A phase locking scheme of two-mode squeezed microwave preparation

Abstract

As the core of quantum entanglement, two-mode squeezing is manifested in cross-correlations of incompatible observables between two subsystems, which makes the two-mode squeezed microwave an ideal resource for applications in quantum communication, quantum illumination, and quantum microwave navigation. Currently the preparation scheme of two-mode squeezed microwave, based on the Josephson parametric amplifier (JPA) and a superconducting 180° hybrid ring coupler, proves to be the most efficient and excellent in quantum properties. Nevertheless, the difficult phase locking processing restricts the further improvement of entanglement. There is no effective solution but the dual-path receiver with phase stabilization measures, and the phase error reaches as high as 0.3°, which still does not meet the requirements for phase locking precision and entanglement stability. To overcome the academic obstacle, we propose a phase locking scheme to achieve a stable two-mode squeezed microwave. There are two JPAs used to separately generate single-mode squeezed microwaves, between which the difference lies in the fact that the input of one JPA is phase-modulated but the other is not. A superconducting 180° hybrid ring coupler is used to distribute the two single-mode squeezed microwaves into two output paths, which are two-mode squeezing if the squeezing directions of the two single-mode squeezed microwave are orthogonal. That is to say, the relative phase satisfies the condition <inline-formula><tex-math id="M65">\begin{document}$\theta = {\text{π}}/2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20191348_M65.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20191348_M65.png"/></alternatives></inline-formula>. By mixing the unmodulated single-mode squeezed microwave and one output of the superconducting 180° hybrid ring coupler, a relative phase is obtained in subsequent process. Proportional integral derivative (PID) controller is used as the input of phase error, and the output is used to adjust the pump phase of JPA, which is the key to phase locking and stable two-mode squeezing. The present research not only provides an effective strategy to achieve stable two-mode squeezed microwave, but also may attract more attention to the precisive measurement of two-mode squeezed microwave.