Understanding Quantum Synchronization of Self-Sustained Oscillators through Coherence

Abstract

Quantum synchronization, the emergence of phase locking in quantum systems, has gained significant attention due to its potential applications in quantum technologies. In this thesis, we analytically investigate the resources responsible for synchronization in various setups and the generation of these resources via different forms of interactions and drives. We further investigate the connection of coherences and correlations to the synchronization of various systems. We further dive into many examples and counter examples to show that there is no one-to-one correspondence between synchronization and the existence of coherence, correlations, or entanglement. As model examples we study synchronization in infinite dimensional systems with a clear classical analog, like a quantum harmonic oscillator, and in purely quantum mechanical f inite-dimensional spin systems. We use the Lindblad formalism to model self-sustained oscillators with a free phase in continuous variable and discrete variable systems and we use tools from quantum optics like phase space representations and coherent states to quantify synchronization. Our findings show how specific coherences are the deciding factor for synchronization and how their existence still doesn’t guarantee synchronization due to the possibility of destructive interference.