Precise Temperature Control by Locking on the Fixed point of Gallium

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The new enhanced method of temperature control need not any reference temperature, the system itself can find the melting temperature of gallium as a reference point by dithering input heat flux. If gallium is in melting state, the latent heat of fusion works, so gallium temperature does not change on dithering input heat flux. Also, the control method can determine the state of gallium; solid, liquid, or melting state by investigating the temperature in gallium. We apply this new temperature stabilization method to stabilize a Fabry-Perot cavity, which serves as a ultimate length measurement technique. We achieved 1 mK-temperature stability and 1.5426 nm/ 95 mm-length stability over 10 hours.