Thermometry below 1 K

The thesis focuses on the metrology of temperatures below 1 kelvin, a range where quantum effects strongly influence the physical properties of fluids and materials. Reliable thermometry, closely aligned with thermodynamic temperature, is essential in this domain, both for fundamental research and for technological applications, particularly with the rise of low-temperature space experiments and quantum technologies operating at millikelvin temperatures.

The International Temperature Scale of 1990 (ITS-90) is defined down to 650 mK. Below this, the only internationally recognised reference is the Provisional Low Temperature Scale of 2000 (PLTS-2000), which covers the range from 0.9 mK to 1 K, based on the universal melting curve of ultrapure helium-3. In parallel, secondary thermometers calibrated against PLTS-2000 play a key role in disseminating this scale to laboratories that do not have direct access to measurements of the helium-3 melting curve.

The primary objective of this work was to implement PLTS-2000 at LNE-Cnam, ensuring the rigorous measurement of the helium-3 melting curve and its relationship with temperature in accordance with the recommendations for the scale. Secondly, a comparison was carried out with a magnetic field fluctuation thermometer (MFFT), a relative primary thermometer that provides independent access to thermodynamic temperature via the measurement of thermal magnetic noise. Finally, two secondary thermometers commonly used below 1 kelvin, a paramagnetic salt thermometer (CMN) and a superconducting reference device (SRD1000), were calibrated against PLTS-2000, and their performance assessed in terms of stability and reproducibility.

The main results of this work are :

1. The most-accurate realization of PLTS-2000 achieved with the relative uncertainty u_r(T₂₀₀₀) ≈ 0.025×[T₂₀₀₀/(1 mK)]−0.82 in the range 8 mK to 800 mK. Two other realizations (using different melting curve thermometers) had uncertainties approximately four times larger.

2. We calibrated a commercially-manufactured magnetic field fluctuation thermometer (MFFT) at a fixed point temperature (λ point or melting curve minimum) and then achieved the relative uncertainty u_r(T_MFFT) ≈ 0.002 from 0.9 mK to the calibration temperature. This performance exceeds the manufacturer’s specification by a factor of 5.

3. By direct comparison, we showed the MFFT was consistent with PLTS-2000, within combined uncertainties, throughout the range. This agreement reinforces the validity of PLTS-2000. It also demonstrates that a laboratory can achieve TPLTS-2000 with the small uncertainty u_r(T_MFFT) ≈ 0.002 without installing a complex melting curve thermometer.

4. We detected a temperature-independent offset : T_MFFT−T₂₀₀₀ ≈ 0.2 mK. We attribute the offset to external noise from an unidentified source that affected the MFFT. The offset implies that a laboratory that uses a calibrated MFFT to approximate TPLTS-2000 should also use a check standard such as a superconducting reference device that could detect changes in an offset.

5. We conducted detailed studies of the transition temperatures Tc of three commercially manufactured superconducting reference devices SRD 1000. They led to our:

— confirming that the apparent values of T_c are sensitive to residual magnetic fields, measuring

currents, and noise filters;

— fitting the entire transition curve of non-ideal transitions to obtain more precise values of T_c than alternative methods of identifying T_c;

— measuring the long-term (20 years) stability of Tc of six materials in one device;

— demonstrating that the variation of T_c among different devices is much larger than the precision of determining T_c. Therefore, individual calibration can improve the accuracy of T₂₀₀₀ dissemination via SRD 1000.

6. We verified that a particular CMN thermometer has high resolution and a short response time. This thermometer is well suited for temperature control at ultra-low temperatures.

7. The optimal solder for delicate cryogenic lines is a silver-tin alloy containing 6% silver.

This body of work contributes to strengthening the metrological framework of thermometry below 1 kelvin at LNE, reinforcing both the validation of PLTS-2000 and its practical dissemination within the cryogenic measurement community.

metrology, low temperature thermometry, PLTS-2000, Helium-3 melting curve, primary thermometry, secondary thermometry, magnetic field fluctuation thermometry, CMN thermometer, superconducting reference device, dilution refrigerator.