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We develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. Our unified description allows us to identify the resource on which quantum synchronization relies, and to compare quantitatively the synchronization behavior of different limit cycles and signals. We focus on the most elementary quantum system that is able to host a self-sustained oscillation, namely a single spin 1. Despite the spin having no classical analogue, we first show that it can realize the van der Pol limit cycle deep in the quantum regime, which allows us to provide an analytical understanding to recently reported numerical results. Moving on to the equatorial limit cycle, we then reveal the existence of an interference-based quantum synchronization blockade and extend the classical Arnold tongue to a snake-like split tongue. Finally, we derive the maximum synchronization that can be achieved in the spin-1 system, and construct a limit cycle that reaches this fundamental limit asymptotically.
We report the first experimental demonstration of quantum synchronization. This is achieved by performing a digital simulation of a single spin-$1$ limit-cycle oscillator on the quantum computers of the IBM Q System. Applying an external signal to th
Classical optomechanical systems feature self-sustained oscillations, where multiple periodic orbits at different amplitudes coexist. We study how this multistability is realized in the quantum regime, where new dynamical patterns appear because quan
A driven high-Q Si microcavity is known to exhibit limit cycle oscillation originating from carrier-induced and thermo-optic nonlinearities. We propose a novel nanophotonic device to realize synchronized optical limit cycle oscillations with coupled
We study the quantum synchronization between a pair of two-level systems inside two coupled cavities. By using a digital-analog decomposition of the master equation that rules the system dynamics, we show that this approach leads to quantum synchroni
We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode LC resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both