[pt] Nas últimas décadas, interações entre luz e matéria provaram ser uma ferramenta versátil para medir e controlar sistemas mecânicos, encontrando aplicações desde detecção de forças até resfriamento ao estado fundamental de nanoesferas. Nesta dissertação, nós apresentamos algumas das ferramentas teóricas necessárias para descrever interferômetros, pinças ópticas e cavidades ópticas, constituintes fundamentais da caixa de ferramentas optomecânica. No regime clássico, estudamos o campo eletromagnético circulante em interferômetros lineares e mostramos como encontrar o campo resultante transmitido, apresentando exemplos de cavidades ópticas com um número arbitrário de elementos dispersivos. Nós também estudamos as forças de pressão de radiação que feixes ópticos podem imprimir em partículas dielétricas e mostramos como o aprisionamento óptico 3D é possível em focos claros e escuros. A potencial aplicação para captura de organismos vivos é estudada. No regime quântico, nós estudamos como o campo ressonante de cavidades ópticas pode interagir de forma dispersiva com diferentes sistemas mecânicos, dando origem a uma dinâmica quântica fechada emaranhante. Ao considerar uma nuvem ultra resfriada de átomos interagindo com dois modos ópticos, mostramos o surgimento de emaranhamento óptico que evidencia a natureza não-clássica do conjunto atômico macroscópico. A viabilidade experimental deste experimento com tecnologia atual é estudada. Além disso, nós investigamos o cenário em que uma pinça óptica posiciona uma partícula levitada dentro de uma cavidade óptica de forma que os fótons da pinça espalhados pela partícula possam sobreviver dentro da cavidade. Já foi demonstrado que esta interação, chamada de espalhamento coerente, pode resfriar nanopartículas até números de fônons menores do que um, atingindo profundamente o regime quântico. Nós mostramos que esta interação também pode gerar emaranhamento mecânico entre muitas partículas levitadas, mesmo em um ambiente a temperatura de 300K. Um resumo sobre sistemas de variáveis contínuas e a caixa de ferramentas numérica customizada usada ao longo deste trabalho são apresentados. / [en] Over the last decades, light-matter interactions have proven to be a versatile tool to measure and control mechanical systems, finding application from force sensing to ground state cooling of nanospheres. In this dissertation, we present some of the theoretical tools that describe interferometers, optical tweezers and optical cavities, fundamental constituents of the optomechanical toolbox. In the classical regime, we study the circulating electromagnetic field within linear interferometers and show how one can find the resulting transmitted field, presenting examples of optical cavities with an arbitrary number of dispersive elements. Moreover, we also study the radiation-pressure forces that optical beams can imprint on dielectric particles and show how 3D optical trapping is possible in both bright and dark focuses. Potential application to trapping of living organisms is studied. In the quantum regime, we study how the resonant field of optical cavities can dispersivelly interact with different mechanical systems, giving rise to an entangling closed quantum dynamics. When considering an ultracold cloud of atoms interacting with two optical modes, we show the emergence of optical entanglement which evidences the nonclassical nature of the macroscopic atomic ensemble. The experimental feasibility of this experiment with current technology is studied. Furthermore, we investigate the scenario where a finely tuned optical tweezer places a trapped particle inside an optical cavity such that the tweezer s scattered photons can survive inside the cavity. This so-called coherent scattering interaction has been shown to cool nanoparticles to phonon numbers lower than one deep into the quantum regime. We show that it also can generate mechanical entanglement between many levitated particles even in a room temperature environment. An overview on continuous variable systems and the custom numerical toolbox used throughout this work are presented.

This dissertation documents works on two projects, which are broadly related to photonic integration using III-V semiconductor platform for fiber-based optical communication. Our principal project aims to demonstrate continuous variable quantum key distribution (CV-QKD) with InP-based photonic integrated cir cuit at the 1550 nanometer of optical wavelength. CV QKD protocols, in which the key is encoded in the quadrature variables of light, has generated immense interest over the years because of its compatibility with the existing telecom infrastructure. In this thesis, we have proposed a design of a photonic inte grated circuit potentially capable of realizing this protocol with coherent states of light. From the practical perspective, we have basically designed an optical transmitter and an optical receiver capable of carrying out coherent communi cation via the optical fiber. Initially, we established a mathematical model of the transceiver system based on the optical transfer matrix of the foundry spe cific (Fraunhofer Heinrich Hertz Institute-Germany) building blocks. We have shown that our chip design is versatile in the sense that it can support multiple modulation schemes. Based on the mathematical model, we estimated the link budget to assess the feasibility of on-chip implementation of our protocol. Then we ran a circuit level simulation using the process design kit provided by our foundry to put our analysis on a better footing. The encouraging result from this step prompted us to generate the mask layout for our transceiver chips, which we eventually submitted to the foundry. The other project in the thesis grew out of a collaboration with one of our industry partners. The goal of the project is to enhance the performance of a distributed feedback laser emitting at the 1310 nanometer of optical wavelength by optimizing its design. To that end, we first derived the expression for transmission and reflection spectrum for the laser cavity. Those expressions contained parameters which needed to be obtained from the transverse and the longitudinal mode analysis of the laser. We performed the transverse mode analysis and the longitudinal mode analysis with commercially available numerical solvers. Those mode profiles critically depend on the grating physical parameters. Therefore by tweaking grating dimensions one can control the transmission characteristics of the laser.