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Conference on Lasers and Electro-Optics

Few Photon – Qubit Scattering in Dispersive Waveguides

Şükrü Ekin Kocabaş

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Dispersion in waveguides leads to atom-photon bound states in qubits embedded in waveguides. We utilize Feynman diagrams and numerical simulations to analyze one-and two-photon scattering from qubits with the aim to test different quantum information processing schemes.
DOI
10.1364/cleo_at.2016.jtu5a.1

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We study one- and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed-form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.
We extend the Krylov-subspace-based time-dependent numerical simulation technique for a qubit interacting with photons in a waveguide to the multiple qubit case. We analyze photon scattering from two qubits and derive expressions for the bound states in the continuum (BICs). We show how the BIC can be excited. We use the BIC in a recent Pauli-Z gate proposal involving decoherence free subspaces and obtain the gate fidelity as a function of the gate parameters. The techniques presented in this Letter are useful for investigating the time evolution of quantum gates and other many-body systems with multiple quenches in the Hamiltonian.
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.
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 one- and two-photon scattering in a one-dimensional waveguide coupled to a giant atom within the non-Markovian regime using the resolvent approach. The non-Markovian behavior gives rise to an atom-photon bound state that cannot be excited by a single incident photon. However, the bound state can be excited via the two-photon scattering process described by multichannel scattering theory, from which an analytical trapping probability of a photon in the bound state can be achieved. Additionally, we analyze the two-photon scattering process, obtaining the analytical expressions for scattered states. As non-Markovian effects strengthen, two peaks appear in the incoherent power spectrum, attributed to the system behaving as a leaky cavity formed by the giant atom's coupling points. Through the analysis of second-order correlation functions, we observe the bunching behavior for transmitted photons, antibunching behavior for reflected photons, and the distinctive retrieval behavior at the coupling points' separation.