An expansion for Neutrino Phenomenology

We develop a formalism for constructing the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix and neutrino masses using an expansion that originates when a sequence of heavy right handed neutrinos are integrated out, assuming a seesaw mechanism for the origin of neutrino masses. The expansion establishes relationships between the structure of the PMNS matrix and the mass differences of neutrinos, and allows symmetry implications for measured deviations from tri-bimaximal form to be studied systematically. Our approach does not depend on choosing the rotation between the weak and mass eigenstates of the charged lepton fields to be diagonal. We comment on using this expansion to examine the symmetry implications of the recent results from the Daya-Bay collaboration reporting the discovery of a non zero value for theta_{13}, indicating a deviation from tri-bimaximal form, with a significance of 5.2 sigma.Comment: 16 pp, 1 figure v2: Jhep version, more exposition/description,results unchange

Advances in quantum optical metrology and the establishment of an invisible quantum tripwire

This thesis presents a summary of the foundation and background of the field of quantum optics, and an analysis of some recent discoveries in various fields of which I have aided in furthering investigative research and advancement through publications. Such topics include numerical optimization of generalized quantum states used in phase sensitive quantum metrology, an analysis of object detection through the use of quantum interferometry in the presence of lossy conditions, and the use of the latter technique to propose an invisible quantum tripwire. First is a collaborative effort to numerically optimize quantum optical states for quantum metrological applications. We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss the optimal state is the so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss. The next topic is statistical hypothesis testing of interaction free measurement and a quantitative limit on the obtainable error. Previous analyses have been based solely on detection probabilities known only in the infinite photon limit. Our analysis assumes a finite number of photons, and an investigation of reliability in the presence of photon loss and phase fluctuations. We use symmetric hypothesis testing and the Chernoff bound to provide error estimation after N independent, single photon trials. Finally, we present a quantum optical interrogation technique capable of detecting an intrusion with very low probability of the quantum “tripwire” being revealed to the intruder. The tripwire exploits a curious nonlinear behavior of the quantum Zeno effect we discovered, which occurs in a lossy system. We also employ statistical hypothesis testing, allowing us to calculate a confidence level of interaction-free measurement after a given number of trials