Study of the Temporal-Evolution of a Star-like Quantum State of Light Through the Wigner Function

Abstract

In this work the time evolution of a star-like state was studied. The state gets his name after the shape of it’s corresponding Wigner function. The physical situation considered is a confined atom inside a microcavity, whose boundaries are made of Bragg reflectors. After the atom is confined, a beam made of a Star state of light incides against the microcavity. The Bragg reflectors are made to let the radiation go inside the microvacity an to keep it inside the microcavity, in order to let it interact with the atom. The matter-radiation interaction was described using the Jaynes-Cummings model.The time evolution was made into two different parts. In the first one, the evolution we studied was purely hamiltonian; that is, there was no disipation terms. Once we did such evolution we saw that the Wigner function rotated and that furthermore, the rotation had a given frecuency. In order to fully characterize these behavior, an analitical expression for the rotation period was found. It was also seen that, while the Wigner function was rotating, it also varied between the star state and the vacuum state corresponding Wigner functions.When the dissipative terms were considered into the time evolution of the state, it was clear that the Wigner function does not rotate in the same way as when there were no dissipative terms. Moreover it was seen, that there were several time intervals in which the Wigner function did not rotate at all and that these behavior usually took place after sudden and fast oscilations. The latest oscilations meant that there were happening some phase swifts, in the sense that there were different physical situations taking place. In order to determine which states were involved in such phase swifts, a tomography of the density matrix corresponding to the time evolution was made. At last it was studied, if there were a set of dissipative parameters such that the stationary state reached by the time evolution coincided with the initial star state. To verify how similar those two states were, the fidelity parameter was used.In both cases entanglement measurements were used to characterized the states in which the system went throught during the time evolution.