Radiation From Josephson Junctions Into Free Space L'N' Bulaevskii, LANL A'E' Koshelev, ANL Content

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Radiation From Josephson Junctions Into Free
SpaceL.N. Bulaevskii, LANLA.E. Koshelev,
ANLContent

• Motivations to revive the old problem wanted and
  unwanted radiation from JJ.
• Rigorous description of radiation from a single
  JJ.
• Radiation decoherence in JJ-based qubits (with
  I. Martin).
• Radiation from intrinsic JJ in layered
  superconductors.
• Similarity with radiation from vortex flow in
  bulk superconductors (with E. Chudnovsky).
• Future study.

• 1,2,4 cond-math/067348

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Early measurements and estimates

• Prediction of radiation from tunneling junction,
  Josephson, 1962.
• Experimental observation, Dmitrenko et al.,
  Langenberg et al.,1965.
• Radiation power 1 pW from 0.16 cm X 0.025
  cm Sn-SnO-Sn junction.
  
  Power fed into junction W.
• Langenberg et al. estimated radiation power
  in terms of transmission coefficient depending on
  mismatch of impedances

Detector
I
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What is wrong with transmission conception for
radiation from JJ ?

• Assumes electromagnetic wave has only one attempt
  to escape junction, true at high dissipation.
• At low dissipation multiple reflections lead to
  formation of almost standing wave.
• In linear regime we anticipate
• Derivation should be based on the phase
  difference approach.
• No quantitative measurements of radiation power
  into free space ?
• New developments wanted and unwonted radiation
  from JJ.

if

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Rigorous description of radiation from a single JJ

• Standard approach in terms of with
  
• and boundary condition
  gives
• We start from Maxwell equations for ac fields
• inside leads,
• inside dielectric layer,
• and in free space,
• fields are related by
• continuity of
• transverse fields.

l
H0
Jx
2l
d
y
Jx-
z
x
x0
x-l
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Steps in rigorous description

• Express inside leads and dielectric
  layer via (smoothed over distance ) as
  Josephson current and currents inside leads
  depend on .
• Find equation (sG) for using charge
  conservation.
• Find boundary cond. for from free
  space.
• 4. This gives boundary conditions for at JJ
  edges and Poynting vector in terms of at
  boundary.
• Solve sG eq. for with dynamic boundary
  cond. and find radiation power and I-V
  characteristics.

We solved 1D broad JJ, and small
circular JJ, .
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1. Ac fields inside leads in terms of ac
component of the phase difference
l
H0
Jx
2l
d
y
Jx-
z
x
x0
x-l
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3. Boundary conditions for ac fields.

• Assuming only out-going electromagnetic waves in
  the outer free space.
• Maxwell equations result in the relation between
  magnetic and electric fields at the boundary

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3. Dynamic boundary conditions for phase,
Poynting vector (circular JJ)

Gives pW at 10 GHz and
1 for JJ studied by Langenberg et al..


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4. Solution for , linear regime, 1D junction

• In high magnetic fields or at high frequencies
  amplitude of phase oscillations is small,
• Perturbation theory with respect to Josephson
  current to solve sG equation with dynamic
  boundary conditions.
• For we get linear equation.

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Radiation power and conversion efficiency Q in
linear regime

• In broad1D JJ Q depends on dissipation,
  and (via dynamic boundary conditions)

• The product has Fiske resonances at
• their widths depend on
  and
• In small circular JJ 1 pW if
• Nonlinear regime - numerical solution of sG.

• .
• .

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Effect of radiation on JJ qubits

• Radiation from JJ causes decoherence.
• Quasiclassical approach

1
0

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Radiation decoherence time

• Short radiation time for unshielded JJ
  

ns
Simmonds et al. ns ( Cu
shielded JJ). Shielding increases radiation time

for pF, m,
GHz,
A.
Consequence of shielding extra degrees of
freedom, , and no sG !
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Intrinsic JJ as a source of THz radiation
How to calculate the radiation power ?

How to synchronize oscillations in different
junctions ?
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Boundary conditions and Poynting vector

• Differential finite-difference coupled eqs. for
  
• Boundary conditions for at
  

• Poynting vector at

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Super-radiation flux flow regime I, high-field
rectangular moving lattice

• Radiation comparable with dissipation
  

(0.25 mm).
mm at THz.

• High-field limit

• At Fiske resonances

mW/cm.

• -independent,

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Super-radiation from flux flow II, high-field
rectangular moving lattice

• Large-crystal limit

mm.

• No Fiske resonances.

W/cm


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Synchronization of Josephson oscillations

• Radiated electromagnetic field in large crystals
  helps to synchronize flux flow in different
  junctions as well as Josephson oscillations in
  the absence of applied magnetic field.
• Stability of in-phase oscillations in these cases
  was not studied yet.

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Radiation from flux flow in bulk superconductors
rectangular lattice

• Discrete spectrum,
  up to
• Power from large crystal with weak disorder

YBCO film at 72 K, B1.8 T,
m/s, cooling rate 1 W/cm ,
0.1 mW/cm , conversion
efficiency 10 .
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Would be interesting to study

• experimentally and numerically radiation into
  free space from a single JJ in nonlinear regime,
• dependence of decoherence rate on shielding in
  small-size JJ (qubits),
• radiation from BISCO crystal thin along c-axis,
  in super-radiation regime (large ),
• experimentally similar radiation at washboard
  frequencies,
  due to flux flow in bulk superconductors.