1. Heat conduction by photons through superconducting leads W.Guichard Université Joseph Fourier and Institut Neel, Grenoble, France M. Meschke, and J.P. Pekola Low Temperature Laboratory, Helsinki University of Technology, Espoo, Finland

2. Thermal conductance T1T1 Heat flow (T 1 > T 2 ) T2T2 Heat flow Thermal conductance What conducts heat in a solid ? Phonons (lattice vibrations) Quantum of thermal conductance T T +  T Q and what about photons ? Electrons (important for metals)

3. Measurement of quantized thermal conductance 2DEG in a GaAs-AlGaAs heterostructure Molenkamp et al. Phys. Rev. Lett 68 (1992) Quantized electronic thermal conductance Quantized phonon thermal conductance K. Schwab et al., Nature 404 (2000) Silicon nitride membrane

4. Energy relaxation in a submicron metal island M.Meschke et al. In thermal equilibrium: Electron-electron collissions Electron-phonon collisions P ex P ep

5. Energy relaxation in a submicron metal island M.Meschke et al. In thermal equilibrium: Electron-electron collisions Electron-phonon collisions +Electron-photon „radiative“ relaxation ? P ex P ep P e

6. Heat transported between two resistors Voltage noise emitted by resistor R i : G e = ? 1D Black body radiation R 2,T 2 R 1,T 1 Quantum of thermal Conductance: Net heat flow from hot to cold resistor: Schmidt et al.,Phys. Rev. Lett., 93 (2004)

7. Competition between ep- and e - coupling T CO Cross-over temperature:

8. Typical experimental set-up Island size: 6.6  m x 0.8  m x 20 nm SINIS junction size: 3  m x 0.1  m SQUID junction size: 3  m x 0.1  m I heat V IbIb Electrical circuit

9. Actual experimental configuration: tunable impedance between the resistors

10. Electrical Model I Transmission line: C0C0 C0C0 C0C0 L0L0 L0L0 L0L0 C0C0 C0C0 C0C0 L0L0 L0L0 L0L0 R1 R2 R1 R2 Tunable inductance: Here: L~30 μm

11. Electrical Model II L SQ C SQ R2 R1 L SQ C SQ C SQUID =30fF

12. Thermal model Typical parameter values: P 1 = 1 fW P 2 = 0

13. SINIS thermometer Probes electron temperature of N island (and not of S!) in the case of T/T c <0.4 Low leakage of junctions

14. Measured variation of island temperature:

15. Measured variation of island temperature: variation of bath temperature Flux Φ 0 I c =20nA C SQUID =15fF R 1 =R 2 =200  P 1 =1fW P 2 =0

16. Increase island temperature Te 1 Flux Φ 0 T 0 <40mK T 0 =150mK

17. Measured variation of island temperature: amplitude of modulation

18. Conclusion -First observation of the crossover from phonon relaxation to radiative photon relaxation at temperatures of about 100 mK -Thermal and electrical model explain quite well the measured data -Implications on: performance of bolometers (sensitivity): coupling to the heat bath removing excessive heat from devices at milli-kelvin range