1. The Shot Noise Thermometer Lafe Spietz, K.W. Lehnert, I. Siddiqi, R.J. Schoelkopf Department of Applied Physics, Yale University Thanks to: Michel Devoret, Daniel E. Prober, and Wes Tew

2. Introduction Johnson-Schottky transition of the noise in tunnel junctions Relates T and V using only e and k B  primary thermometer Demonstrate operation from T=0.02 K to 300 K* *Lafe Spietz et al, Science 300, 1929 (2003)

3. Thermometry Secondary: Needs to be calibrated from some outside standard, e.g. resistive thermometers Primary: Needs no outside calibration—based on understood physics, e.g. ideal gas thermometer Desirable Characteristics for a Thermometer: Wide Range Fast Primary Accurate Easy and simple to use Physically compact

4. Resistance Thermometers Cryogenic Thermometry: Overview 1 K 300 K 10 K 0.1 K 0.01 K 100 K RuOx50 mK 3 He Melting Curve CBT Johnson Noise Nuclear Orientation

5. The Kelvin Water Triple Point = 273.16 K By Definition The Kelvin (K) unit of thermodynamic temperature is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

6. { 5 K 0.65 K } Vapor Pressure Thermometry Constant Volume Gas Thermometry 3 K 25 K 13.8 K 962 K Platinum Thermometer ITS-90: Overview Not Primary! Below 0.65 K Nothing! Radiation Thermometer T=1000 K

7. PLTS 2000: 0.9 mK-1 K Scale 3 He Melting Curve Superconducting Fixed Points

8. Fundamental Noise Sources Johnson-Nyquist Noise Frequency-independent Temperature-dependent Used for thermometry Frequency-independent Temperature independent Shot Noise

9. Conduction in Tunnel Junctions Assume: Tunneling amplitudes and D.O.S. independent of energy Fermi distribution of electrons Difference gives current: Conductance (G) is constant Fermi functions

10. Thermal-Shot Noise of a Tunnel Junction* Sum gives noise: *D. Rogovin and D.J. Scalpino, Ann Phys. 86,1 (1974)

11. Thermal-Shot Noise of a Tunnel Junction Johnson Noise 2eI Shot Noise 4k B T R Transition Region eV~k B T

12. Self-Calibration Technique P(V) = Gain( S I Amp +S I (V,T) ) P(V) { V

13. Al-Al 2 O 3 -Al Junction Experimental Setup: RF + DC Measurement SEM 55 P

14. High-Bandwidth Measurement  = 1 second

15. Noise Versus Voltage

16. Universal Functional Form Agreement over four decades in temperature

17. Comparison With Secondary Thermometers

18. High Precision Measurement Residuals

19. Uncertainty vs. Integration Time

20. Correlations of Fit Parameters

21. Thermodynamic Uncertainties of Temperature Scales 500 mK Thermodynamic Uncertainty of PLTS-2000 SNT

22. High Bias Nonidealities High T High Bias

23. Nonlinear Current and Noise

24. Shot Noise and Inelastic Tunneling 117 mV T=4 K  Al 2 O 3 Vibrational mode

25. Self-Heating V~T, P~T 2, G~T   T/T ~ constant V 2 /R junction Thermal Circuit: R lead Even with all cooling through leads, can have negligible effect on SNT measurement

26. Null-Balancing Noise Measurement for High Precision Noise Contours in Voltage-Space Small range of noise keeps detector in linear range

27. Modular SNT Package Total cost of package <10$ Tunnel Junction Built-in Bias Tee (on-board SMT Components) Copper Plumbing parts SMA Connectors for RF Copper Tubing for DC lines

28. Work In Progress: High Accuracy Comparisons Water Triple Point (273.16 K) High Precision 4 K to 300 K Cryostat - Calibrated RhFe Comparison - Hydrogen Triple Point (13.8033 K)

29. Future Work Determine effect of nonlinearity on shot noise Measure heating effects with dirty film Improve room temperature results Measure hydrogen triple point Make SNT more modular and easy to use for use in other labs and for commercialization Push the lower temperature end with lower system noise temperature and more careful filtering

30. Summary Demonstrate functional form of junction noise 0.02 - 300 Kelvin* Use as fast, accurate thermometer As good as 200 ppm precision, 0.1% accuracy Relates T to V using only e and k B Possible k B determination? *Lafe Spietz et al, Science 300, 1929 (2003)

31. END

32. Tien-Gordon Theory Tucker and Feldman, 1985

33. Tien-Gordon for Noise of Junction

35. Diode Nonlinearity V diode = GP +  G 2 P 2  = -3.1 V -1 1mV => 3x10 -3 fractional error

36. Conductance R=31.22Ohms

37. More Conductance

38. Fano Factor Has No Effect:

39. Temperature Measurements Over Time

40. Experimental Setup:RF + DC Measurement and Thermometry capacitors inductors RhFe Thermometer RuOx Thermometer device

41. Fit With Two Parameters Residuals

42. Merits Vs. Systematics *R. J. Schoelkopf et al., Phys Rev. Lett. 80, 2437 (1998) Possibility to relate T to frequency!* Compact electronic sensor No B-dependence Wide T range (mK to room temperature) Fast and self-calibrating Primary MeritsSystematics I-V curve nonlinearities Amplifier and diode nonlinearities Frequency dependence* Self-heating

43. Tunnel Junction (AFM image) Al-Al 2 O 3 -Al Junction R=33  Area=10  m 2 I+I+ I-I- V+V+ V-V-