Two coupled quantum oscillators: an approach beyond the rotating waves aproximation

Abstract

This project aims to study the coherence dynamics and decoherence of quantum states in a network composed of two dissipative quantum oscillators. We consider that these oscillators are coupled strongly by rotating and counter rotating wave terms. We understand the dynamics of the coherent state transfer process between the oscillators of the network and its subsequent recurrence to oscillators which were originally prepared. We intend to analyze the effects of these processes in the presence of the interaction of this system with a reservoir (system with many degrees of freedom), which we assume, in the same way that the two quantum oscillator system, the interaction occurs through a rotating and counter rotating terms (weakly, that still allow perturbation theory). In the case where the interaction between the system oscillators and its interaction with the reservoir occurs only through rotating terms it was analyzed in Refs. M1, M2, considering the degenerate case in which all network oscillators have the same natural frequency in addition to the same coupling constant. We are also interested in analyzing the emergence of a decoherence-free subspace as a result of the new interaction terms, and a possible application in quantum theory of games with the inclusion of the effects of decoherence, something little studied in the literature.