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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. Thermal conductance. T 2. T 1. Heat flow.

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Heat conduction by photons through superconducting leads
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


Thermal conductance
Thermal conductance

T2

T1

Heat flow

Thermal conductance

Heat flow (T1 > T2)

What conducts heat in a solid ?

Electrons (important for metals)

Phonons (lattice vibrations)

Q

T

T +T

Quantum of thermal conductance

and what about photons ?


Measurement of quantized thermal conductance
Measurement of quantized thermal conductance

Quantized electronic thermal conductance

2DEG in a GaAs-AlGaAs heterostructure

Molenkamp et al. Phys. Rev. Lett 68 (1992)

Quantized phonon thermal conductance

Silicon nitride membrane

K. Schwab et al. , Nature 404 (2000)


Energy relaxation in a submicron metal island
Energy relaxation in a submicron metal island

Pex

In thermal equilibrium:

Electron-electron collissions

Electron-phonon collisions

Pep

M.Meschke et al.


Energy relaxation in a submicron metal island1
Energy relaxation in a submicron metal island

Pex

Pe

In thermal equilibrium:

Electron-electron collisions

Electron-phonon collisions

Pep

+Electron-photon „radiative“ relaxation ?

M.Meschke et al.


Heat transported between two resistors
Heat transported between two resistors

Ge= ?

Voltage noise emitted by resistor Ri:

1D Black body radiation

R1,T1

R2,T2

Net heat flow from hot to cold resistor:

Quantum of thermal

Conductance:

Schmidt et al.,Phys. Rev. Lett., 93 (2004)


Competition between ep and e coupling
Competition between ep- and e- coupling

Cross-over temperature:

TCO


Typical experimental set up
Typical experimental set-up

Island size:

6.6 mm x 0.8 mm x 20 nm

SQUID junction size:

3 mm x 0.1 mm

SINIS junction size:

3 mm x 0.1 mm

Electrical circuit

Ib

Iheat

V


Actual experimental configuration tunable impedance between the resistors
Actual experimental configuration: tunable impedance between the resistors


Electrical model i
Electrical Model I

L0

L0

L0

Transmission line:

C0

C0

C0

Here:

R2

R1

L0

L0

L0

C0

C0

C0

L~30 μm

Tunable inductance:

R2

R1


Electrical model ii
Electrical Model II

CSQUID=30fF

LSQ

CSQ

R2

R1

LSQ

CSQ


Thermal model
Thermal model

Typical parameter values:

P1 = 1 fW

P2 = 0


Sinis thermometer
SINIS thermometer

Probes electron temperature of N island

(and not of S!) in the case of T/Tc<0.4

Low leakage of junctions



Measured variation of island temperature variation of bath temperature
Measured variation of island temperature:variation of bath temperature

Flux Φ0

Ic=20nA

CSQUID=15fF

R1=R2=200

P1=1fW

P2=0


Increase island temperature te 1
Increase island temperature Te1

T0=150mK

T0<40mK

Flux Φ0

Flux Φ0



Conclusion
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


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