Synchronisation has been explored extensively for classical systems from the mid-1600s, and is a phenomenon widely understood in many diverse systems. In the age of technology miniaturisation, there are great incentives to develop an understanding of quantum synchronisation, where quantum fluctuations become the dominant source of noise and non-classical features become important. This thesis considers different types of synchronisation in systems that can display highly non-linear, quantum behaviours. Phase synchronisation for a micromaser coupled to an external drive is initially considered, and it is found that for low photon numbers a semiclassical approximation underestimates phase synchronisation, but a perturbation theory can be accurate for sufficiently weak coupling in either a quantum or semiclassical regime. When a small detuning between the drive and micromaser is introduced, frequency entrainment is also found to exist. Then two micromasers are coupled with each other, in two different configurations, and synchronisation through a relative phase preference is found for each. A semiclassical approximation once again underestimates the phase synchronisation. Entanglement and mutual information are found to behave differently to the relative phase preference depending on each system's parameters. Finally, a mean-field theory is considered for many coupled van der Pol oscillators and micromasers respectively. As the coupling between the oscillators is increased, a critical point is reached and the systems undergo a transition to a phase synchronised state. This bistability appears via a saddle-node bifurcation, and in addition to examining a variety of properties before and after the transition the critical scaling behaviour was investigated close to the transition.
We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which the system can access for oscillator couplings above a critical value, is characterised not just by a lower phase uncertainty than the corresponding unsynchronised state, but also a higher number uncertainty. Just below the critical coupling the system can evolve to the unsynchronised steady state via a long-lived transient synchronised state. We investigate the way in which this transient state eventually decays and show that the critical scaling of its lifetime is consistent with a simple classical model.
It is essential to establish precise times in future communication networks. Any real-time task's function depends on the system's ability to synchronise time. Time synchronisation is critical in the current communication network and must be maintained to transmit data packets. The functionality of 6G, the Tactile Internet, Time-Sensitive Networking, and ultra-reliable low-latency communications is highly susceptible to time synchronisation. We investigated the idea of employing time synchronisation across different communication network nodes. The current state-of-the-art employs network protocols like Precision-Time Protocol for synchronising clocks across different nodes. These network protocols are not robust and can generate jitters in data transmission. In this paper, we suggested synchronising the time of the node clocks at three different places using quantum technology. Notably, the oscillation frequencies of each qubit (or oscillator) located at these nodes can be synchronised using the quantum synchronisation technique. This set of three oscillators will work as a single clock and will be the master clock of the network. We propose distributing precise time and frequency standards using quantum synchronisation on node clocks. We can synchronise the three qubits (each placed at one node) to oscillate at an identical frequency by applying an external field of a wavelength of
813.32 nm. We analysed our model for different coupling constants and dissipation rates to provide an analysis of the behaviour of the amount of synchronisation in different experimental configurations. The optimal accuracy for our system is
1.6×1015 signals per second. Further, we used the Allan deviation to examine the stability of our system for various noise strengths.