Two Level Systems and Kondo-like traps as possible sources of decoherence in superconducting qubits

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Two Level Systems and Kondo-like traps as
possible sources of decoherence in
superconducting qubits
Lara Faoro and Lev Ioffe
Rutgers University (USA)
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Outline

• Decoherence in superconducting qubit
  experimental state of the art
• low frequency noise (1/f noise)
• high frequency noise (f noise)
• We discuss two possible microscopic mechanisms
  for the fluctuators
• weakly interacting quantum Two Level Systems
  (TLSs)
• environment made by Kondo-like traps
• TLSs model
• significant source of noise
• detailed characteristics of the noise power
  spectrum are in a qualitative and
  quantitative disagreement with the data
• Kondo-like traps model
• significant source of noise
• agreement with most features observed in the
  experiments

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What are the sources of noise?
Electromagnetic fluctuations of the circuit
(gaussian)
Discrete noise due to fluctuating background
charges (BC) trapped in the substrate or in
the junction
There are several experiments in different
frequency regimes but the dominant source of
noise is yet to be identified!
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Experimental picture ofthe noise power spectrum
?
T
Origin of both types of noise are
the same ?
Zimmerli et al. 1992 Visscher et al. 1995 Zorin
et al. 1996 Kenyon et al. 2000 Nakamura et al.
2001 Astafiev et al. 2004 Wellstood et al. 2004
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Low frequency noise ( 1/f )

• - Temperature dependence of the noise

• 1/f spectrum up to frequency 100-1000 Hz.
  where is the upper cut-off ???
• The intensity is in the range of
  at f10Hz
• some samples clearly produce a telegraph noise
  but 1/f spectrum
• points to numerous charges participating in
  generating the noise.
• This noise dominates and it is greatly
  reduced by echo technique.

high frequency noise ( f )
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Theoretical analysis
Upper level use a proper model to study
decoherence. fluctuators
model and not spin boson model

Paladino, Faoro, Falci and Fazio
(2002)
Galperin, Altshuler,
Shantsev (2003)
Lower level understanding which is the
microscopic mechanism of
decoherence that originate the fluctuators


Faoro, Bergli, Altshuler and Galperin (2004)

Faoro and Ioffe (2005)

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Quantum TLSs model
with
Relaxations for TLSs

• interaction with low energy phonons Tgt100 mk

• Many TLSs interacts via dipole-dipole
  interactions

The effective strength of the interactions is
controlled by and it is always very weak.
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Dipole and qubit interaction
Each dipole induces a change in the island
potential or in the gate charge
i.e.
barrier

- - -
substrate
Charge Noise Power Spectrum
Rotated basis
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Dephasing rates for the dipoles

• The weak interaction
• causes a width in each TLS
• at low frequency some of the TLSs become
  classical

Effective electric field
pure dephasing
N.B density of thermally activated TLSs enough
(Continuum)
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Relaxation rates for the dipoles
Fermi Golden Rule
But in presence of large disorder, some of TLSs
These dipoles become classical and will be
responsible for 1/f noise
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at high frequency
white!
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In the barrier...
The density of TLSs too low!
Strongly coupled TLS
Astafiev et al. 2004
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In the substrate...
Astafiev et al. 2004

• Comparison with experiments

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at low frequency

• it has a 1/f dependence for
  
• it has only linear dependence on Temperature
• it has intensity in agreement with experimental
  data

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What did we learn from the dipole picture?
dependence
Number of thermally activated TLSs
dependence
Search for fluctuators of different nature ...
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Andreev fluctuators model
Faoro, Bergli, Altshuler and Galperin (2004)
qubit
dependence

• correlations are short range
• amplitude of oscillations increases with
  increasing ?

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Kondo-like traps model
Kondo Temperature
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Properties of the ground state and the localized
excited state
Weak coupling
Strong coupling
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Physics of the Kondo-like traps
Density of states close to the Fermi energy
bare density
weight of the Kondo resonance
barrier
Transition amplitude
Fast processes
superconductor
Slow processes
Superconductor coherence lenght
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at high frequency

• This noise is dominated by fast tunneling
  processes between traps
• effectively the motion of electrons between trap
  acts as resistor R

From the conductance G we calculate the
resistance R
The noise power spectrum raises linearly with the
frequency!
NB Andreev fluctuators have the same but
and
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at low frequency

• in the barrier

estimates
experimental value
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Conclusions

• We have discussed a novel microscopic mechanism
• (Kondo-like traps) that might be the dominant
  source of noise for dephasing
• But the physics of the device is complex
  Kondo-like TLSs
• TLSs are killed by the T-dependence!
• Our analysis cannot be done in greater details,
  due to the lack of
• an analytical theory of kondo-like impurites
  with superconductor
• Try to measure 1/f noise after suppressing the
  superconductivity. We
• expect reduction of 1/f noise
• Reasonable level of noise even only in the
  barrier.
• Different substrates no changes in the
  intensity of the noise (NEC)
• relevant for phase qubit.