As an important quantum resource, the squeezed state can not only be employed for quantum teleportation in quantum information technology but also can be adopted to improve the detection sensitivity of laser interferometer in quantum precision measurement. In the above applications, the quantum state fidelity and interferometer sensitivity are directly determined by the noise level of the squeezed state. Therefore, previous research focuses on improving the squeezing degree of squeezed state. However, with the deepening research, the optical power of the squeezed state is another factor limiting its application, and thus it is important to improve the optical power of the squeezed state.

The experimental preparation system is built as shown in Fig. 1. The most important part of the experimental system is the optical parametric amplifier (OPA), which generates the high-power bright squeezed state. The OPA is a semi-monolithic standing cavity composed of periodically poled KTiOPO₄(PPKTP) crystal and concave cavity mirror. Then the balanced homodyne detection device can divide the high-power bright squeezed state and the local oscillator into two parts with equal power, and inject the balanced homodyne detector respectively after interference. The squeezing degree is measured by scanning the relative phase of the high-power bright squeezed state and the local oscillator.

The thermal lens effect of PPKTP crystal exerts a very adverse effect on the parametric conversion. The method of simultaneously injecting high-power seed light and pump light into OPA is adopted especially in the experimental system of preparing high-power bright squeezed state. This method will increase the nonlinear absorption of high-power seed light and pump light, resulting in thermal deposition and then a thermal lens effect in the PPKTP crystal. Finally, the mode matching efficiency of the seed light and pump light with OPA is decreased. To improve the mode matching efficiency of seed light and pump light with OPA and enhance the squeezing degree, we should quantitatively analyze the thermal lens focal length of PPKTP crystal under OPA working state and then adjust the lens group in the optical path of seed light and pump light to realize the rematch of seed light and pump light with the intrinsic mode of OPA with thermal lens effect.

According to the experimental parameters and theoretical calculation, under the OPA without thermal lens effect, the waist radii corresponding to the seed light and pump light in the OPA cavity are ω1=31.3 μm and ω2=19.9 μm respectively. The distance between the waist and the front convex surface of PPKTP crystal is L₁=0.75 mm and L1'=0.47 mm respectively. When the pump light power is 145 mW and the seed light power is 500 mW, the equivalent focal length of the thermal lens in the PPKTP crystal can be calculated to be about 182 mm. Under the OPA with thermal lens effect, the waist radii corresponding to seed light and pump light in OPA are ω1'=30.6 μm and ω2'=19.4 μm respectively. The distance between the waist and the front convex surface of PPKTP crystal corresponding to seed light and pump light is L₁=0.68 mm and L1'=0.43 mm respectively. The above calculation results show that the thermal lens changes the intrinsic mode waist of OPA. The theoretical calculation results confirm that the mode matching efficiency of seed light and pump light with OPA decreases to 99.8% and 99.9% respectively, while the OPA produces bright squeezed light with high power.

When the powers of seed light and pump light are further increased, the high-power seed light and pump light will cause more intense and complex thermal deposition in the PPKTP crystal (such as the green light-induced infrared absorption effect). This is because the intensification trend of the thermal lens effect is not linear, but may be an approximate exponential increase. Therefore, the thermal lens effect will cause sharply decreased mode matching efficiency between the seed light (the pump light) and the OPA. Thus, the thermal lens effect will significantly affect the squeezing degree. The mode matching efficiency of seed light and pump light with OPA is reduced by the thermal lens effect, which mainly affects the power of seed light and pump light injected into OPA. Theoretically, the change of seed light power has no effect on the squeezing degree. Therefore, it is only necessary to consider the influence of pump light power in OPA on the squeezing degree of the bright squeezed state. Finally, according to Eqs. (4)-(12), the quantitative relationship between the focal length of the thermal lens and the squeezing degree can be derived.

According to the working conditions of the experimental system in Ref. [20], there is a thermal lens in the OPA, and the high-power bright squeezed state of -10.7 dB±0.2 dB is measured without optimizing the mode matching of seed light and pump light with the OPA. The squeezing degree comparison reveals that with the thermal lens effect, the mode matching efficiency reduction of seed light and pump light with the OPA has little effect on the squeezing degree. This means the thermal lens effect in OPA has little effect on the squeezing degree of the high-power bright squeezed state. Additionally, the different effects of thermal lens effect on the squeezing degree of high-power bright squeezed state and squeezed vacuum state are compared and analyzed. Meanwhile, the following conclusions are drawn. In the same experimental conditions, the squeezing degree of the squeezed vacuum state generated by optical parametric oscillator (OPO) will be higher than that of the high-power bright squeezed state generated by OPA if other effects between the high-power seed light and pump light in PPKTP crystal are not considered, with the thermal lens effect only considered.

In the high-power bright squeezed state experiment system, the thermal lens effect of high-power seed light and pump light in PPKTP crystal is studied experimentally and theoretically. The equivalent focal length of the thermal lens and the mode mismatch between seed light and OPA, and between pump light and OPA are quantitatively analyzed by the theoretical model of thermal lens and mode matching. The equivalent focal length of the thermal lens in the PPKTP crystal can be calculated as 182 mm by theoretical analysis and calculation. In the working condition of the experimental system, due to the thermal lens generated in the PPKTP crystal, the mode matching efficiency of the high-power seed light and pump light with the OPA decreases to 99.8% and 99.9% respectively. Then the mode matching of high-power seed light and pump light with the OPA cavity is re-optimized. Finally, under the seed light power of 500 mW and pump light power of 145 mW, a bright squeezed state with power of 200 μW and squeezing degree of -10.8 dB±0.2 dB is obtained at the analysis frequency of 3 MHz. The results show that during the preparation of a high-power bright squeezed state, the squeezing degree of the high-power bright squeezed state is basically unaffected, since the thermal lens effect in PPKTP crystal caused by the high-power seed light and pump light does not significantly reduce the mode matching efficiency of the high-power seed light and pump light with OPA.