Synchronization and quantum correlations in harmonic networks

We initially considered a fundamental quantum system, two coupled and detuned quantum harmonic oscillators dissipating into the environment. Different dissipation mechanisms, corresponding to the situations in which (i) every oscillator dissipate in an independent bath (separate baths, SB), or (ii) the correlations length in the bath is larger than the oscillators systems (common bath, CB), are considered. Analyzing the dynamics of the system for Gaussian states, we identify the conditions leading to spontaneous synchronization. The mechanism of synchronization in this linear system is novel and the ability of the system to oscillate at a common frequency is related to the existence of disparate decay rates of the normal modes. We then analyzed different measures of correlations and their temporal decay due to decoherence. We showed that this phenomenon is accompanied by robust quantum discord and mutual information between the oscillators, preventing the leak of information from the system.