Synchronisation in coupled quantum systems

Abstract

The synchronisation of oscillators is a universal phenomenon which is seen everywhere in the world around us, where objects spontaneously start oscillating in phase, in anti-phase or with an arbitrary phase difference. Synchronisation is thus an example of complex behaviour emerging from the interaction between relatively simple systems. The simplest and most well-known example is a system consisting of two coupled pendulums known as Huygens's pendulums. As early as 1655, Huygens noted that two identical pendulum clocks suspended on a beam will end up in a state of anti-phase synchronisation swinging in exactly opposite directions. If we were to consider a system consisting of two oscillators, they would need to be very similar for synchronisation to occur. A quantitative relation exists that shows that the more dissimilar the oscillators are, the stronger the connection between them must be for synchronisation to happen. This is commonly shown through what is known as Arnold Tongue, which defines a region in parameter space where synchronisation occurs.