Development of ultra-stable cryogenic silicon optical resonators for laser frequency stabilization
Final Report Abstract
The main goal of this project was the demonstration of laser frequency stabilization to 5x10-17 for integration times 10^2 - 10^4 s (after drift removal) using a cryogenically-cooled, monocrystalline silicon resonator as a frequency reference. As we used a pulse-tube cryostat, its substantial internal vibrations required particular attention. We designed and developed three vertically-oriented silicon resonators (5 cm, 19 cm and 21 cm long) with low sensitivity to vibrations. Two of them (5 cm and 19 cm) were operated continuously in the cryostat, over a time period of more than ½ year. To minimize the vibrations acting on the resonators, we developed an efficient passive two-stage cryogenic vibration isolation system. This is the first such system ever described, having a compact size. Finally, we also had to introduce a novel method for interrogating the cryogenic resonator mode, that uses a special interrogation laser. The 5 cm and 19 cm resonators were characterized in terms of their vibration sensitivity. We used cryogenically operated geophones and an interferometric sensor located outside of the cryostat to characterize the accelerations acting on the resonators. From the frequency modulation of the resonators’ TEM00 mode frequencies we deduced their acceleration sensitivities. They were found to be 6.9x10^-10/g and 1x10^-10/g for the 5 cm resonator and 19 cm resonator, respectively. The sensitivity to temperature was carefully measured for two resonators (25 cm and 5 cm) in the temperature interval from 1.5 to 22 K. We discovered a zero coefficient of frequency sensitivity of the 5 cm vertical resonator near 4 K and confirmed, for both resonators the already known zero coefficient of thermal sensitivity of silicon near 17 K. The frequency instability of the 5 cm, 19 cm and 25 cm resonators was measured for integration times τ <10^4 s by comparing their optical resonance frequency with an in-house hydrogen maser by means of a fiber frequency comb. The observed frequency instability of the frequency ratio was found to be restricted by the instability of the hydrogen maser used as reference. Because of this limitation, we made a theoretical estimate of the actual frequency instability of the overall system. We deduce that the performance of the 19 cm resonator nearly achieves the project goal. We also performed extensive studies of the suitability of cryogenic resonators for long-term operation (as would be required for fundamental physics studies) and of their drift. First, we operated the 25 cm horizontally-oriented silicon resonator at 1.5 K for more than three years uninterruptedly, a record long time. During this time the long-term intrinsic frequency drift of the resonator was measured almost daily with respect to the maser. For this purpose, the maser frequency had to be monitored against atomic clocks, using a GNSS-provided 1 pps signal. During a particularly stable 163-day time interval a fractional frequency drift of less than 1.4x10^-20/s was measured. This exceptional frequency stability was used for performing tests of fundamental physics. We also studied the long-term frequency drift of the 19 cm resonator over 5 months. It was found to be comparable to that of the 25 cm resonator. A study was made of the effect of changing the power of the laser that interrogates the 5 cm resonator. We found that this modified significantly the long-term frequency drift rate. The same effect was independently reported by Robinson et al. 2019. This effect could in principle allow to null the long-term frequency drift of the resonator by careful adjustment of the laser light power used for interrogation. We made extensive theoretical studies of novel resonator designs suitable for cryogenic operation with the goal of finding vibration-insensitive solutions. We were successful. We believe that by continuing the developments demonstrated in this work (improved passive vibration isolation within the cryostat and resonator designs with ultra-low vibration sensitivity), it will eventually be possible to achieve frequency instability at 1×10^-17, together with ultra-low drift. Such a performance could allow more precise tests of fundamental physics or even improve the performance of transportable optical clocks.
Publications
- “Resonator with Ultrahigh Length Stability as a Probe for Equivalence-Principle-Violating Physics”, Phys. Rev. Lett. 117, 271102 (2016)
E. Wiens, A. Yu. Nevsky, S. Schiller
(See online at https://doi.org/10.1103/PhysRevLett.117.271102139) - “Simulation of Force-Insensitive Optical Cavities in Cubic Spacers”, Applied Physics B 124, 140 (2018)
E. Wiens, S. Schiller
(See online at https://doi.org/10.1007/s00340-018-7000-3) - “A simplified cryogenic optical resonator apparatus providing ultra-low frequency drift”, Rev. Sci. Instrum. 91, 045112 (2020)
E. Wiens, C. J. Kwong, T. Müller, S. Schiller
(See online at https://doi.org/10.1063/1.5140321)
