Schrodinger's lion or Schrodinger's kitten?---Gauging the size of large quantum superposition states.

摘要

This dissertation discusses how to find suitable ways to measure the effective "size" of a quantum superposition state (aka a Schrodinger cat state), and analyzes the microscopic dynamics of flux/current superposition states in superconducting loops containing Josephson junctions. These states have been claimed to be examples of macroscopic or at least mesoscopic cat states.;In Part I, I define one class of measures based on how many microscopic degrees of freedom would need to be measured to distinguish the two branches of a superposition from each other, as well as one simpler measure based on differences in mode occupation numbers in systems of indistinguishable particles. Along the way, I review and extend many results related to quantum state estimation and quantum state discrimination. I pay special attention to the crucial distinction between systems of distinguishable and indistinguishable particles, something which has not always been done in earlier literature on the subject.;In Part II, I develop a method based on functional integrals to calculate correlation functions for the microscopic electronic degrees of freedom in a superconductor. I use this approach to estimate the effective size of superposed current states. This appears to be the first time that these states have been carefully analyzed at the microscopic level rather than in terms of macroscopic observables. The conclusion is that the superposition states produced in the two most celebrated experiments of this kind to date are not macroscopic according to the measures used in this dissertation, and will likely not be according to any other measure that is based on whether or not a large number of microscopic degrees of freedom are in different states in the two branches of a superposition state. The vast majority of electrons do not effectively participate in the superposition behavior in any significant way. Finally, I find that although larger superpositions of flux/current states in superconducting loops can in principle be realized, it is almost certainly not possible to push them anywhere close to the macroscopic scale.