Research On Vibration And Thermal Expansion Effect For 30cm Ultra-stable Optical Resonators

With the development of science and technology,research areas like national defense,fundamental research have stricter requirements for the precision of the definition of“second”.Optical frequency standards(OFS)with higher stability and accuracy are expected to replace microwave frequency standards.The time and frequency group at Huazhong University of Science and Technology is carrying out the aluminum ion(²⁷Al⁺)optical frequency standard project.The ²⁷Al⁺OFS is mainly composed of the ion trapping system,the ultra-stable laser system and the femtosecond optical frequency comb system.The ultra-stable laser system is the core of the ²⁷Al⁺OFS system as its local oscillator.To improve the frequency stability,we build an ultra-stable laser system based on a 30-cm long cavity.The thermal noise limit of the ultra-stable cavity can be reduced by increasing the spacer length of the cavity and using low mechanical loss mirrors,like Fused Silicon(FS)mirrors.We evaluate the frequency stability of the laser locked to the30 cm cavity to be 3.3×10^-16,and the major noise contributions are from vibration and temperature fluctuations.Vibration noise effect becomes more significant with the increasing of the cavity length.Usually,vibration noise is the most significant noise to be overcome for an ultra-stable laser system which is locked to a cavity longer than 30 cm.We reduce the influence of vibration on the ultra-stable cavity by both changing the supporting position and mounting structure of the cavity.We change the cavity supporting positions step-by-step and also replace the mounting structure to a monolithic design.After that,the vibration sensitivities of the 30 cm ultra-stable cavity reduce from S_V=1.46 MHz/g(vertical direction),S_E-W=0.12 MHz/g(orthogonal direction),and S_N-S=1.30 MHz/g(optical axis direction)to S_V=0.08 MHz/g,S_E-W=0.08 MHz/g,and S_N-S=0.11 MHz/g.The frequency noise caused by vibration noise in the three directions reduces from 2×10^-2 Hz/Hz^1/2 to2×10^-3 Hz/Hz^1/2@1 Hz,with one order of magnitude reduction in the range of 0.01-50Hz.In addition,the thermal expansion coefficient(CTE)of FS is 5×10^-7/K,which is one order of magnitude larger than that of ultra-low expansion glass(ULE)spacer.Therefore,the equivalent CTE of the ultra-stable cavity changes and the equivalent zero expansion temperature of the ultra-stable cavity becomes lower than the one at the room temperature.Consequently,the cavity is much more sensitive to the temperature fluctuation.To deal with the temperature fluctuation noise of the ultra-stable cavity,we build an ultra-stable laser system based on a home-made re-entrant 30-cm long ultra-stable cavity.I evaluate the key parameters such as zero expansion temperature,the CTE,and so on.The zero expansion temperature is measured to be 6.9?,and the slope of the CTE is fitted to be1.2×10^-9/K²,which is smaller than that of the first 30 cm ultra-stable cavity.It is verified that the CTE of the combined re-entrant cavity meets the experimental requirement.Through the research of the re-entrant 30-cm long cavity,valuable experiences are gained for the design and the manufacturing of the ultra-stable cavity with adjustable zero expansion temperature in the future.