Entanglement signatures for quantum synchronization with single-ion phonon laser.

The entanglement properties of quantum synchronization, based on a single-ion phonon laser subjected to an external drive, have been studied. It is found that the maximum value of steady-state entanglement between the ion's internal and external states occurs near the noiseless boundary from synchronization to unsynchronization, accompanied by noticeable oscillatory behaviors during the corresponding time evolution of entanglement. In addition, the later time dynamics of entanglement also indicates the occurrence of frequency entrainment, as evidenced by the strong consistency between the bending of the observed frequency and the emergence of Liouvillian exceptional points (LEPs) in the first two eigenvalues of the Liouvillian eigenspectrum. Moreover, the emergence of LEPs, which is intimately associated with frequency entrainment, should be widely observed in quantum synchronization and can be explored in LEPs-based applications.

Entanglement optimization of filtered output fields in cavity optomechanics.

Output entanglement is a key element in quantum information processing. Here, we show how to obtain optimal entanglement between two filtered output fields in a three-mode optomechanical system. First, we obtain the key analytical expression of optimal time delay between the two filtered output fields, from which we can obtain the optimal coupling for output entanglement without time delay. In this case, our linearized analysis predicts that the entanglement saturates to an optimal value as the optomechanical coupling is increased. Furthermore, we obtain the optimal output entanglement with time delay. These results should be very helpful in conceiving new optomechanical schemes of quantum information processing with their efficiency depending critically on the degree of output entanglement.