Few Level Models in Atomic Radiation Theory

University Of Rochester, Rochester NY

Investigators

Abstract

This research program deals with the basic interactions of light and matter, studying entanglement and how entangled states evolve in time. Entanglement refers to the situation in which widely separated particles cannot be described independently of each other (or, mathematically, when the whole is not equal to the sum of its parts). An important direction for the research is to use mathematical models to explore these entangled states. This may have important applications, for example in managing the security of communication channels and in quantum information science. The goal of the project is to develop a complete catalog of correlation relations among a large number N of fundamental physical systems (spins, atoms, photons). This will be done by the technical process of bi-separation of quantum states. We have used both analytic and computer-based mathematical procedures to carry out, but have not yet published, a preliminary exploration of pure state bi-separations. These lead to constraints on occupation of what can be called entanglement-shared quantum state space. These constraints have a geometrical interpretation via simplexes and polytopes in N dimensions. The consequent description of N-party additivity leads to entanglement sharing relations and they substantially extend in a new direction the concurrence-based results called quantum monogamy. In the important but still simple case of 3 entangled parties, there are three bi-separations: a|bc, b|ac, and c|ab, and the consequent polytope in this case is a pair of base-to-base tetrahedrons inside a unit cube. Cross sections of the polytope transverse to the body diagonal of the cube are triangles, and we have found that their areas serve to quantify the amount of entanglement sharing that is possible among the three parties a,b,c. Exchanges with the fields of quantum information and quantum optics appear desirable and feasible, for example in developing protocols for multi-mode entanglement swapping at the macroscopic level.