Development of ultra-stable cryogenic silicon optical resonators for laser frequency stabilization

光学谐振器对温度和机械力的敏感性很低，对于光学和微波频域的精确测量具有重要意义。在光学领域，它们用于稳定激光的频率，用于光谱应用，特别是光学原子钟，并用于探索基本的物理概念，如时空属性。此外，通过通过光学频率梳将超稳定的光学频率转换到射频域，可以实现具有超低相位噪声的射频源，其适用于例如具有更高灵敏度的雷达测量。超稳定光学谐振器的传统方法是使用ULE(超低膨胀玻璃)材料，在接近室温的温度下操作。这必然导致一定程度的布朗长度波动，这对可实现的频率稳定度施加了基本限制。共振器的低温运行为减少这些布朗涨落提供了一条途径。这提供了降低激光频率不稳定性的可能性，比使用ULE谐振器低一个数量级以上。由于近乎完美的晶格结构，晶体低温光学谐振器的特点是几乎没有长度漂移。最近人们研究了两种结构的硅光谐振器：首先，在124K，硅谐振器被用来在短时间尺度上将激光频率稳定在1E-16的分数不稳定水平。其次，在我们自己的工作中，对低温(1.5K)下的硅谐振器进行了详细的表征，证实了最终导致1E-17频率不稳定的可能性。在这些重要的原理证明研究的基础上，我们建议在1.5K下对低温硅谐振器进行进一步的开发，目标是头两年在中长积分时间1E2 S-1E4 S(有漂移消除)的水平上达到&lt；5e-17的频率不稳定性。这是一个在短时间和中长时间尺度上最终达到1E-17水平的中间目标，1 S-1E4 S为了展示我们两年目标中的性能目标，需要开发第二个低温谐振器系统，因为没有具有5E-17不稳定性的参考。它将在与第一个现有谐振器相同的低温恒温器中运行，并将通过拍频测量进行相互比较。此外，先前已确定的几个关键问题将通过实施适当的子系统加以解决：减少或保留激光幅度调制、安装主动隔振装置以减少低温恒温器的振动、在低温恒温器内安装光学电路板、将激光器预稳定到室温ULE谐振器以实现赫兹级别的线宽。

Optical resonators with low sensitivity to temperature and mechanical forces are of great importance for precision measurements in the optical and microwave frequency domains. In the optical domain, they serve to stabilize the frequencies of lasers for spectroscopic applications, notably for optical atomic clocks, and for probing fundamental physics concepts such as the properties of space-time. Also, by conversion of ultra-stable optical frequencies to the radio-frequency domain via an optical frequency comb, radio-frequency sources with ultralow phase noise can be realized, applicable to, e.g., radar measurements with improved sensitivity. The conventional approach for ultra-stable optical resonators is the use of ULE (ultra-low expansion glass) material, operated at temperatures near room temperature. This necessarily leads to a level of Brownian length fluctuations which imposes a fundamental limit to the achievable frequency stability. Cryogenic operation of a resonator provides one avenue towards reduction of these Brownian fluctuations. This offers the possibility of reduction of laser frequency instability more than one order of magnitude lower than with ULE resonators. Crystalline cryogenic optical resonators are furthermore characterized by the near-absence of length drift thanks to the near-perfect lattice structure. Silicon optical resonators have recently been studied in two configurations: first, at 124 K, a silicon resonator has been used to stabilize a laser frequency to the fractional instability level of 1E-16 on short time scales. Second, in our own work, detailed characterizations of a silicon resonator at cryogenic temperature (1.5 K) were performed, which confirmed the potential of eventually leading to 1E-17 frequency instability. Based on these important proof-of-principle studies, we propose here to perform further developments on cryogenic silicon resonators at 1.5 K, with the goal of the first 2 years being to reach a frequency instability on the level of < 5E-17 for medium-long integration times 1E2 s - 1E4 s (with drift removal). This is an intermediate goal towards eventually reaching the 1E-17 level on both short and medium-long timescales, 1 s - 1E4 s To demonstrate the performance aimed for in our 2-year goal, a second cryogenic resonator system needs to be developed, since no reference having 5E-17 instability is available. It will be operated in the same cryostat as the first, existing resonator, and will allow intercomparisons via beat frequency measurements. Moreover, several key issues, previously identified, will be taken care of by implementing suitable subsystems: reduction or residual laser amplitude modulation, installation of an active vibration isolation to reduce cryostat vibrations, implementation of optical breadboards inside the cryostat, prestabilization of the laser to a room-temperature ULE resonator in order to achieve Hz-level linewidth.