Enhancing quantum phase synchronization through squeezed-reservoir engineering

We investigate the enhancement of quantum phase synchronization in a two-level system (TLS) coupled to a squeezed reservoir. Our study reveals that the squeezed reservoir induces a stable limit cycle in the TLS, enhancing the quantum phase synchronization. We utilize the Husimi Q-function to describe the phase portrait of the driven TLS, and the S-function to quantitatively illustrate the effects of signal strength and detuning on phase synchronization. Remarkably, we demonstrate that the squeezed reservoir imparts its squeezing characteristics to the TLS, leading to a more localized and pronounced synchronization. Additionally, we observe typical features of the Arnold tongue in the synchronization regions. The experimental feasibility of our findings is discussed in the context of a circuit QED system, suggesting that squeezed-reservoir engineering is an effective approach for achieving quantum phase synchronization.