# Utilizing Sequential Control Scheme to Stabilize Squeezed Vacuum States
## 2 Experimental Setup  
The schematic of our experimental setup is shown in Figure 1. We used a home-made single-frequency Nd:YVO\({}_{4}\) laser at 1064 nm as the laser source. A Faraday isolator (FI) was inserted between the laser and OPO to reduce the backscatter disturbance. Three mode cleaners (MC) were used not only to provide spatial-temporal filtering and polarization purifying for the downstream experiment, but also as an auxiliary cavity for high-efficiency mode-matching. The majority of the laser power was frequency doubled in a second harmonic generator (SHG) to produce a pump beam of up to 600 mW for the parametric downconversion processes. We actually used a 90:10 beamsplitter to split a fraction of the laser to use as the local beam. A half wave plate and a polarization beamsplitter (not shown in the figure) were also used to adjust the power of the local beam. Our OPO was a semi-monolithic cavity consisting of a piezo-actuated concave mirror and a periodically poled potassium titanyl phosphate (PPKTP) crystal with dimensions of 1 mm \(\times\) 2 mm \(\times\) 10 mm. The crystal end face with a curvature radius of 12 mm was coated for high-reflection (HR) for the fundamental beam and high-transmission (HT) for the pump beam, thus serving as one of the cavity mirrors. The plane front face of the crystal was coated for antireflection (AR) for both wavelengths. An air gap of 26 mm existed between the AR-coated side of the crystal and the coupling mirror. The concave mirror with a radius of curvature of 30 mm had a transmissivity of 12% for 1064 nm and HR for 532 nm, and it was used as the output coupler. The squeezed vacuum states interfered with an local oscillator (LO) on a 50:50 beamsplitter. The output beam from the 50:50 beamsplitter was directed towards a balanced homodyne detector (BHD) to detect the noise level. In our setup, the optical path was as short as possible, aiming to minimize the phase drift over the experiment, and the distance between OPO (1064 MC2) and the 50:50 beamsplitter was about 10 (16) cm. The squeezed light emitting from the concave mirror was separated from the pump light by a dichroic beamsplitter and directed towards a BHD to detect the noise level. The BHD, with a common mode rejection ratio of 75 dB [42; 43; 44], was built from a pair of p-i-n semiconductor structure (PIN) photodiodes (Laser Components, Germany) with a quantum efficiency of more than 99%. The phase modulation signal, having a frequency of 35.6 MHz, was imprinted on the locking beam to generate error signals for all three control loops [45; 46]: the error signal for stabilizing the OPA cavity length on resonance was demodulated from the output of the photodetector PD3; the error signal of locking the relative phase between the pump and the signal beams was obtained from the photodetector PD2 placed at the reflected end of the OPA, and the relative phase between the LO beam and signal beam was locked by demodulating the output signal of the homodyne detector and feeding back to the piezoelectric transducer PZT2 on the optical path of the LO beam. When the lock power  
Figure 1: Schematic of the experimental setup. The seed beam was switched on/off by two AOMs manipulated by an FPGA. Laser:single-frequency Nd:YVO\({}_{4}\) laser; EOM, electro-optic modulator; AOM, acousto-optic modulator; FI, Faraday isolator; MC, mode cleaner; SHG, second harmonic generator; OPO, optical parametric oscillator; OPA, optical parametric amplifier; DBS, dichroic beamsplitter; BS, beamsplitter; PBS, polarization beamsplitter; PZT1-2, piezoelectric transducer; PD1-3, photodetector; BHD, balanced homodyne detector. was less than 15 mW, the amplitude of the error signal was insufficient to obtain a stable locking for the OPA cavity and relative phase. It is worth mentioning that two acousto-optic modulators (AOMs), which were driven at the same frequency, were inserted before the OPO in our experimental setup to switch on/off the locking beam.