## 4 Results
In addition, the linearity of the BHD system was checked by measuring the SNL versus the total power of the LO, as shown in Figure 6. With the power of the LO doubly increasing, a clearance of 3 dB at analysis frequencies from 3.5 kHz to 20 kHz could be obtained from the total power of from 250 \(\mu\)W to 2 mW. The results show that the photodetector has linear response property in the given power range, and a larger clearance to mitigate the influence of dark noise. The total power of the LO of 1 mW was chosen for measuring the generated squeezed vacuum states because it could offer an electronic noise clearance of more than 20 dB at audio-band frequencies. In this case, the influence on measurement from the electronic noise could be ignored. Increasing the total power of the LO, it is possible that the extra noise of the LO would contaminate the observed squeezing level. Figure 5: Measured noise power from unbalanced detector and balanced detectors as a function of analysis frequencies: Curve (i), detector unbalanced; and Curve (ii), detectors balanced. The CMRR of photodetectors in the BHD system was determined by the difference of noise power from balanced detectors and that from unbalanced detector. The inset is the measurement for the CMRR of photodetectors at the analysis frequency of 5 kHz. Figure 6: Linearity and clearance of photodetectors in the BHD system: Curve (i), the ENL; and Curves (ii)–(v), the SNL versus the total power of the LO (250 \(\mu\)W, 500 \(\mu\)W, 1 mW and 2 mW). The measured threshold power of the OPO was 350 mW in the experiment. When the pump with the power of 100 mW and the CCF with the power of 100 \(\upmu\)W were injected into the OPO, the OPO was operated below the threshold. The generated squeezed vacuum states were measured using the BHD system with the LO power of 1 mW and the fringe visibility of 99%. In the measurement of squeezed vacuum states at audio-band frequencies, the noise power traces also need to be averaged for some times to obtain the accurate result, thus requiring the experimental setups involved to be stable at the timescale of several tens of minutes [22]. When the relative phase between the squeezed vacuum states and LO was locked to \(\pi\)/2 and the relative phase between the pump and CCF was fixed to 0, the generated phase squeezed vacuum states could be measured stably. Figure 7 shows the measured noise power of phase squeezed vacuum states at analysis frequencies from 3.5 kHz to 20 kHz recorded by SA with an RBW of 50 Hz, a VBW of 100 Hz and the sweep time of 1 s. All noise power traces were averaged 20 times. Curves (i)-(iv) are the SNL, the squeezing noise, the anti-squeezing noise and the ENL, respectively. The measured squeezing degree of phase squeezed vacuum states at audio-band frequencies from 5 kHz to 20 kHz was approximately 6.1 \(\pm\) 0.3 dB. The corresponding anti-squeezing was 10.1 \(\pm\) 0.3 dB. A 3.0 \(\pm\) 0.3 dB phase squeezed vacuum state was obtained at the audio frequency of 3.5 kHz. Considering the total detection losses of \(\eta_{\text{esc}}\) = 0.95, \(\eta_{\text{det}}\) = 0.96, \(\eta_{\text{prop}}\) = 0.94, and \(\eta_{\text{hom}}\) = 0.98, the theoretical calculated squeezing level is 6.25 dB, which is not dependent on the CMRR of the detectors. The theoretical prediction has a discrepancy with experimental results, a possible reason being that the anti-squeezed quadrature contaminates the measured squeezing level due to the phase jitter. Owing to the coherent locking scheme, the actual phase jitter was only about 1.7\({}^{\circ}\), which was calculated according to the discrepancy between the theoretical prediction and experimental results. The measured squeezing level has a sharp reduction below around 4.5 kHz. The possible reason is squeezed variance spectra at these frequencies were contaminated by additional noise from scattered fields [23]. They were identified to originate from the micro-roughness of the optical surfaces, non-perfect anti-reflection coatings and residual transmissions of high reflection mirrors.