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

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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.