Source: http://aoot.osa.org/oe/abstract.cfm?uri=oe-19-15-14495
Timestamp: 2019-04-22 18:30:33+00:00

Document:
Temperature measurement with nano-Kelvin resolution is demonstrated at room temperature, based on the thermal dependence of an optical crystal anisotropy in a high quality whispering gallery mode resonator. As the resonator’s TE and TM modes frequencies have different temperature coefficients, their differential shift provides a sensitive measurement of the temperature variation, which is used for active stabilization of the temperature.
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Fig. 1 The experimental setup. Temperature of the brass cube on the photo is set to 76 °C and stabilized to a few hundred nanodegrees using the dual-mode stabilization technique.
Fig. 2 (a) A pair of TE and TM WGMs with a small frequency detuning Δf = fo – fe . (b) Temperature dependence of Δf (T) is linear with a −89.8 MHz/K slope. The inset shows a small distortion around the set point Δf (Tset ) = 0 which is due to the WGMs cross-coupling.
Fig. 3 (a) The WGMs shown in Fig. 2 are brought on-resonance by temperature control. These modes have weak nonlinear coupling. (b) Another pair of modes couples strongly and is not suitable for our application.
Fig. 4 The Allan variance of the temperature fluctuations in the stabilized WGM resonator in nano-Kelvin and in terms of the expected fractional frequency stability. The straight line has a slope of 0.5 μK / s1/2. The error bars are based on the measurements statistics. On the inset: the spectral density of the temperature fluctuations measured in our system (below) and the noise-equivalent temperature spectral density in  (above).
(2) 1 f d f d T + 1 n d n d T + 1 R d R d T = 0.
(5) d d T Δ f = − c λ ( α n ( o ) − α n ( e ) ) ≈ − 79.1 MHz / K .

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