Microfabricated resonators play a crucial role in the development of quantum measurement, including future gravitational wave detectors. We use a micro-genetic algorithm and a finite element method to design a microresonator whose geometry is optimized to maximize the sub-Standard Quantum Limit (SQL) performance including lower thermal noise (TN) below the SQL, a broader sub-SQL region, and a sub-SQL region at lower frequencies. For the proposed design, we study the effects of different geometries of the mirror pad and cantilever microresonator on sub-SQL performance. We find that the maximum ratio of SQL to TN is increased, its frequency is decreased, and the sub-SQL range is increased by increasing the length of the microresonator cantilever, increasing the radius of the mirror pad, decreasing the width of the microresonator cantilever, and shifting the laser beam location from the mirror center. We also find that there exists a trade-off between the maximum ratio of SQL to TN and the sub-SQL bandwidth. The performance of this designed microresonator will allow it to serve as a test-bed for quantum non-demolition measurements and to open new regimes of precision measurement that are relevant for many practical sensing applications, including advanced gravitational wave detectors.

中文翻译：

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微谐振器的设计可将热噪声降至标准量子极限以下

微制造谐振器在量子测量的发展中起着至关重要的作用，包括未来的引力波探测器。我们使用微遗传算法和有限元方法设计了一种微谐振器，其几何结构经过优化，以最大限度地提高亚标准量子极限 (SQL) 性能，包括 SQL 下方更低的热噪声 (TN)、更宽的亚 SQL 区域、和较低频率的子 SQL 区域。对于所提出的设计，我们研究了镜面垫和悬臂微谐振器的不同几何形状对 sub-SQL 性能的影响。我们发现，通过增加微谐振器悬臂的长度、增加镜垫半径、减小微谐振器悬臂的宽度，SQL与TN的最大比值增加，其频率降低，sub-SQL范围增加, 并将激光束位置从反射镜中心偏移。我们还发现 SQL 与 TN 的最大比率和 sub-SQL 带宽之间存在权衡。这种设计的微谐振器的性能将使其成为量子非破坏测量的试验台，并开辟与许多实际传感应用相关的精密测量新机制，包括先进的引力波探测器。