable dissipative channel for qubit-qubit interactions, and opens the door to the exploration of many-body physics between guided photons.This physics is universal as it only relies on photon interference and can also be observed with other types of quantum emitters, such as those in molecular or solid-state systems.
Non-trivial dispersion relations engineered in photonic waveguide for the precise control of atomic dynamics has recently attracted considerable attention. Here, we study a system in which atoms are coupled to one-dimensional coupled-resonator waveguides with long-range hoppings. By carefully engineering the jth-order nearest neighbor (JNN) hoppings between resonators, we construct linear dispersion relations with the chiral characteristic. To quantify the degree of linearity, we analyze the propagation fidelities of Gaussian wave packets in these waveguides. Furthermore, we demonstrate that such coupled-resonator waveguides can serve as versatile platforms for enabling directional atomic radiation and absorption. Beyond linear dispersion relations, more general forms, including quadratic and cubic relations, can also be achieved through tailored JNN-hoppings. Our study thus provides a unified framework for simulating atom-environment couplings with arbitrary dispersion relations.
Experiments utilizing quantum optics have progressed rapidly in last few decades, particularly in the context of quantum computation, simulation, and communication. Early work in this field focused on implementations of cavity quantum electrodynamics (QED), where atoms, either natural or artificial, are strongly coupled to the confined photonic modes of cavities. However, in recent years, achieving strong coupling between atoms and itinerant photons has also gained significant interest for its applications in quantum networking. To this end, many atomic platforms are attempting to realize the waveguide QED architecture: atoms that interact with the continua of propagating photonic modes within a waveguide. In this thesis, we realize the strong-coupling regime of a waveguide QED architecture by coupling superconducting artificial atoms, typically operated as qubits, to one-dimensional transmission lines. We first demonstrate that superconducting qubits in a waveguide QED system can be used as high-quality quantum emitters. We then leverage the quantum interference between the simultaneous emission from multiple qubits in order to generate non-classical, spatially entangled, and directional itinerant microwave photons. These types of photons are particularly useful for remote entanglement and quantum communication protocols. Finally, we demonstrate that superconducting qubits can be engineered to enter novel regimes of light-matter interactions that are difficult, or even impossible, to achieve in other atomic platforms. In particular, we realize the giant-atom regime of waveguide QED, where the atom can no longer be treated as a point-like object. We use our giant atoms to implement tunable atom-waveguide couplings, as well as decoherence-free waveguide-mediated interactions between multiple atoms.
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 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.
Quadratic light-matter interactions are nonlinear couplings such that quantum emitters interact with photonic or phononic modes exclusively via the exchange of excitation pairs.Implementable with atomic and solid-state systems, these couplings lead to a plethora of phenomena that have been characterized in the context of cavity QED, where quantum emitters interact with localized bosonic modes.Here, we explore quadratic interactions in a waveguide QED setting, where quantum emitters interact with propagating fields confined in a one-dimensional environment.We develop a general scattering theory under the Markov approximation and discuss paradigmatic examples for spontaneous emission and scattering of biphoton states.Our analytical and semianalytical results unveil fundamental differences with respect to conventional waveguide QED systems, such as the spontaneous emission frequency-entangled photon pairs or the full transparency of the emitter to single-photon inputs.This unlocks new opportunities in quantum information processing with propagating photons.As a striking example, we show that a single quadratically coupled emitter can implement a two-photon logic gate with unit fidelity, circumventing a no-go theorem derived for conventional waveguide-QED interactions.