2004
DOI: 10.1103/physrevlett.93.250602
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Thermal-Noise Limit in the Frequency Stabilization of Lasers with Rigid Cavities

Abstract: We evaluate thermal noise (Brownian motion) in a rigid reference cavity used for frequency stabilization of lasers, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with the direct application of the fluctuation dissipation theorem. This noise sets a fundamental limit for the frequency stability achieved with a rigid frequency-reference cavity of order 1 Hz/ square root Hz (0.01 Hz/ square root Hz) at 10 mHz (100 Hz) at room temperature. This level coin… Show more

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Cited by 496 publications
(382 citation statements)
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“…High performance dielectric mirror coatings that have low optical and mechanical loss are required for use in ring laser gyroscopes [1], frequency comb techniques [2], optical clocks [3] and precision interferometry [4].…”
Section: Introductionmentioning
confidence: 99%
“…High performance dielectric mirror coatings that have low optical and mechanical loss are required for use in ring laser gyroscopes [1], frequency comb techniques [2], optical clocks [3] and precision interferometry [4].…”
Section: Introductionmentioning
confidence: 99%
“…We have made an estimate of the thermal noise limit of our cavities based on the values reported for ULE, fused silica and mirror coatings in reference [12]. The resulting limit, ∼3.8 × 10 −16 , is about three times smaller than the noise level in all-ULE cavities realized at the same wavelength for a similar purpose [24].…”
Section: Ultra-high-finesse Cavities For a High-stability Lasermentioning
confidence: 99%
“…The employment of ultra-low thermal expansion materials as spacers between the cavity mirrors and the increasing level of engineering in their shape design have allowed several optical cavities to reach a stability level σ y 6 × 10 −16 [10,11] at 1 s. This instability level is limited by thermal fluctuations of the mirror substrates and coatings [12]. Although some theoretical ideas have been proposed to reduce or circumvent the thermal noise [13,14], it currently sets the ultimate limit for cavity frequency-stabilization techniques.…”
Section: Introductionmentioning
confidence: 99%
“…For macroscopic ultra-stable cavities, TRN has been observed to be a limitation on frequency stability at room temperature [284], and demonstrated to be suppressed at cryogenic temperatures [287]. For small mode-volume microcavities, TRN poses a much larger problem, and has been observed to limit frequency imprecision at the level of 10 3 Hz 2 /Hz at Fourier frequencies of about 1 MHz, at room temperature [277].…”
Section: Imprecision Due To Cavity Substrate Noisementioning
confidence: 99%
“…In all position sensors, extraneous thermal fluctuations pose a fundamental limit to the achievable imprecision. In cavity-optomechanical sensors, the main sources of extraneous imprecision arise from thermomechanical [279,280] and thermodynamic fluctuations of the cavity substrate [281][282][283][284]. These result in excess cavity frequency noise,S imp,ex ω , and limit the measurement rate to…”
Section: Measurement At the Thermal Decoherence Ratementioning
confidence: 99%