As a novel hybrid quantum system, cavity optomechanical system shows super strong coupling strength, extremely low noise level and considerable coherent time under superconducting condition. In this paper, we briefly introduce basic principles of cavity optomechanics and cavity optomechanical systems. Meanwhile, we also classify the widely studied cavity optomechanical systems as five categories in their materials and structures. Significant parameters of these optomechanical systems, such as quality factor, mass and vibrating frequency of mechanical oscillator, are listed in detail. Technical merits and defects of these optomechanical systems are summarized. Furthermore, we introduce the research progress of non-classical microwave quantum states preparation by utilizing generalized cavity optomechanical systems, and we also analyze the performance advancements and remaining problems of this preparation method. In the end, we summarize the application cases at present and look forward to the potential application scenarios in the future. Our summary may be helpful for researchers who are focusing on quantum applications in sensing, radar, navigation, and communication in microwave domain.

We study tunable double-channel microwave-optical (M-O) entanglement and coherent conversion by controlling the quantum interference effect. This is realized in a two-mechanical-mode electro-opto-mechanical (EOM) system, in which two mechanical resonators (MRs) are coupled with each other by phase-dependent phonon-phonon interaction, and link the interaction between the microwave and optical cavity. It’s demonstrated that the mechanical coupling between two MRs leads to the interference of two pathways of electro-opto-mechanical interaction, which can generate the tunable double-channel phenomena in comparison with a typical three-mode EOM system. In particular, by tuning of phonon-phonon interaction and couplings between cavities with MRs, we can not only steer the switch from the M-O interaction with a single channel to that of the double-channel, but also modulate the entanglement and conversion characteristics in each channel. Moreover, our scheme can be extended to an N-mechanical-mode EOM system, in which N discrete channels will be observed and controlled. This study opens up prospects for quantum information transduction and storage with a wide bandwidth and multichannel quantum interface.

As a widely utilized information carrier, polarization microwave shows plenty of merits. Quantum microwave is booming gradually due to the development of superconducting technology, which makes it a promising potential to apply quantum entanglement to polarization microwave. In this paper, we introduce the concept of continuous variable polarization entanglement. Meanwhile, a scheme of polarization entanglement in microwave domain is proposed and simulated. The detail derivations are given and discussed. Polarization entangled microwaves are prepared by combining quadrature entangled signals and strong coherent signals on polarization beam splitters, and quadrature entangled signals are prepared by utilizing Josephson mixer. In order to probe the polarization entanglement between output signals, inseparability of Stokes vectors \begin{document}$I({\hat S_1},{\hat S_2})$\end{document} and \begin{document}$I({\hat S_2},{\hat S_3})$\end{document}, is analyzed in 100 MHz operation bandwidth of Josephson mixer. The relation between inseparability I and squeezing degree r and between inseparability I and amplitude ratio Q are analyzed respectively. The results show that \begin{document}$I({\hat S_1},{\hat S_2})$\end{document} is sensitive to the variation of Q, while \begin{document}$I({\hat S_2},{\hat S_3})$\end{document} is sensitive to the change of r. The physical reasons for these results are explored and discussed. Apart from these, \begin{document}$I({\hat S_1},{\hat S_2})$\end{document} remains its value above 1 under the condition in this paper, but on the contrary, \begin{document}$I({\hat S_2},{\hat S_3})$\end{document} keeps its value well below 1. It proves that \begin{document}${\hat S_2}$\end{document} and \begin{document}${\hat S_3}$\end{document} of Stokes vectors are inseparable from each other, thus output signals \begin{document}${\hat E_a}$\end{document} and \begin{document}${\hat E_b}$\end{document} of our scheme exhibit bipartite entanglement. The best entanglement appears nearly at about 70 MHz, at this point the minimum \begin{document}$I({\hat S_2},{\hat S_3})$\end{document} value is 0.25.

In order to transfer two-mode quantum state from optical input to microwave output, we propose a scheme based on double cavity electro-opto-mechanical converters. Principles and operation modes of cavity electro-opto-mechanical converter are introduced in detail, and theoretical model of transferring Einstein-Podolsky-Rosen state via our scheme is built. The dynamics and corresponding scattering matrixes of our scheme are analyzed carefully. Meanwhile, Ulhmann fidelity is utilized to quantify the similarity of initial state and final state, which also stands for the performance of our scheme. Influences of coupling rates and optical input bandwidth on fidelity are well discussed, and some significant factors are also taken into consideration, such as transmission spectrum, interaction rates and decoherence rates. Furthermore, Wigner distributions of initial state and final state as well as the von Neumann entropy are obtained to verify the performance of our scheme. The results show that our scheme could transfer the Einstein-Podolsky-Rosen state from optical input to microwave output with high fidelity (0.74), and the entropy ratio between initial and final states is about 0.78, which is quite close with the fidelity. Besides, Wigner distributions also show that initial state and final state are slightly different in phase structures. In case of strong coupling rates, ultralow temperature and narrow input bandwidth, the performance of our scheme could be further enhanced.