In recent years, more and more researchers have paid attention to the hyperentanglement, because it plays a very important role in the quantum information and quantum communication. Continuous-variable hyperentangled state with orbital angular momentum and spin angular momentum has a promising application in the parallel processing of continuous-variable multi-channel quantum information and multiparameters quantum metrology. Recently Liu et al. (2014 <i>Phys. Rev. Lett.</i> <b>113</b> 170501) have produced a quantum correlation of about 1.00 dB for the continuous-variable hyperentangled state by a type-II non-degenerate optical parametric amplifier. The generation of continuous-variable hyperentangled state is affected by the mode matching between the pump field and the down-conversion field, since the hyperentanglement contains spatial high-order transverse mode entanglement. In the present paper, we first theoretically analyze the relationship between the pump and the two down-conversion modes and demonstrate the dependence of the inseparability on normalized pump power for the different pump modes. Hence, we find that the optimal pump mode is the superposition of <inline-formula><tex-math id="M3000">\begin{document}${\rm{LG}}_0^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3000.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3000.png"/></alternatives></inline-formula> mode and <inline-formula><tex-math id="M3001">\begin{document}${\rm{LG}}_1^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3001.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3001.png"/></alternatives></inline-formula> mode. However, the optimal pump mode is rather complicated and difficult to experimentally generate, in the alternative scheme the <inline-formula><tex-math id="M3002">\begin{document}${\rm{LG}}_1^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3002.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3002.png"/></alternatives></inline-formula> mode is used as the pump field to obtain the optimal entanglement. In the experiment, the <inline-formula><tex-math id="M3003">\begin{document}${\rm{LG}}_1^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3003.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3003.png"/></alternatives></inline-formula> mode is produced by converting the HG<sub>11</sub> mode with a π/2 converter, and here the HG<sub>11</sub> mode is achieved by tailoring the fundamental mode with a four-quadrant phase mask and a filtering cavity. Then the <inline-formula><tex-math id="M304">\begin{document}${\rm{LG}}_0^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M304.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M304.png"/></alternatives></inline-formula> mode or <inline-formula><tex-math id="M3005">\begin{document}${\rm{LG}}_1^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3005.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3005.png"/></alternatives></inline-formula> mode is used as the pump field to drive the non-degenerate optical parametric amplifier operating in spatial multimode. When the non-degenerate optical parametric amplifier is operated in the de-amplification, the hyperentanglement with orbital angular momentum and spin angular momentum is produced. The output entangled beams pass through polarization beam splitter and are analyzed by using the balanced homodyne detection systems with the local oscillator operating in the HG<sub>01</sub> and HG<sub>10</sub>. The noise of the phase quadrature or the amplitude quadrature is obtained, when the relative phase between the local oscillator and the signal beam is locked to π/2 or 0. Then the quantum correlations of orbital angular momentum and spin angular momentum can be deduced. The experimental results show that the continuous-variable hyperentanglement of light with a quantum correlation of (4.00 ± 0.02) dB is produced. Compared with the results of Liu et al. obtained by using the <inline-formula><tex-math id="M3006">\begin{document}${\rm{LG}}_0^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3006.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3006.png"/></alternatives></inline-formula> mode, the inseparability of orbital angular momentum and spin angular momentum entanglement are enhanced by approximately 96.2% and 96.3%, respectively, through using the <inline-formula><tex-math id="M3007">\begin{document}${\rm{LG}}_1^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3007.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20181625-e-zhengbs-revised_M3007.png"/></alternatives></inline-formula> mode. Such a continuous-variable hyperentanglement may have promising applications in high-dimensional quantum information and multi-dimensional quantum measurement, and this approach is potentially extended to a discrete variable domain.
Squeezed states, which have fewer fluctuations in one quadrature than vacuum noise at the expense of increasing fluctuations in the other quadrature, can be used to enhance measurement accuracy, increase detection sensitivity, and improve fault tolerance performance for quantum information and quantum computation. In this paper, the influences of relative intensity noise (RIN) of all-solid-state single-frequency laser and single-frequency fiber laser on the squeezing factor of squeezed vacuum states are experimentally and theoretically studied. Here, an all-solid-state single-frequency laser and a single-frequency fiber laser each are used as a light source of the system generating squeezed vacuum states. The homodyne detection is used to compare the RIN of all-solid-state single-frequency laser and that of single-frequency fiber laser at the analysis frequency of 1 MHz. The results show that the RIN of the all-solid-state single-frequency laser and single-frequency fiber laser are higher than those of the shot noise limitation 2.3 dB and 30 dB at the analysis frequency of 1 MHz, respectively. The RIN of all-solid-state single-frequency laser is far less than that of the single-frequency fiber laser. As a result, squeezed vacuum state with maximum quantum noise reduction of (13.2 ± 0.2) dB and (10 ± 0.2) dB are directly detected. Theoretical calculation shows that the influence of the RIN on the measurement accuracy is the major factor of degrading the squeezing factor with the fiber laser as the pump source. The measurement error of squeezed vacuum state caused by the RIN of single-frequency fiber laser is about 2.6 dB. The discrepancy of the pump power between the two lasers is another factor of affecting the squeezing factor, corresponding to 0.6 dB quantum noise difference. The theoretical calculations are consistent with the experimental results, which provides some guidance for developing the practical squeezed states with highly squeezing level.
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