1.State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China 2.Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
Fund Project:Project supported by the National Key R&D Program of China (Grant No. 2020YFC2200402), the National Natural Science Foundation of China (Grant Nos. 62027821, 11654002, 11874250, 11804207, 11804206, 62035015, 62001374), the Key R&D Project of Shanxi Province, China (Grant No. 201903D111001), the Program for Sanjin Scholar of Shanxi Province, China, the Fund for Shanxi “1331 Project” Key Subjects Construction, China, and the Program for Outstanding Innovative Teams of Higher Learning Institutions of Shanxi Province, China
Received Date:01 February 2021
Accepted Date:11 May 2021
Available Online:18 August 2021
Published Online:20 October 2021
Abstract:Quantum noise has become an important limiting factor in the application of precision measurement, and its relevant problems have become a research hotspot. As an important optical device to manipulate quantum noise, the optical resonator possesses the transmission characteristics that determine the evolution characteristics of output signal’s noise. According to their impedance matching factor a values, the resonators can be divided into three categories: over-coupled cavity for $a \in [ - 1, 0)$, impedance matched cavity for $a{{ = }}0$, and under-coupled cavity for $a \in (0, 1]$. When the resonator fully meets the resonant conditions, its output field can be regarded as a low-pass filter, the high-frequency noise is directly reflected. The high-frequency noise at the output end is greatly suppressed, and the noise at the frequency far larger than the linewidth reaches the shot noise standard. Therefore, the noise of the optical field beyond the linewidth range can be greatly suppressed by the narrow linewidth optical resonator. At the same time, from the three kinds of optical resonator phase diagrams it can be found that the over-coupled cavity is in a state of half a detuning and the sideband frequency phase rotates ± 90° relative to the carrier frequency. In this case, the phase noise of light field can be converted into amplitude noise by an over-coupled cavity, which can be used for the phase noise measurement or squeezing angle rotation of squeezed light and has important applications in analyzing the laser noise component and manipulating the quantum noise. At the same time, the energy loss of the over-coupled cavity is the largest among the three types of cavity structures. Through theoretically analysing the corresponding relation among optical resonator output intensity, phase and frequency, and by making a comparison of comparing transfer function, energy transmission, spectrum characteristics of noise transmission among over-coupled cavity, impedance matched cavity and under-coupled cavity, in this paper the power splitter, frequency filtering, and noise transformation features of the optical resonator are demonstrated. The analysis results in this paper provide a basis for applying various optical resonators to different occasions, and promote the development of using the optical resonators to control the quantum noise of light field and improving the precision of precision measurement. Keywords:optical resonator/ transfer function/ noise spectrum/ quantum noise
图 1 两镜腔结构简图
图 2 不同腔型的特性 (a)能量传输特性; (b)循环功率特性
图 3 传输函数
图 4 光学谐振腔光强反射率和反射位相
图 5 三镜环形谐振腔的噪声模型
图 6 腔输出场的量子噪声限制 (a)阻抗匹配腔中噪声随频率的变化; (b)非阻抗匹配腔中噪声随频率的变化; (c)反射光场噪声随阻抗匹配因子a的变化
