# Utilizing Sequential Control Scheme to Stabilize Squeezed Vacuum States
## 4 Experimental Process and Results  
The threshold power of our OPO was 160 mW. First, we measured the squeezing strength of squeezed vacuum states without the locking beam by manually applying offset voltage to the piezo, which was attached to the output mirror of the OPO. The best squeezing factor, recorded by a spectrum analyzer (FSW8 with 0.2 dB uncertainty, Rohde & Schwarz, Germany) was 11.6 dB at the analysis frequency of 2 MHz. The total LO power before the beamsplitter was 5.5 mW, corresponding to the dark noise clearance of 28 dB [49]. Subsequently, we repeated the above measurement with the locking beam power of 50 mW, corresponding to the quantum noise reduction of 10 dB. While the above data were collected, no experimental parameters other than the locking beam being injected were varied. The squeezing factor degradation originated from the noise coupling between the pump and locking beams. Then, we performed the above measurements again with the sequential control scheme. The measured results are shown in Figure 4; the discontinuity along the time axis corresponds to the switchover point from carry mode to ready mode. Trace (a) corresponds to the shot-noise limit of 5.5 mW LO power. Trace (b) and trace (c) are, respectively, the squeezing and anti-squeezing factors at the pump power of 125 mW. Trace (d) is the measured noise level with the LO phase scanned. The generation of squeezed vacuum states corresponds to carry mode; the squeezing factor was 11.6 dB. Moreover, a bright squeezed state was generated in ready mode with the squeezing factor of 10 dB. These results are in good agreement with those without the sequential control scheme. The cycle time and duty ratio of the time sequence were 2 s and 50%, respectively. Carry mode lasted for 1 s, and the ready process also lasted for 1 s. The squeezing factor in carry mode was independent of the locking beam and without the need for manual control. Therefore, the sequential control scheme opens up a new path of manipulating squeezed vacuum states based on the idea of time-division multiplexing. Figure 3: Time sequence of the experimental cycle. SA, spectrum analyzer. We repeated the above experimental process at a Fourier frequency of 500 kHz. First, we independently measured the quadrature noise variances of the squeezed vacuum state and bright squeezed state. The squeezing factor of the squeezed vacuum states was 10.4 dB, while the squeezing strength disappeared for the bright squeezed state. Then, we continuously measured the quadrature noise variances by utilizing the sequential control scheme, which is shown in Figure 5. Trace (a) corresponds to the shot-noise limit of 5.5 mW LO power and was measured with the squeezed light blocked. Trace (b) and trace (c) are the squeezing and anti-squeezing factors with the LO phase locked at the pump power of 125 mW. Trace (d) is a noise level with the LO phase scanned. It is worth noting that the squeezing factor reduced to 0 dB with the locking beam at the analysis frequency of 500 kHz, which can be attributed to the increase of laser intensity noise with the decrease of analysis frequency. The results further demonstrate the significance of the sequential control scheme, especially for squeezed state generation below the MHz range. Figure 4: Balance homodyne measurements of the quadrature noise variances with the sequential control scheme. The measurement was recorded at a Fourier frequency of 2 MHz, with an resolution bandwidth (RBW) of 300 kHz and a video bandwidth (VBW) of 200 Hz. The data represent direct observations and contained electronic noise. Figure 5: Balance homodyne measurements of the quadrature noise variances at a Fourier frequency of 500 kHz, with an RBW of 10 kHz and a VBW of 20 Hz. The data contained electronic noise and represent direct observations. To evaluate the long-term stability of the generated squeezed vacuum states, the quadrature noise variances of the squeezed state at the pump power of 125 mW (2 MHz) were recorded continuously for 3 h by utilizing the sequential control scheme.