## 3 Experimental Setup  
The schematic of the experimental setup used to generate squeezing vacuum states is shown in Figure 2. The laser source was a homemade low noise cw single-frequency dual-wavelength laser with output power of 7 watts at 532 nm and 3 watts at 1064 nm. Optical isolators (OIs) were used to eliminate the back-reflection light of the infrared and green laser. The longitudinal mode of the laser was monitored by a scanning Fabry-Perot (F-P1) interferometer. A small part of the infrared laser was injected into the F-P2, which was used as a frequency standard to lock the frequency of the laser. The frequency shift was less than \(\pm 1.5\) MHz for a given 1 h when the laser was frequency stabilized employing the Pound-Drever-Hall (PDH) technique [21]. The main part of the infrared laser and the green laser were sent through a ring mode cleaner (MC1) cavity with a finesse of 300 and a linewidth of 1.0 MHz and MC2 with a finesse of 270 and a linewidth of 1.1 MHz, respectively, for filtering the laser spatial mode and excess intensity noise. The two MCs were locked by the PDH technique. The power transmittances of the two MCs were approximately 78%. Using the MCs, the intensity noises of the infrared and green laser reached the SNL for analysis frequencies higher than 1.8 MHz. The infrared output from MC1 was divided into three parts and used as the LO beam for the BHD system, the auxiliary beam to lock the length of the subthreshold OPO cavity and the coherent control field (CCF) to control the relative phase between the LO and squeezed vacuum states, separately. The green output from MC2 acted as the pump of the OPO. Figure 1: Dependence of normalized noise power of squeezed vacuum states at the analysis frequency of 5 kHz on the \(R_{CMRR}\), the phase jitter and \(V_{LO}\): Curves (i) and (a), \(G=1\), \(V_{LO}=0\) dB with \(\delta\varphi=0^{\circ}\) and \(2^{\circ}\), respectively; Curves (ii)–(iv) and (b)–(d), \(G\
eq 1\) and \(V_{LO}\) exceeds the SNL 0 dB, 35 dB and 50 dB with \(\delta\varphi=0^{\circ}\) and \(2^{\circ}\), respectively. The OPO was a semi-monolithic cavity composed of a PPKTP crystal with dimensions of 10 mm (length) \(\times\) 2 mm (width) \(\times\) 1 mm (thickness) and a concave mirror with a radius of 25 mm. The concave face of concave mirror acted as input and output couplers was partial transmission coated at 1064 nm and 532 nm (\(T_{1064\,\text{nm}}\) = 13% and \(T_{532\,\text{nm}}\) = 80%). The flat face of concave mirror was antireflection (AR) coated at 1064 nm and 532 nm (\(R_{1064\text{ and }532\text{nm}}\) < 0.2%). One end of the PPKTP crystal was convex surface with a radius of 12 mm and HR coated at 1064 nm and 532 nm (\(R_{1064\text{ and }532\text{nm}}\) > 99.9%). Another end of the PPKTP crystal was flat surface and AR coated at 1064 nm and 532 nm (\(R_{1064\text{ and }532\text{nm}}\) < 0.2%). The concave mirror was mounted on a piezo-electric transducer (PZT1) to control the length of OPO cavity. The PPKTP crystal was housed in a copper oven and temperature-controlled by a homemade temperature controller with an accuracy of 0.01 \({}^{\circ}\)C. The temperature of PPKTP was controlled at 40.0 \({}^{\circ}\)C to realize the optimum phase matching. The optical cavity length of the OPO was 33 mm and the measured linewidth was 102 MHz. PPKTP is a type-I phase matched crystal. The \(s\)-polarized squeezed vacuum states from the subthreshold OPO was generated when pump power of green laser was below the threshold of OPO, which was separated from the residual pump field by a dichroic beam splitter (DBS). The generated squeezed vacuum states were measured using the BHD system and recorded by a spectrum analyzer (SA). The auxiliary beam was generated by frequency shifting 1064 nm laser using a fiber-coupled electro-optical modulator (FCEOM), which was driven by a sinusoidal signal. The \(p\)-polarized auxiliary beam was injected into the OPO cavity.