Exploring quantum synchronization with a composite two-qubit oscillator

Synchronization has recently been explored deep in the quantum regime with elementary few-level quantum oscillators such as qudits and weakly pumped quantum van der Pol oscillators. To engineer more complex quantum synchronizing systems, it is practically relevant to study composite oscillators built from basic quantum units that are commonly available and offer high controllability. Here we consider a minimal model for a composite oscillator consisting of two interacting qubits coupled to separate baths and show that this system exhibits a wide variety of synchronizing behaviors. We study the phase response of the constituent qubits as well as the system as a whole, when one of the qubits is weakly driven. We consider the thermal baths to have positive as well as effective negative temperatures and discover effects that occur only when the temperatures of the baths for the two qubits are of opposite signs. We propose and analyze a circuit quantum electrodynamics implementation of this model, which exploits recent advances in dissipation engineering to realize effective negative temperature baths. Our work demonstrates the potential for assembling complex quantum synchronizing systems from basic building units, which is of pragmatic importance for advancing the field of quantum synchronization.