1.Collaborative Innovation Center of Extreme Optics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China 2.Science and Technology on Optical Radiation Laboratory, Beijing 100854, China
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 ($\hat a_{{\rm{i}}, + n\varOmega }^{{\rm{out}}}$) and signal light($\hat a_{{\rm{s}}, + n\varOmega }^{{\rm{out}}}$) is generated by the NOPA whose free spectral range (Ω) 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 $\omega \pm n\varOmega $ (n = 0, 1, 2). The local light of BHD with frequency $\omega \pm n\varOmega $ 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 $\hat a_{\rm{i}}^{{\rm{out}}}$ and $\hat a_{\rm{s}}^{{\rm{out}}}$, the correlation noise of $\hat a_{{\rm{i}}, + \varOmega }^{{\rm{out}}}$ and $\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$, the correlation noise of $\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$ and $\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$, the correlation noise of $\hat a_{{\rm{i}}, + 2\varOmega }^{{\rm{out}}}$ and $\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$ and the correlation noise of $\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$ and $\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$. 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. Keywords:quantum optics/ frequency comb entanglement/ optical parametric amplifier
4.实验结果图3为不同频率梳边带处的关联噪声测量结果随本地光相位变化的归一化噪声功率曲线, 即 图 3 不同频率梳边带处的关联噪声随本地光相位变化的归一化噪声功率曲线(其中蓝线为散粒噪声基准, 绿线为关联噪声谱) (a)$\hat a_{\rm{i}}^{{\rm{out}}}$与$\hat a_{\rm{s}}^{{\rm{out}}}$的关联测量结果; (b)$\hat a_{{\rm{i, }} + \varOmega }^{{\rm{out}}}$与$\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$的关联测量结果; (c)$\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$与$\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$的关联测量结果; (d)$\hat a_{{\rm{i, }} + 2\varOmega }^{{\rm{out}}}$与$\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$的关联测量结果; (e)$\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$与$\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$的关联测量结果; 谱仪的分析频率为3 MHz, 分辨率带宽为300 kHz, 视频带宽为1 kHz Figure3. The correlation noise of sideband frequency combs normalized to the shot noise limit depending on the phase of local oscilla-tor beam (the blue light is shot noise limit, the green light is correlation noise): (a) The correlation noise of $\hat a_{\rm{i}}^{{\rm{out}}}$ and $\hat a_{\rm{s}}^{{\rm{out}}}$; (b) the correlation noise of $\hat a_{{\rm{i, }} + \varOmega }^{{\rm{out}}}$ and $\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$; (c) the correlation noise of $\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$; (d) the correlation noise of $\hat a_{{\rm{i, }} + 2\varOmega }^{{\rm{out}}}$ and $\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$; (e) the correlation noise of $\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$ and $\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$. The analysis frequency of 3 MHz with resolution bandwidth of 300 kHz and video bandwidth of 1 kHz.