# Laser Intensity Noise Suppression for Preparing Audio-Frequency Squeezed Vacuum State of Light
## 1 Introduction
Demand for Laser Intensity Noise Suppression for Preparing Audio-Frequency Squeezed Vacuum State of Light  
For the singly-resonant OPO (no seed light) or the singly-resonant optical parametric amplifier (OPA) (with the seed light), the corresponding amplitude (+) and phase (-) quadrature variance \(V^{\pm}_{\text{sqz}}(\omega)\) can be expressed as follows [32]:  
\[V^{\pm}_{\text{sqz}}(\omega)=\frac{\left\{C_{\text{s}}V^{\pm}_{\text{s}}(\omega )+C_{\text{l}}V^{\pm}_{\text{l}}(\omega)+C^{\pm}_{\text{o}}V^{\pm}_{\text{v}}( \omega)+\alpha^{2}[C_{\text{p}}V^{\pm}_{\text{p}}(\omega)+C^{\pm}_{\text{$ \Delta$}}V_{\text{$\Delta$}}(\omega)]\right\}}{\left|D^{\pm}(\omega)\right|^{2 }}, \tag{1}\]  
where \(V^{\pm}_{\text{s}}(\omega)\) is the noise of seed fields, \(V^{\pm}_{\text{l}}(\omega)\) is the vacuum fluctuation caused by intra-cavity loss, \(V^{\pm}_{\text{v}}(\omega)\) is the vacuum fluctuation from output coupler, \(V^{\pm}_{\text{p}}(\omega)\) is the noise from pump fields, and \(V_{\text{$\Delta$}}(\omega)\) is the noise of detuning fluctuation in the cavity, respectively. Additionally, \(C_{\text{s}}\), \(C_{\text{l}}\), \(C^{\pm}_{\text{v}}\), \(C^{\pm}_{\text{p}}\) and \(C^{\pm}_{\text{$\Delta$}}\) are their respective coefficients; \(D^{\pm}(\omega)\) is the description of the performance of the OPO cavity, independent of the light field; \(\alpha^{2}\) is the number of photons of the seed light into the OPO. In theory, the OPO mode (\(\alpha^{2}=0\)) can avoid the destruction of the audio-frequency squeezed vacuum state as it eliminates the possibility that the obvious fluctuation of pump fields and the noise of detuning fluctuation are brought into the audio-frequency squeezed vacuum state of light. In order to reduce the negative impact on the audio-frequency squeezed state of light, the polarization of lock beam with a certain frequency shift (140 MHz) should be P polarization, perpendicular to the pump light (S polarization), and the propagation direction should be opposite to the pump light. If the scattering and residual reflection of the lock beam on the surface of nonlinear crystal (PPKTP crystal in our experiment) inside OPO cavity are not considered, OPO runs as an ideal OPO mode for generation of audio-frequency squeezed vacuum state of light. However, actually, the lock beam's polarization degree is limited and that is normally not a pure P-polarization beam as we hope, and it contains a residual weak S-polarization component. Due to roughness of surface of nonlinear crystal (PPKTP) and imperfect anti-reflection coating, the scattering and residual reflection of the lock beam cannot be simply ignored. Some fundamental-wave photons with S polarization along the direction of OPO's pump beam actually serve as \"_seeding signal_\" (\(\alpha^{2}\
eq 0\)), and will partially blur the audio-frequency squeezed state of light. This point was addressed by [PERSON] et al. [31], and if the seeding signal's power is \(>\)1 nW, the audio-frequency squeezing level will be degraded, and OPO actually will run as an OPA mode. Since intensity noise of \"_seeding signal_\" is the key factor affecting squeezing level, introducing the feedback system is particularly important, which not only can reduce classical noise but also can benefit the stable locking of OPO/OPA cavity. In addition, the intensity of pump beam has close relationships with the audio-frequency squeezed state of light, which not only brings considerable classical gain, but also introduces some extra noise including thermal instability and NIR laser's absorption induced by UV laser, especially when the intensity noise is large [8]. The drift of thermal noise and other classical noise can be mitigated by stabilizing its intensity fluctuation, which is also more conductive to the stable output of squeezed light for a long time. [PERSON] et al. [11] have analyzed the intensity noise of local oscillator (LO) beam and the common mode rejection ratio (CMRR) of balanced homodyne detector (BHD) at different analysis frequency.