Interacting Photons in Waveguide-QED and Applications in Quantum Information Processing

<p>Strong coupling between light and matter has been demonstrated both in classical</p><p>cavity quantum electrodynamics (QED) systems and in more recent circuit-QED</p><p>experiments. This enables the generation of strong nonlinear photon-photon interactions</p><p>at the single-photon level, which is of great interest for the observation</p><p>of quantum nonlinear optical phenomena, the control of light quanta in quantum</p><p>information protocols such as quantum networking, as well as the study of</p><p>strongly correlated quantum many-body systems using light. Recently, strong</p><p>coupling has also been realized in a variety of one-dimensional (1D) waveguide-</p><p>QED experimental systems, which in turn makes them promising candidates for</p><p>quantum information processing. Compared to cavity-QED systems, there are</p><p>two new features in waveguide-QED: the existence of a continuum of states and</p><p>the restricted 1D phase space, which together bring in new physical effects, such</p><p>as the bound-state effects. This thesis consists of two parts: 1) understanding the</p><p>fundamental interaction between local quantum objects, such as two-level systems</p><p>and four-level systems, and photons confined in the waveguide; 2) exploring</p><p>its implications in quantum information processing, in particular photonic</p><p>quantum computation and quantum key distribution.</p><p>First, we demonstrate that by coupling a two-level system (TLS) or three/fourlevel</p><p>system to a 1D continuum, strongly-correlated photons can be generated</p><p>inside the waveguide. Photon-photon bound states, which decay exponentially as a function of the relative coordinates of photons, appear in multiphoton scattering</p><p>processes. As a result, photon bunching and antibunching can be observed</p><p>in the photon-photon correlation function, and nonclassical light source can be</p><p>generated on demand. In the case of an N-type four-level system, we show</p><p>that the effective photon-photon interaction mediated by the four-level system,</p><p>gives rise to a variety of nonlinear optical phenomena, including photon blockade,</p><p>photon-induced tunneling, and creation of single-photon states and photon</p><p>pairs with a high degree of spectral entanglement, all in the absence of a cavity.</p><p>However, to enable greater quantum networking potential using waveguide-</p><p>QED, it is important to study systems having more than just one TLS/qubit.</p><p>We develop a numerical Green function method to study cooperative effects in</p><p>a system of two qubits coupled to a 1D waveguide. Quantum beats emerge in</p><p>photon-photon correlations, and persist to much longer time scales because of</p><p>non-Markovian processes. In addition, this system can be used to generate a</p><p>high-degree of long-distance entanglement when one of the two qubits is driven</p><p>by an on-resonance laser, further paving the way toward waveguide-QED-based</p><p>quantum networks.</p><p>Furthermore, based on our study of light-matter interactions in waveguide-</p><p>QED, we investigate its implications in quantum information processing. First,</p><p>we study quantum key distribution using the sub-Possonian single photon source</p><p>obtained by scattering a coherent state off a two-level system. The rate for key</p><p>generation is found to be twice as large as for other sources. Second, we propose</p><p>a new scheme for scalable quantum computation using flying qubits--propagating</p><p>photons in a one-dimensional waveguide--interacting with matter qubits. Photonphoton</p><p>interactions are mediated by the coupling to a three- or four-level system,</p><p>based on which photon-photon -phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is</p><p>possible given recent dramatic experimental progress in superconducting circuits</p><p>and photonic-crystal waveguides. The proposed system can be an important</p><p>building block for future on-chip quantum networks.</p>Dissertatio

Waveguide QED: Many-Body Bound State Effects on Coherent and Fock State Scattering from a Two-Level System

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. Multi-photon 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 wavepackets, 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.Comment: 10 page

Strongly correlated photons generated by coupling a three- or four-level system to a waveguide

We study the generation of strongly correlated photons by coupling an atom to photonic quantum fields in a one-dimensional waveguide. Specifically, we consider a three-level or four-level system for the atom. Photon-photon bound states emerge as a manifestation of the strong photon-photon correlation mediated by the atom. Effective repulsive or attractive interaction between photons can be produced, causing either suppressed multiphoton transmission (photon blockade) or enhanced multiphoton transmission (photon-induced tunneling). As a result, nonclassical light sources can be generated on demand by sending coherent states into the proposed system. We calculate the second-order correlation function of the transmitted field and observe bunching and antibunching caused by the bound states. Furthermore, we demonstrate that the proposed system can produce photon pairs with a high degree of spectral entanglement, which have a large capacity for carrying information and are important for large-alphabet quantum communication.Comment: 13+ pages, 7 figure