The rapidly growing field of quantum information can benefit greatly from quantum nonlinear optics, which has the potential to generate highly correlated optical states with a sufficiently large interaction strength per photon. Such states play a crucial role in various quantum applications. While the traditional approach to generating correlated optical states involves controlled interactions between individual single photons through nonlinear mediums, a more efficient approach is to use the evolution of multiphotons in the highly nonlinear optical medium. To facilitate this approach, we propose a scheme that traces the time evolution of the photons encoded in Fock space to generate complex correlated states. Our approach mimics the dynamics of many-body systems with adjustable interaction strength, allowing us to simulate state transfer on a spin chain by tuning the interaction. We also investigate the feasibility of our scheme based on current technologies and explore the potential of quantum nonlinear optics in quantum simulation.
The rapidly growing field of quantum information can benefit greatly from quantum nonlinear optics, which has the potential to generate highly correlated optical states with a sufficiently large interaction strength per photon. Such states play a crucial role in various quantum applications. While the traditional approach to generating correlated optical states involves controlled interactions between individual single photons through nonlinear mediums, a more efficient approach is to use the evolution of multiphotons in the highly nonlinear optical medium. To facilitate this approach, we propose a scheme that traces the time evolution of the photons encoded in Fock space to generate complex correlated states. Our approach mimics the dynamics of many-body systems with adjustable interaction strength, allowing us to simulate state transfer on a spin chain by tuning the interaction. We also investigate the feasibility of our scheme based on current technologies and explore the potential of quantum nonlinear optics in quantum simulation.
The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an N-photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of a bosonic mode involving the vacuum and an M-Fock state, with M<N. In addition, driving a bosonic mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {|0⟩,|1⟩,…,|N-1⟩} can be populated; i.e., we show how to implement a Fock state filter, or quantum scissor, that restricts the dynamics of a given bosonic mode to a limited Hilbert space. Such a device can be employed as a generator of finite-dimensional quantum-optical states and also as a quantum-optical intensity limiter, allowing as a special case the generation of single-photon pulses. On the other hand, our system also provides a very rich physics in the weak atom-field coupling regime, in particular, multiphoton electromagnetically induced transparencylike phenomena, inducing a narrow (controllable) reflectivity window for nonlinear probe fields. These results are useful for applications in quantum information processing and also motivate further investigations, e.g., the use of an N-photon Jaynes-Cummings system as a qudit with harmonic spectrum and the exploration of multiphoton quantum interference.
With the goal of achieving all-optical quantum information processing, singlephoton engineering has become one of the hottest research topics in physics. Rapid progress has been made in generating and detecting single photons, and also in information processing based on linear optics. Furthermore, the discovery of optical nonlinearity that is sensitive to individual photons has raised the possibility of using one photon to control another photon, increasing the need to develop a quantitative theory of nonlinear quantum optics.The simplest method to analyze the nonlinear dynamics of photons is to introduce an effective nonlinearinteraction Hamiltonian based on the singlemode approximation. For example, the following time evolution operator has conventionally been used for the self-Kerr interaction: ˆ
Controlling light photon-by-photon is central to quantum optics. At a fundamental level, photon interactions are mediated by their coupling to atoms, and ultimate control requires deterministic light-matter interfacing of single photons to single atoms. Extending this paradigm to radiatively couple multiple individual atoms in a deterministic and scalable manner opens the arena of many-body quantum optics. Here, we realize such a setting by coherently coupling solid-state artificial atoms to a nanophotonic waveguide and demonstrate higher-order photon correlations that are controlled by the number of quantum emitters. We study the scaling of nonlinear photonic transport induced by emitter-photon scattering and demonstrate that adding a quantum emitter generates higher-order photon correlations. Specifically, we experimentally observe genuine three-photon correlations from a pair of collectively coupled emitters, while contributions from lower photon numbers are suppressed. In addition, we scale to three resonant quantum emitters coupled to the waveguide. These advancements demonstrate the onset of many-body quantum optics in waveguide quantum electrodynamics, enabling new photonic quantum simulators, the creation of many-body entangled states, and the exploration of novel quantum phase transitions.
This paper investigates the application of adaptive topology to the simulation of quantum entanglement and quantum information. Traditional approaches often focus on manipulating individual quantum states, but this work proposes a novel method leveraging the inherent dynamic nature of quantum states to mimic complex phenomena like quantum entanglement and quantum information. The core of this approach involves constructing a topological structure that evolves in response to the quantum state's dynamics, allowing for the visualization and analysis of these intricate correlations. This method offers a new perspective on simulating these crucial phenomena, potentially leading to advancements in quantum information processing and understanding.
The NOON states play a critical role as physical resources in quantum information processing and quantum metrology, yet their preparation efficiency and applicability are often constrained by complicated operational procedures or the requirement for nonlinear interactions. In this paper, we propose an efficient protocol to generate the NOON states within two microwave cavities embedded in a superconducting system, assisted by an auxiliary five-level qudit. The state preparation is accomplished in three steps for an arbitrary photon number N by adjusting only external classical fields, while keeping the qudit-cavity coupling strengths and the qudit level spacings fixed. Based on parameters accessible in superconducting systems, numerical simulations show that the protocol achieves relatively high fidelity for the NOON states preparation even in the presence of parameter fluctuations and decoherence effects. Thus, this protocol may provide a practical approach for preparing the NOON states with current technology. Notably, since nonlinear interactions are not required, the protocol is flexible and has the potential to be applied across various physical systems.
Photons travelling through free space do not interact with each other. This characteristic makes them perfect candidates to carry quantum information over long distances. On the other hand, processing the information they encode requires interaction mechanisms. In recent years, there have been growing efforts to realize strong, controlled interactions between photons by making them interact with individual atoms, which are intrinsically nonlinear objects. This, and the efforts to understand the phenomena that can emerge, have spawned the new field of`"quantum nonlinear optics." A number of approaches have been pursued to attain near-deterministic atom-photon interactions, including the use of cavities (CQED), of atomic ensembles, and more recently of dielectric nanostructures able to confine light without defocusing, thus enabling the interaction with atoms trapped in the proximity of the structures. While for the CQED case powerful theoretical tools have been developed to treat the interactions of photons, in the case of atomic ensembles, either in free space or coupled to nanophotonic structures, there is a general lack of theoretical methods beyond the linear regime. This relative lack of understanding also implies that there could be rich new physical phenomena that have thus far not been identified. The overall goal of this thesis is to explore these themes in greater detail. In Chapter 2 of this thesis we develop a new formalism to calculate the properties of quantum light when interfaced with atomic ensembles. The method consists of using a "spin model" that maps a quasi one-dimensional (1D) light propagation problem to the dynamics of an open 1D interacting spin system, where all of the photon correlations are obtained from those of the spins. The spin dynamics can be numerically solved using the toolbox of matrix product states (MPS), thus providing a technique to study strongly interacting photons in the true many-body limit. In Chapter 3 we investigate the possibility of creating exotic phases of matter using the recently realized photonic crystal waveguide (PCW)-atoms interface. In particular, we examine the consequences that arise from the strong interatomic forces mediated by the exchange of band gap photons, whose strengths also depend strongly on the internal atomic states (¿spins¿). Taking one realistic model, we show that "quantum crystallization" can occur, in which the emergent spatial orders of atoms depend intricately on the spin correlations. In Chapter 4 we investigate the possibility of implementing second-order nonlinear quantum optical processes with graphene nanostructures, as a more robust alternative to the use of atomic systems. We quantify the second-order nonlinear properties, showing that the tight confinement of surface plasmons (SP) in graphene gives rise to extraordinary interaction strengths at the single-photon level. Finally, we predict that opportunely engineered arrays of graphene nanostructures can provide a second harmonic generation efficiency comparable with that of state-of-the-art nonlinear crystals, with the high Ohmic losses of graphene serving as the fundamental limitation for deterministic processes. In Chapter 5 we investigate a new paradigm for quantum memories of light based upon ordered atomic arrays. In particular, we show that the strong constructive interference in optical emission can give rise to a significantly enhanced atom-light interface, as compared to a standard, disordered atomic ensemble. In the case of a single, 2D atomic layer, we find the impressive result that a memory realized with 16 atoms can have the same storage efficiency as an atomic ensemble with optical depth larger than 100. Los fotones que viajan por el espacio libre no interactúan entre sí. Esta característica los hace perfectos candidatos para transportar la información cuántica a largas distancias. Por otro lado, el procesamiento de la información que codifican requiere mecanismos de interacción. En los últimos años se han realizado esfuerzos crecientes para realizar interacciones fuertes y controladas entre los fotones y para comprender las leyes subyacentes que describen los fenómenos que pueden surgir, generando así el nuevo campo de la "óptica cuántica no lineal". Mientras que los materiales tridimensionales tienen coeficientes no lineales extremadamente débiles, se pueden obtener interacciones entre los fotones haciéndolos interactuar con átomos individuales, que son objetos intrínsecamente no lineales, teniendo la capacidad de absorber únicamente un solo fotón a la vez. La realización de interacciones determinísticas entre fotones y átomos es uno de los principales retos de la óptica cuántica no lineal. Para eludir las limitaciones debidas a la pequeña sección eficaz óptica de los átomos y el límite de difracción en el espacio libre, se han aplicado diferentes estrategias, entre ellas el uso de cavidades (CQED), de colectividades atómicas y, más recientemente, de nanoestructuras dieléctricas capaces de confinar la luz sin desenfocarse, permitiendo así la interacción con átomos atrapados en la proximidad de esas estructuras. Mientras que para el caso de la CQED se han desarrollado potentes herramientas teóricas para tratar las interacciones de los fotones, en el caso de colectividades atómicas hay una falta general de métodos teóricos más allá del régimen lineal. Esta relativa falta de comprensión también implica que podría haber nuevos fenómenos físicos interesantes que hasta ahora no se han identificado. El objetivo general de esta tesis es explorar estos temas con mayor detalle. En el capítulo 2 de esta tesis desarrollamos un nuevo formalismo para calcular las propiedades de la luz cuántica cuando interactúa con sistemas atómicos. El método consiste en utilizar un"`modelo de espines" que mapea un problema de propagación de luz cuasi unidimensional (1D) a la dinámica de un sistema abierto unidimensional de espines que interactúan entre sí, donde todas las correlaciones de fotones se obtienen a partir de las de los espines. La dinámica de los espines se puede resolver numéricamente utilizando la caja de herramientas de los estados producto de matrices (MPS), proporcionando así una técnica para estudiar los fotones que interactúan fuertemente en el regimen de la física de muchos cuerpos. En el capítulo 3 se investiga la posibilidad de crear fases exóticas de la materia utilizando la interfaz entre guía de ondas de cristales fotónicos (PCW) y átomos recientemente realizada experimentalmente, donde los modos de la banda de frecuencias prohibidas de la PCW se utilizan para mediar las interacciones de largo alcance entre los átomos. Encontramos un rico diagrama de fases de órdenes emergentes. En el capítulo 4 se investiga la posibilidad de implementar procesos ópticos cuánticos no lineales de segundo orden con nano-estructuras de grafeno, como una alternativa más robusta al uso de sistemas atómicos. Cuantificamos las propiedades no lineales de segundo orden, mostrando que el estrecho confinamiento da lugar a extraordinarias fuerzas de interacción a nivel de un solo fotón y predecimos que un diseño apropiado de las nano-estructuras del grafeno permitiría generar el segundo armónico con una eficiencia comparable a la de los cristales no lineales de última generación. En el capítulo 5, investigamos cómo la emisión cooperativa en memorias cuánticas realizadas con reticulos atómicos afecta su eficiencia, encontrando el impresionante resultado de que una memoria realizada con 16 átomos puede tener la misma eficiencia que un gas cuántico atómico de profundidad óptica mayor que 100.