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Additional file 4. Supplemental Figure 3.

Additional file 3. Supplemental Figure 2.

Additional file 5. Supplemental Figure 4.

Additional file 2. Supplemental Figure 1.

Additional file 1. Supplemental Digital Content.

Generation and manipulation of continuous variable quantum states are the building blocks of quantum communication, quantum key distribution and quantum networks. According to the second-order nonlinear process of the periodically-poled potassium titanyl phosphate (PPKTP) crystal, we design a semi-monolithic optical parametric amplifier (OPA) cavity to generate the bright squeezed light at a wavelength of 1064 nm. With the injection of a seed beam, the squeezed state generated by the OPA has a coherent amplitude, so called bright squeezed state. The squeezing level is directly observed to be –11.6 dB when the pump power is 310 mW at an analysis frequency of 3 MHz. However, with the increase of the pump power, the purity of the squeezed state gets lower and lower due to the increased influence of the anti-squeezing quadrature component on the squeezed quadrature component in the detection process. To obtain a higher purity of the squeezed state for achieving linear optical manipulation and quantum tomography, we choose the pump power of 50 mW, the squeezing level decreases to –6 dB, and the purity of the squeezed state is 98.5% in this case. An electro-optic modulator is adopted to realize the liner manipulation of the squeezed light in the phase space. During the measurement of the bright squeezed state, all the data are taken on condition that the length of the OPA cavity and relative phase between the seed beam and the pump beam are locked by a locking loop. The direct current (DC) signal of the balanced homodyne detection (BHD) is used to accurately determine the phase corresponding to the time domain signal of the squeezed state, while the alternate current (AC) signal of the BHD is mixed with the signal generated by the function generator, after passing through a low-pass filter and a high-pass filter, the signal is then amplified by using a low-noise amplifier. A high-performance oscilloscope is finally used to simultaneously collect the signals, thus obtaining the quantum noise signal of the bright squeezed light after linear manipulation. Together with the maximum likelihood estimation algorithm, the quantum tomography, the density matrix and the Wigner function of the bright squeezed light are obtained, that is, all the information such as the photon number distribution of the quantum state is determined. Multiple iterations are taken in the maximum likelihood estimation algorithm process to eliminate the influence of the low quantum efficiency on the detection system, so that the density matrix is fitted well with the theoretical results.

Second harmonic generation (SHG) is used to get continuous wave laser with a lot of applications, it is a major way to provide pump power for generating nonclassical states, especially for squeezed states and entanglement states. High-efficiency SHG resonant on atoms lines also provides laser sources for atomic entanglement generation, light-atom interaction and high-speed quantum memory. For the frequency-doubling process at 426 nm, the major challenge of increasing the conversion efficiency is the thermal effect caused by the absorption in crystal. The degradation of mode-match efficiency induced by the severely thermal effect limits the conversion efficiency of the second harmonic generator. Furthermore, the blue light induced infrared absorption (BLIIRA) in the nonlinear crystal intensifies the thermal effect, it makes the conversion efficiency of the frequency-doubling cavity and the stability of the output blue laser worse, and it is more serious at high input power. Based on the theoretical analysis of thermal lens, we find that the thermal lens should not be placed at the center of the crystal, the location of the equivalently thermals lens has a deviation from the center of the crystal. Follow the theoretical analysis of thermal lens, we design a ring cavity with a 10 mm-long periodically poled potassium titanyle phosphate (PPKTP) crystal to reduce the thermal lens effect induced mode-mismatch. The location of nonlinear crystal is adjusted precisely to reduce the mode-mismatch caused by the thermal lens under our theoretical analysis. Finally, we realized a high conversion efficiency blue laser at 426 nm with the conversion efficiency up to 83.1% with an output power of 428 mW after the adjustment of the crystal location, corresponding to our theoretical analysis well. The measured beam quality factors (M2 value) of the generated blue laser are \begin{document}$ M^2(x) = 1.05 $\end{document} and \begin{document}$ M^2(y) = 1.02 $\end{document}, respectively. The measured power stability of Generated Blue laser in 15 mins is 1.25%. The output power of the SHG is strong enough to provide pump power for the generation of the continuous variable squeezed vacuum state at 852 nm and the long-term stability of the output blue laser is also measured to be fine. To the best of our knowledge, the conversion efficiency is the highest-reported one at this wavelength. We believe that such high-performance frequency doubling system is a fundamental building block for quantum information science based non-classical states.