Generación de entrelazamiento y simulación relativista con osciladores paramétricos en cQED

Resumen

We are living in an age where our understanding of quantum mechanics is increasing at an exciting pace. Since its inception, we have always considered it at the foundation of a great variety of physical phenomena. However, it was often used as a first step in the creation of effective theories about, for instance, properties of semiconductors or statistics of processes involving fundamental particles. But nowadays, we are learning to harness the theory to its full extent. Nowadays, we can explore its most intimate and shocking features with the most exquisite control. It is close to become a technology. The development of quantum technologies is clearly motivated by their applications. The oddities of quantum mechanics have become opportunities to store, transfer and process information in ways impossible to the classical sciences. Therefore, the task of designing a quantum computer capable of delivering said advantages is central to the research being done today. This interface, between scientific curiosity and technological possibility, is where this thesis stands. Attention will be paid to the current state of the art in quantum technologies, mainly in circuit quantum electrodynamics (cQED). This acronym is an umbrella term that encompass any circuit designed to operate with superconducting material, most often composed of versatile Josephson junctions. Then, we will model existing circuits or propose new designs that may shed light on interesting topics in quantum mechanics. This thesis explores two specific topics: On one hand, we study the generation and detection of new entangled non-gaussian states of microwave radiation. These states are produced in a new parametric oscillator, built recently within the field of cQED, capable of down-converting a microwave tone into three different tones at once. These new three photons share among their magnitudes quantum correlations, in particular genuine entanglement. This kind of entanglement is considered one of the resources that allow for the quantum processing of information impossible to the classical sciences. In this text we refer to it as non-Gaussian because of its manifestation on statistical moments higher than covariances and we propose a simple and practical criterion for the design of witnesses capable of detecting it: they must be built from higher statistical moments that change through time. Additionally, we speculate on the theoretical implications of the criterion and find suggestive connections to other entanglement classes, such as the paradigmatic nonequivalent GHZ and W three qubit states. On the other hand, we explore one of the possible applications of quantum technologies: the simulation of quantum systems. The literature prior to this thesis showcases multiple examples of superconducting circuits capable of mimicking systems in which one must consider both quantum and relativistic phenomena, such as the dynamical Casimir and Unruh effects. These effects have not been observed in their original setting, and some have only been observed in their analogue circuits. This work explores the information that can be obtained through analog simulation, proposing a circuit capable of featuring the internal dynamics of a mirror experiencing a relativistic trajectory, that is, a mirror producing the dynamical Casimir effect.