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The Shot Noise Thermometer

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. Introduction.

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The Shot Noise Thermometer

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  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 kB •  primary thermometer • Demonstrate operation from T=0.02 K to 300 K* *Lafe Spietz et al, Science 300, 1929 (2003)

  3. Thermometry Desirable Characteristics for a Thermometer: • Wide Range • Fast • Primary • Accurate • Easy and simple to use • Physically compact 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

  4. Cryogenic Thermometry: Overview 300 K 100 K Johnson Noise Resistance Thermometers 10 K 1 K RuOx 50 mK CBT 0.1 K 3He Melting Curve 0.01 K Nuclear Orientation

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

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

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

  8. Thermal-Shot Noise of a Tunnel Junction 2eI Shot Noise Transition Region eV~kBT 4kBT Johnson Noise R

  9. Self-Calibration Technique P(V) = Gain( SIAmp+SI(V,T) ) P(V) { V

  10. Experimental Setup: RF + DCMeasurement P 5m SEM Al-Al2O3-Al Junction

  11. High-Bandwidth Measurement t= 1 second

  12. Noise Versus Voltage

  13. Universal Functional Form Agreement over four decades in temperature

  14. Comparison With Secondary Thermometers

  15. High Precision Measurement Residuals

  16. Uncertainty vs. Integration Time

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

  18. High Bias Nonidealities High Bias High T

  19. Nonlinear Current and Noise

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

  21. 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

  22. 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 kB Possible kB determination? *Lafe Spietz et al, Science 300, 1929 (2003)

  23. END

  24. Tien-Gordon Theory Tucker and Feldman, 1985

  25. Tien-Gordon for Noise of Junction

  26. Diode Nonlinearity Vdiode = GP + bG2P2 b= -3.1 V-1 1mV => 3x10-3 fractional error

  27. Conductance R=31.22Ohms

  28. More Conductance

  29. Fano Factor Has No Effect:

  30. Correlations of Fit Parameters

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

  32. Temperature Measurements Over Time

  33. Experimental Setup:RF + DCMeasurement and Thermometry RhFe Thermometer capacitors device RuOx Thermometer inductors

  34. Fit With Two Parameters Residuals

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

  36. Tunnel Junction(AFM image) R=33 W Area=10 mm2 Al-Al2O3-Al Junction V+ I+ I- V-

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