Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light.
Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light.
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.
We investigate the problem of arbitrary photonic-Fock-state scattering in a waveguide-QED system which consists of a one-dimensional waveguide coupled to a two-level system. By imposing the open boundary conditions that directly describe the physical settings, we construct a complete set of eigenstates of the system, and elucidate the mathematical structures of the eigenstates. In particular, we show that the eigenstates include a set of multiphoton extended states and multiphoton bound states, formed by all possible partitions of the photon number N. The total number of the eigenstates is exactly described by the integer number partition function Z(N). Using the set of eigenstates, we form the scattering matrix, which facilitates the calculations of the scattered photon states, for the scattering processes. With the scattered photon states, we compute the photon correlation functions that manifestly exhibit the bunching and antibunching behaviors in the scattered photon states. As a concrete example, we discuss in detail with a focus on the three-photon Fock state. Such a capability to generate photonic entanglement from unentangled Fock states will have broad applications in quantum information processing.
We theoretically study the few-and many-body dynamics of photons in chiral waveguides.In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide.We show that the system supports correlated multiphoton bound states, which have a welldefined photon number n and propagate through the system with a group delay scaling as 1=n 2 .This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system.For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency.Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition.Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons.Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters.Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.
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.
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.