Echo of superconductivity and superfluidity

1
Echo of superconductivity and superfluidity

• A.G.Rudavets, MPTI, Russia

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Motivation

• Experimental Observation of Echo signals in
  electrical circuits of Josephson junctions (weak
  superconductors)
• Experimental implementation of Fermi Bose gas
  mixture with composite order parameter
• Broken symmetry and coherence of molecular
  oscillations in tunneling transitions
• Microscopic theory of transients and revivals in
  a time-dependent many-body system with BCS
  pairing

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BCS Hamiltonian and Wave Function

• We consider dynamic system where scattering and
  pairing of particles switched on faster then
  the time of quasiparticle energy relaxation
  and time of order parameter change
  t ltlt ltlt
• Magnetoassociation
• Photoassociation
• Many-body state
• where u and v are Bogolubov amplitudes.
• Characteristic times of making and breaking
  fermionic pairs are defined by the Hamiltonian

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Scattering length and Coupling a

• - volume of the system,
• a and a0 - scattering length in magnetic field
  and in background.
• m - chemical potential to form a pair of atoms
  as a result of total number of particles fixed
  that defines Fermi levels
• B and B0 - magnetic field and its value at
  magneto association resonance. B swept fast
  across resonance forth and back

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Pairing function

• Bogolubov de Gennes equations read
• A time-dependent pairing function of mean field is

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Cooper instability

• The pairing function measures the success of the
  fermion pairing in lowering total energy of the
  many body system. The free states of unpaired
  particles become unstable. New bound state sets
  in. Stability analysis reveals how D grows. At
  constant a , the growth exponent and the steady
  state gap coincides.
• We estimate tD 1/ D
• Self-consistency

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Transients

• We will proceed step by step using perturbation
  series.
• First pulse gives in first order
• Second pulse in first order additionally produces
  

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Second order coherence

• In second order we have

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Echo of third order gap
For linear dispersion near Fermi level gap is
peaked at exactly double time delay between pulses
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Summary

• Mechanism of gap reconstruction clear indicates
  to existence of echo superconductivity and
  superfluidity