Controlling the interaction between photons is one of the important technologies applied to quantum information processing at the few-photon level. We investigate the two-photon interaction via a Ξ-type atom, where one atomic transition is coupled to a one-dimensional waveguide, and the other transition is coupled to a cavity field. Whether the cavity is initially in the vacuum state or not, determines the effective configuration of the quantum emitter. When the cavity is in the vacuum state, only one bound state appears. We further found that the joint probability of transmitted photons oscillates with their spatial separation due to the coexistence of two bound states, if the cavity is in fock state |n〉 (n ≠ 0). With the incoming wave function consists entirely of plane waves, we present the exact out-state function that exhibit the bunching and antibunching behaviors. And, we discuss in detail with the behaviors of varying both the photon pair energy(E) and the energy difference between the two photons (Δ). Moreover, the spatial attraction and repulsion between the two transmitted photons can be controlled by the parameters of the cavity.
Controlling the interaction between photons is one of the important technologies applied to quantum information processing at the few-photon level. We investigate the two-photon interaction via a Ξ-type atom, where one atomic transition is coupled to a one-dimensional waveguide, and the other transition is coupled to a cavity field. Whether the cavity is initially in the vacuum state or not, determines the effective configuration of the quantum emitter. When the cavity is in the vacuum state, only one bound state appears. We further found that the joint probability of transmitted photons oscillates with their spatial separation due to the coexistence of two bound states, if the cavity is in fock state |n〉 (n ≠ 0). With the incoming wave function consists entirely of plane waves, we present the exact out-state function that exhibit the bunching and antibunching behaviors. And, we discuss in detail with the behaviors of varying both the photon pair energy(E) and the energy difference between the two photons (Δ). Moreover, the spatial attraction and repulsion between the two transmitted photons can be controlled by the parameters of the cavity.
We investigate the two-photon transport properties inside one-dimensional waveguide side coupled to a cavity. The cavity is doped with a four-level atom. By employing dressed state basis, we show that the atom-cavity molecule produces a nonlinear interaction. The bunching and antibunching of the transmitted and reflected photons can be observed due to the nonlinearity. By tuning the Rabi frequency of the classical field, the transmission and reflection of the correlated photons can be controlled.
Slowing/stopping the light travelling in free space with electromagnetically induced transparency to im- plement the optical quantum information processings and store information has been paid much attention in recent years. For the waveguide photons, here, we propose an approach to stop them with a controllable atomic cavity generated by a pair of atomic mirrors; one of them reflects the photon completely and an- other one with the adjustable reflected/transmitted probability of the photons. Based on the full quantum mechanical theory in real space, we show that the reflected/transmitted probability of the waveguide photon with a fixed frequency can be controlled by adjusting the energy-splitting of the driven two-level atomic scatters (i.e., atomic mirrors). As a consequence, the photon can be controllably transmitted/reflected along the waveguide by the aside atomic mirrors with the adjustable atomic energy levels. Ideally, the photons could be stopped in the atomic cavity. This provides a novel mechanism to stop/retravel the waveguide photon in a controllable ways. The feasibility of the proposal with the current integrated optical devices is also discussed.
We investigate few-photon scattering properties in two one-dimensional waveguides chirally coupled to a nonlinear cavity. The quantum states of scattered few photons are solved analytically via a real-space approach, and the solution indicates the few-photon reflection and transmission properties. When inputting two photons of equal energy to resonate with the cavity, the propagation characteristics of the two photons will be interesting, which is different from the previous anti-bunching effects with a quantum emitter. More importantly, when the total energy of the two incident photons equals the energy of a nonlinear cavity accommodating two photons, influence of the bound state will become larger to result in disappearance of antibunching effect. However, the bound state has no effect on probability of routing to another waveguide.
The area of waveguide quantum electrodynamics plays a signi cant role in many quantum technology applications. Photonic waveguides can be used to coherently transport photon pulses and can also efficiently increase the light-matter interaction strength. The work is done by Shen and Fan [1, 2] on the propagation of a photon pulse in a 1-D waveguide coupled to a single two-level emitter shows that a photon pulse can undergo complete reflection or transmission through the waveguide by controlling the coupling strength between the atom and the guided photon. We propose a V-type atomic system embedded in a 1-D waveguide and study the properties of an incoming photon pulse in the waveguide. We show that the driving field, which couples one of the atomic transitions, can be used as a controlling parameter to allow the photon pulse to be reflected or transmitted through the waveguide. As there reflection and transmission of the incident photon pulse can be externally controlled in our system, in comparison to the system suggested by Shen and Fan [1, 2], the proposed system in this thesis is more practiced than the system [1, 2]
Transmission and correlation properties of a two-photon pulse are studied in a one-dimensional waveguide (1DW) in the presence of three types of quantum emitters: two-level atom (TLA), side optical cavity (SOC), and Jaynes-Cummings model (JCM). Since there are many plane-wave components for a two-photon pulse, a nonlinear waveguide dispersion is used instead of the linearized one. The two-photon transmission spectra become flatter with decreasing the pulse width. With respect to the $\ensuremath{\delta}$ coupling between the 1DW and quantum emitter the transmission dips show a blueshift for the non-$\ensuremath{\delta}$ one and the blueshift first increases and then decreases with increasing the width of the coupling. The TLA and JCM can induce an effective photon-photon interaction that depends on the distance between the two photons, while the SOC cannot. We show that the 1DW coupled with the TLA or JCM is able to evaluate the overlap of the two photons and that the non-$\ensuremath{\delta}$ coupling has potential for controlling the two-photon correlation.
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.