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

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=0.26 K to 300K

3. Fundamental Noise Sources Thermal(Johnson) Noise Frequency-independent Temperature-dependent Used for thermometry Frequency-independent Temperature independent Shot(Schottky) Noise

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

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

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

7. Johnson-Schottky Transition: Direct relationship between T and V

8. 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-

9. Experimental Setup:RF + DC Measurement

10. Experimental Setup: Pumped He Cryostat For  = 1 second, High bandwidth: hence fast Noise power vs. bias voltage:

11. Self-Calibration Technique for Thermometry P = Gain*B( S I Amp +S I (V,T) )

12. Noise Versus Voltage T noise =5.128 K, Gain=29.57  V/K T=4.372 K

13. Universal Functional Form: Agreement over three decades In temperature

14. Comparison With Secondary Thermometers

15. Temperature Measurements Over Time

16. 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

17. Summary Ideal Electron Gas Thermometer based on Johnson-Schottky transition of noise in a tunnel junction (thermal-shot noise.) Fast, accurate, primary thermometer Works over a wide temperature range Relates T to V using only e and k b applications for metrology

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

19. Conductance R=31.22Ohms

20. More Conductance

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