Quantum squeezing effects in coupled van der Pol oscillators

The article investigates the synchronization phenomena in coupled van der Pol oscillators, focusing on the transformative impact of quantum squeezing. It begins by discussing the fundamental concept of synchronization, where oscillating systems adjust their rhythms to become harmonized. The study then delves into the challenges faced in observing genuine quantum phenomena due to high excitation levels in experimental setups involving micromechanical and nanomechanical resonators. Recent advancements have introduced novel approaches for self-sustained oscillators to operate deeply within the quantum realm, where quantum fluctuations become more evident. The introduction of a squeezing Hamiltonian is shown to counteract the detrimental influence of noise, unlocking the prospect of witnessing quantum synchronization. The article explores how squeezing improves synchronization, steady-state power spectrum, and nonclassical traits such as enhanced quantum correlations and reduced decoherence effects. It provides a detailed analysis of reactively and dissipatively coupled van der Pol oscillators, demonstrating the effects of squeezing and coupling parameters on frequency entrainment and synchronization. Experimental setups using trapped ions and optomechanical systems are presented, offering practical methods for realizing the discussed phenomena. The study concludes by highlighting the potential applications of stronger synchronization in quantum optics, particularly in generating entangled photon pairs with improved temporal correlations for quantum information processing and communication protocols.