Cryogenic monocrystalline silicon Fabry–Perot cavity for the stabilization of laser frequency

Richard, J. P.; Hamilton, J. J.

doi:10.1063/1.1142249

Cited by 32 publications

(18 citation statements)

References 15 publications

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“…Such resonators have been applied for tests of Lorentz invariance [10], local position invariance [11] and quantum space-time fluctuations [12]. Silicon, a machinable optical material available with high purity and large size, having interesting CTE properties [13], high stiffness and low mechanical dissipation [14], has first been used for an optical reference resonator by Richard and Hamilton [15]. Recently, Kessler et al [16] developed a laser frequency stabilization system based on a vertically supported silicon resonator operated at a temperature of zero CTE, 124 K, and achieved a high frequency stability (1 × 10 −16 ), less than 40 mHz laser linewidth, and an extremely low long-term drift.…”

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Silicon single-crystal cryogenic optical resonator

et al. 2014

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We report on the demonstration and characterization of a silicon optical resonator for laser frequency stabilization, operating in the deep cryogenic regime at temperatures as low as 1.5 K. Robust operation was achieved, with absolute frequency drift less than 20 Hz over 1 hour. This stability allowed sensitive measurements of the resonator thermal expansion coefficient (α). We found α = 4.6 × 10 −13 K −1 at 1.6 K. At 16.8 K α vanishes, with a derivative equal to −6 × 10 −10 K −2 . The temperature of the resonator was stabilized to a level below 10 µK for averaging times longer than 20 s. The sensitivity of the resonator frequency to a variation of the laser power was also studied. The corresponding sensitivities, and the expected Brownian noise indicate that this system should enable frequency stabilization of lasers at the low-10 −17 level. c 2014 Optical Society of America OCIS codes: 120.3940, 120.4800, 140.3425, 140.4780. Optical resonators with low sensitivity to temperature and mechanical forces are of significant importance for precision measurements in the optical and microwave frequency domain. 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 issues such as the properties of space-time. Also, by conversion of ultrastable optical frequencies to the radio-frequency domain via an optical frequency comb, radio-frequency sources with ultralow phase noise can be realized [1], leading 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, where the coefficient of thermal expansion (CTE) exhibits a zero crossing. While ULE resonators with optimized designs (long length, acceleration-insensitive shape) have reached impressive performance [2], their operating temperature near 300 K necessarily leads to a level of Brownian length fluctuations which imposes a fundamental limit to the achievable frequency stability [3], [4]. Cryogenic operation of a resonator provides one avenue towards reduction of these fluctuations. The Allan deviation of length fluctuations decreases proportional to √ T [3], if the mechanical dissipation of the resonator elements, in particular of the mirror coatings, is independent of temperature. Measurements performed thus far indicate that the dissipation of mirrors with crystalline substrates at cryogenic temperature are indeed similar to those of fused silica mirrors at room temperature [5], [6]. Nowadays, robust cryogenic solutions exist for continuous operation of even fairly large objects, such as optical resonators, at temperatures as low as 0.1 K. This offers the possibility of reduction of resonator length fluctuations by more than one order of magnitude compared to today's lowest levels realized at room temperature, with a corresponding reduction in frequency instability of the laser stabiliz...

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Silicon single-crystal cryogenic optical resonator

et al. 2014

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“…Recently, silicon resonators (first studied in Ref. [14]) were investigated at 123 K [9] and at 1.5 K [15,16]. Silicon's advantages are the availability of single crystals of large size at affordable cost, its easy machineability, a flexibility in the choice of resonator shape, and superpolished mirror substrates allowing high-reflectivity mirrors.…”

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Resonator with Ultrahigh Length Stability as a Probe for Equivalence-Principle-Violating Physics

2016

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In order to investigate the long-term dimensional stability of matter, we have operated an optical resonator fabricated from crystalline silicon at 1.5 K continuously for over one year and repeatedly compared its resonance frequency fres with the frequency of a GPS-monitored hydrogen maser. After allowing for an initial settling time, over a 163-day interval we found a mean fractional drift magnitude |f −1 res dfres/dt| < 1.4 × 10 −20 /s. The resonator frequency is determined by the physical length and the speed of light, and we measure it with respect to the atomic unit of time. Thus, the bound rules out, to first order, a hypothetical differential effect of the universe's expansion on rulers and atomic clocks. We also constrain a hypothetical violation of the principle of Local Position Invariance for resonator-based clocks and derive bounds for the strength of space-time fluctuations.In this paper we address experimentally the question about the intrinsic time-stability of the length of a macroscopic solid body. This question is related to the question about time-variation of the fundamental constants and effects of the expansion of the universe on local experiments. It may be hypothesized that, in violation of the Einstein Equivalence Principle (EP), the expansion affects the length of a block of solid matter and atomic energies to a different degree. The length, defined by a multiple of an interatomic spacing, can be measured by clocking the propagation time of an electromagnetic wave across it. This procedure effectively implements the Einstein light clock, or, in modern parlance, an electromagnetic resonator. The hypothetical differential effect would show up as a time-drift of the ratio of the frequency f res of an electromagnetic resonator and of an atomic (or molecular) transition (f atomic ). A resonator and an atom are dissimilar in the sense that the former's resonance frequency intrinsically involves the propagation of an electromagnetic wave, while the latter does not. Specifically, the time-drift would violate the principle of Local Position Invariance (LPI) of EP. The natural scale of an effect due to cosmological expansion, here the fractional drift rate The suitable regime in which to investigate the dimensional stability of matter is at cryogenic temperature, when the thermal expansion coefficient and the thermal energy content of matter are minimized. Ideally, during the cooling down and then permanence at cryogenic temperature, a stable energy minimum of the solid is reached. The expected high dimensional stability and the magnitude of H 0 lead to a challenging measurement problem: how to resolve tiny length changes, and how to suppress the influence of extrinsic disturbances. The problem can be addressed by casting the solid matter into an electromagnetic resonator of appropriate shape, by supporting it appropriately, and by measuring its resonance frequency using atomic time-keeping and frequency metrology instruments, which indeed permit ultra-high measurement precision and accur...

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“…Additionally, the low mechanical loss of silicon at cryogenic temperatures 1,2 suggests its use in low thermal noise experiments such as gravitational wave detectors 3,4 or cavities used for laser frequency stabilization. 5 Applications using optical components at high laser powers can suffer from thermal lensing effects. If light gets absorbed a spatial temperature distribution within the sample is created due to the intensity profile of the laser beam.…”

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confidence: 99%