Generation of continuous variable frequency comb entanglement based on nondegenerate optical parametric amplifier

Abstract

Continuous variable (CV) quantum squeezed state and entangled state are important quantum resources, which have been widely used in quantum communication, quantum metrology and quantum computation. In recent years, people have paid much attention to the multi-mode optical parametric amplifier (OPO) process because the multi-mode non-classical light field is able to construct the multiplexing quantum information system for improving the working efficiency and channel capacity. As a special multi-mode optical field, optical frequency comb has been used in optical frequency measurement, atomic spectroscopy and frequency-division multiplex-based communication. Especially, there are a number of notable researches where quantum frequency combs are used, which exhibit multimode-entangled photon states. The quantum frequency combs provide a promising platform for quantum information technology based on time-bin-encoded qubits. In this paper, the entanglement characteristics of frequency comb in type II nondegenerate optical parametric amplifier (NOPA) below threshold are investigated experimentally. The bipartite entanglement with frequency comb structure between idle light (<inline-formula><tex-math id="M1">\begin{document}$\hat a_{{\rm{i}}, + n\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M1.png"/></alternatives></inline-formula>) and signal light(<inline-formula><tex-math id="M2">\begin{document}$\hat a_{{\rm{s}}, + n\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M2.png"/></alternatives></inline-formula>) is generated by the NOPA whose free spectral range (<i>Ω</i>) is 1.99 GHz operated in the de-amplification state and then analyzed by dual balanced homodyne detection system (BHD) with different values of frequency <inline-formula><tex-math id="M3">\begin{document}$\omega \pm n\varOmega $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M3.png"/></alternatives></inline-formula> (<i>n </i>= 0, 1, 2). The local light of BHD with frequency <inline-formula><tex-math id="M4">\begin{document}$\omega \pm n\varOmega $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M4.png"/></alternatives></inline-formula> is generated by the fiber intensity modulator and tailored by the mode cleaner. Here, we measure the correlation noise of side and frequency combs normalized to the shot noise limit relating to the phase of local oscillator beam, and we show the correlation noise of <inline-formula><tex-math id="M5">\begin{document}$\hat a_{\rm{i}}^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$\hat a_{\rm{s}}^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M6.png"/></alternatives></inline-formula>, the correlation noise of <inline-formula><tex-math id="M7">\begin{document}$\hat a_{{\rm{i}}, + \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M7.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M8.png"/></alternatives></inline-formula>, the correlation noise of <inline-formula><tex-math id="M9">\begin{document}$\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M9.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M10">\begin{document}$\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M10.png"/></alternatives></inline-formula>, the correlation noise of <inline-formula><tex-math id="M11">\begin{document}$\hat a_{{\rm{i}}, + 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M11.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M12">\begin{document}$\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M12.png"/></alternatives></inline-formula> and the correlation noise of <inline-formula><tex-math id="M13">\begin{document}$\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M13.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M14">\begin{document}$\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200107_M14.png"/></alternatives></inline-formula>. The experimental results show that the five pairs of entangled states with 4.5 dB entanglement are simultaneously produced by a type II OPO. Next, we can redesign NOPA to reduce its free spectral range and intracavity loss, and prepare local light with a high-order sideband frequency by fiber modulators with high bandwidth, it promises to obtain huge multiple bipartite entangled states. As a kind of extensible quantum information system, the frequency comb CV entanglement can be used to provide a necessary light source for realizing the experiment of frequency division multiplexing multi-channel teleportation, which lays a foundation for the future large-capacity quantum communication and network.