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 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)

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

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

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

{ 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

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

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

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

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

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

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

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

High-Bandwidth Measurement  = 1 second

Noise Versus Voltage

Universal Functional Form Agreement over four decades in temperature

Comparison With Secondary Thermometers

High Precision Measurement Residuals

Uncertainty vs. Integration Time

Correlations of Fit Parameters

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

High Bias Nonidealities High T High Bias

Nonlinear Current and Noise

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

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

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

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

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

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

Summary Demonstrate functional form of junction noise 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)

END

Tien-Gordon Theory Tucker and Feldman, 1985

Tien-Gordon for Noise of Junction

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

Conductance R=31.22Ohms

More Conductance

Fano Factor Has No Effect:

Temperature Measurements Over Time

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

Fit With Two Parameters Residuals

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

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-