In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices, it is crucial to fully understand the non-equilibrium dynamics of strongly interacting photons. Employing both numerical and analytical approaches we map out the full scattering dynamics for two photons scattering on a two-level emitter in a one-dimensional waveguide. The strongest non-linear interaction arise when the emitter is excited the most, which occurs for incoming photon pulses with a spectral bandwidth comparable to the emitter linewidth. For two identical, counter-propagating photons, the emitter works as a non-linear beam splitter, as the emitter induces strong directional correlations between the scattered photons. Even though the non-linearity also alters the pulse spectrum due to a four-wave mixing process, we demonstrate that input pulses with a Gaussian spectrum can be mapped to the output with up to 80 % fidelity. Using two identical two-level emitters, we propose a setup for a deterministic controlled-phase gate, which preserves the properties of the two incoming photons with almost 80 %, limited by spectral changes induced by the non-linearity and phase modulations upon scattering. Another setup for a controlled-phase operation is suggested with two coupled ring resonators exploiting a strong second-order material non-linearity. By dynamically trapping the first of two temporally separated photons in the non-linear resonator, the scattering of the second photon is altered. Due to the trapping, the undesired aforementioned non-linear effects are avoided, but the gate performance is now limited by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between the electron and hole wavefunction in the QD, we show how the phonon-assisted transition rate to a slightly detuned optical mode may be suppressed. This is achieved by properly matching the electrical carrier confinement with the deformation potential interaction, where the suppression only occurs in materials where the deformation potential interaction shifts the electron and hole bands in the same direction. We demonstrate also how the phonon-induced effects may be altered by placing the QD inside an infinite slab, where the confinement of the phonons is modified instead. For a slab thickness below ∼ 70 nm, the bulk description of the phonon modes may be insufficient. The QD decay rate may be strongly increased or decreased, depending on how the detuning between the QD and the optical mode matches the phonon modes in the slab.
In this thesis we investigate few-photon non-linearities in all-optical, on-chip circuits, and we discuss their possible applications in devices of interest for quantum information technology, such as conditional two-photon gates and single-photon sources. In order to propose efficient devices, it is crucial to fully understand the non-equilibrium dynamics of strongly interacting photons. Employing both numerical and analytical approaches we map out the full scattering dynamics for two photons scattering on a two-level emitter in a one-dimensional waveguide. The strongest non-linear interaction arise when the emitter is excited the most, which occurs for incoming photon pulses with a spectral bandwidth comparable to the emitter linewidth. For two identical, counter-propagating photons, the emitter works as a non-linear beam splitter, as the emitter induces strong directional correlations between the scattered photons. Even though the non-linearity also alters the pulse spectrum due to a four-wave mixing process, we demonstrate that input pulses with a Gaussian spectrum can be mapped to the output with up to 80 % fidelity. Using two identical two-level emitters, we propose a setup for a deterministic controlled-phase gate, which preserves the properties of the two incoming photons with almost 80 %, limited by spectral changes induced by the non-linearity and phase modulations upon scattering. Another setup for a controlled-phase operation is suggested with two coupled ring resonators exploiting a strong second-order material non-linearity. By dynamically trapping the first of two temporally separated photons in the non-linear resonator, the scattering of the second photon is altered. Due to the trapping, the undesired aforementioned non-linear effects are avoided, but the gate performance is now limited by the capturing process. Semiconductor quantum dots (QDs) are promising for realizing few-photon non-linearities in solid-state implementations, although coupling to phonon modes in the surrounding lattice have significant influence on the dynamics. By accounting for the commonly neglected asymmetry between the electron and hole wavefunction in the QD, we show how the phonon-assisted transition rate to a slightly detuned optical mode may be suppressed. This is achieved by properly matching the electrical carrier confinement with the deformation potential interaction, where the suppression only occurs in materials where the deformation potential interaction shifts the electron and hole bands in the same direction. We demonstrate also how the phonon-induced effects may be altered by placing the QD inside an infinite slab, where the confinement of the phonons is modified instead. For a slab thickness below ∼ 70 nm, the bulk description of the phonon modes may be insufficient. The QD decay rate may be strongly increased or decreased, depending on how the detuning between the QD and the optical mode matches the phonon modes in the slab.
Realising a platform for efficiently guiding and manipulating light at the singlephoton level lies at the heart of optical quantum information processing. In this thesis we aid in the pursuit of this goal by analysing few-photon transport properties in photonic devices while keeping in mind possible applications and experimental challenges. We especially focus on single and two-photon transport properties in one-dimensional waveguides coupled to (artificial) atoms modelled as two and three-level emitters. We begin by introducing key concepts relevant for this thesis and then explain how to model such waveguide geometries. We show how directional-dependent coupling between a waveguide and a localized quantum system can be modelled from a chain of harmonic oscillators by allowing the system to couple to more than one site. Using the input-output formalism and scattering matrix theory we determine a general form for the single and two-photon S-matrices for a waveguide coupled to a two-level system. We also explain how to engineer a quantum optical Fanoresonance waveguide geometry and calculate how this modifies the S-matrices, the few-photon scattering probabilities, and the scattered output spectra. We show that the nonlinear effects in such a system generates highly correlated directional scattering probabilities. We device a protocol that can generate maximal entanglement between two spectrally distinct solid-state emitters by the use of multi-photon scattering. The results also reveal a rich structure for multi-photon states interacting with non-identical emitters. As a final investigation, we quantify how spectral diffusion in quantum dots affects finite-width single and two-photon scattering. Single-photon scattering probabilities are described by a simple convolution but this is not the case for a two-photon state scattering off a two-level emitter. We show that the effect of spectral wandering depletes the nonlinear scattering properties, but that it affects co and counter-propagating output probabilities differently.
Engineering photon-photon interactions is fundamentally challenging because photons in vacuum do not interact with each other. While their interactions can be mediated using optical nonlinearities, these effects are negligible for individual photons. This thesis explores two topics related to optical nonlinearities in waveguides. In the first part, we perform a numerical simulation study of hollow core antiresonant reflecting optical waveguides (ARROWs) fabricated using standard lithographic techniques in the context of their suitability as a platform for on-chip photonic quantum information processing. We investigate the effects of the core size, the number of pairs of antiresonant layers surrounding the hollow core, and the refractive index contrast between cladding materials on propagation losses in the waveguide. Additionally, we explore the feasibility of integrating these waveguides with Bragg gratings and dielectric metasurface mirrors to form on-chip cavities, that when loaded with atomic ensembles could act as nonlinear optical devices controllable with single photons. \n \nThe second part of this thesis studies the application of a 3 level quantum emitter coupled to a directional optical waveguide to deterministically subtract a single photon from a propagating optical pulse. Subtracting a single photon from a light state is one of the most fundamental operations with important applications in quantum information processing. However, current methods to subtract a photon such as using a low reflectivity beam splitter suffer from inherently low success probabilities as well as a strong dependence on the number of photons in the input. We explore implementing this single photon subtraction operation in our proposed system when the optical input is a continuous wave coherent state, coherent pulsed state containing a finite number of photons, or a Fock state.
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 present a scheme for implementing a high-fidelity non-linear phase shift on a photonic state. The scheme is based on repeated scattering off a two-level quantum emitter embedded in a chiral or one-sided waveguide. The waveguide is equipped with elements inducing second-order dispersion and temporal phase shifts, which effectively form a harmonic trap and confine the photon pulses to a Gaussian shape. The same quantum emitter can be used for each scattering, and thus, only one quantum emitter is needed in this scheme. To illustrate the application of our scheme for photonic quantum computing and quantum communication, we analyze the implementation of a control-Z gate and a deterministic Bell-state analyzer for photonic qubits. Through numerical optimization, we show that we can reach a control-Z gate fidelity of F∼99.2% (F∼96%) and a success probability of Ps∼99.6% (Ps∼98%) for a Bell-state measurement with N=17 (N=5) scatterings.
This thesis is devoted to theoretically study the systems of single quantum dots (QDs) embedded in various photonic nanostructures, in close relation with experimental data. The word single is essential: due to their nanometer size, QDs have mainly been studied as ensembles. It is only recently that the experimental progress, in particular in the domain of QDs growth, has allowed to address single QDs. This helped to observe that the confined states in a QD resemble those of an atom, leading in turn to the macro-atom picture for QDs. It opened the path to the study of cavity quantum electrodynamics (CQED) in the solid state, as the analogous of a system of an atom in an electromagnetic cavity. However, already at the level of the QD (i.e. without a solid state cavity), the macro-atom picture has been proven to be oversimplified. Various effects related to the solid state environment of the QD have been experimentally and theoretically evidenced, like the influence of acoustic and optical phonons. These are channels of decoherence for the otherwise well isolated and confined QD levels. When adding the cavity, these effects are possibly enhanced, which can lead to very large deviations from the CQED ideal picture. Therefore the clear understanding of these effects is of essential importance, especially in view of the application of solid state systems to quantum information science. In Chapter 2, we address the radiation-matter coupling between two QDs in a nanocavity. This field of research combines the high quality of light resonators to the nonlinearities of the semiconductor material. It is promising in view of manipulating and transferring single long-lived excitations, an essential goal for quantum information science. Then, we study the deviations of a QD from the idealized macroatom picture. First, in Chapter 3, we include the influence of acoustic phonons on the light emitted by a QD-cavity system. We show that the QD modified susceptibility leads to the qualitative explanation of the cavity feeding effects, which is one of the most striking deviations of the QD-cavity system from the ideal CQED picture. In addition to phonons are extended two-dimensional states populated by the non resonant pumping laser in the QD's wetting layer (WL). In Chapters 4 and 5 we build a Monte-Carlo model of the excitation-decay mechanism in a QD-cavity system. We use it to describe the influence of WL states on the dynamics of the QD, leading in turn to a non-CQED behavior. This approach is particularly successful in the case of large QD-cavity detuning, where it predicts both time-dependent and spectral characteristics of the emitted light. Finally, in Chapter 6, we discuss our conclusions, emphasizing in particular that the knowledge of the actual solid state environment of the QD leads to a better control over the parameters allowing to reach the CQED regime. We also discuss the possible extensions of this work, in particular in relation to the analysis of the stimulated emission regime.
Summary form only given. Optical logic down to the single photon level holds the promise of data processing with a better energy efficiency than electronic devices [1]. In addition, preservation of quantum coherence in such logical components would enable optical quantum logical gates [2-8]. Optical logic requires optical non-linearities to allow for photon-photon interactions. Non-linearities usually appear for large intensities, but discrete transitions in a well coupled single two-level system allow for giant non-linearities operating at the single photon level.This is achieved by engineering what has been coined a "one-dimensional atom" [2], wherein a light emitter is predominantly coupled to a single propagating spatial mode. This favored coupling with a traveling mode is obtained either in a resonant optical cavity [3,4] or with non-resonant field confinement such as in single mode waveguides [5,6] or through the interaction with a focused optical beam [7,8] . Here we take advantage of the large coupling efficiency and the broadband operation of a photonic wire containing a semiconductor quantum dot (QD) [9] to implement a transistor using two different optical QD transitions. Our system is made of a single InAs QD embedded in a GaAs tapered photonic wire (fig. 1a). This system, in which the QD is efficiently coupled to a single guided mode, has been exploited to realize ultrabright single-photon sources [9]. We exploit here its broad operation bandwidth (>100 nm around 950 nm) to efficiently address two different transitions of the QD with two different laser beams to implement a two-color giant non-linearity: a weak probe laser has its reflectivity controlled by a few photons of the control laser.