Josephson Junctions, What are they?

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Josephson Junctions,What are they?
- A Superconductor-Insulator-Superconductor
device, placed between two electrodes.
-Josephson Effect the phase of the wavefunction
of a superconducting electron pair separated by
an insulator maintains a fixed phase relation.
-This means that we can describe the wavefunction
around the loop of a Superconductor, with only a
phase difference due to the presence of the
insulating Gap.
-This is the very basic form of quantum
coherence. The wavefunction in one branch is
coherent with the wavefunction of the second
branch. Thus if we manipulate the state it will
be continuous across the boundary with a
only phase difference.
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Superconductors
A superconductor is a metal that allows a current
to pass through it with no loss due to heat
dissipation.
Typical values for the critical temperature range
from mK to 100K
Metal Critical T(K)
Using Superconductors we can preserve a
wavefunction because the fact that the current
wavefunction is not perturbed by its journey
through the metal means that it will stay in a
given state.
Aluminum 1.2K
Tin 3.7K
Mercury 4.2K
Niobium 9.3K
Niobium-Tin 17.9K
Tl-Ba-Cu-oxide 125K
The current can be seen as a wavefunction, and is
thus A probability distribution of different
current values, this implies that clockwise and
counter clockwise. It is this view of the current
that enables us to create qubits from a simple
loop of superconductor.
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Superconductors II
-When a metal is cooled to the critical
temperature, electrons in the metal form Cooper
Pairs.
-Cooper Pairs are electrons which exchange
phonons and become bound together.
-Bound electrons behave like bosons. Their
wavefunctions dont obey Pauli exclusion rule and
thus they can all occupy the same quantum state.
-The BCS theory of Superconductivity states that
bound photons have slightly lower energy, which
prevents lattice collisions and thus eliminates
resistance.
-As long as kT lt binding energy, then a current
can flow without dissipation.
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Cooper Pairs
-Cooper pairs can tunnel together through the
insulating layer of Josephson Junction.
-This process is identical to that of quantum
barrier penetration in quantum mechanics.
-Because of the superconducting nature (no
resistance) and the fact that Cooper pairs can
jointly tunnel through an insulator we
can maintain a quantum current through the
Josephson Junction without an applied voltage.
-A changing magnetic field induces a current to
flow in a ring of metal, this effect can be used
to detect flux quanta. Radio Astronomy uses these
devices frequently.
-Thus a Josephson Junction can be used as a very
sensitive voltage, current or flux detector.
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Josephson Junction Devices
-There are three primary Josephson Junction
devices.
-The Cooper Pair box is the most basic device. We
can envision it as a system with easily split
levels, and use the degenerate lowest energy
levels as a qubit.
-Similarly to the Cooper Pair box we can use
inductors to adjust,a Josephson Junction, until
the potential represented by the potential well
is a degenerate double well. We can then use
symmetric and anti-symmetric wavefunctions and
their associated eigenvalues as 0gt and 1gt.
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Josephson Junction Devices II
A current-biased Josephson Junction
employscreates a washboard shaped potential.
Splitting in the wells indicates allows us to
usethe lowest two levels as qubit states.
The higher energy state 1gt can be detected
because the tunneling probabilityunder a
microwave probe will be 500 times as probable to
induce a transition.
Creates a detectable voltage by going downhill.
Thus we can know the state.
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Why Josephson Junctions?

• Microscopic implementations
• based on electron spins, nuclei spins, or other
  microscopic properties
• ()decohere slowly as naturally distinguishable
  from environment
• ()single ions can be manipulated with high
  precision
• (-)hard to apply to many qubits
• (-)difficult to implement with devices
• Macroscopic Implementations Solid State
• Semiconductors quantum dots, single donor
  systems
• Superconductors Josephson Junctions
• more success so far
• Josephson tunnel junction is the only
  non-dissipative, strongly non-linear circuit
  element available at low temperature

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Benefits of Josephson Junctions

• Low temperatures of superconductor
• no dissipation of energy?no resistance?no
  electron-electron interactions(due to energy gap
  of Cooper pairs)
• low noise levels
• Precise manipulation of qubits possible
• Scalable theoretically for large numbers of
  qubits
• Efficient use of resources circuit
  implementation using existing integrated circuit
  fabrication technology
• Nonlinear Circuit Element
• Needed for quantum signal processing
• easy to analyze electrodynamics of circuit

Current versus flux across Josephson Junction
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Circuit Implementation Issues

• Electrical measurements of circuit elements
• Classical? Quantum
• Numerical values ?wavefunctions
• - E.g. classical capacitor charge ?
  superposition of positive and negative charge

C 10 pF ? C gt a0gt b1gt

• Need to implement gate operations for
  transferring qubit information between junction
  and circuit via entanglement
• Read, Write, Control
• But need to avoid introducing too much noise to
  system, want to isolate qubits from external
  electrodynamic environment

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Problems

• Intrinsic decoherence due to entanglement
• Statistical variations inherent in fabrication ?
  transition frequencies and coupling strength
  determined and taken into account in algorithms
• Noise from environment causes time dependent
  decoherence and relaxation
• relaxation bloch sphere latitude diffusing,
  state mixing-??
• decoherence bloch sphere longtitude diffusing,
  dephasing -??
• Due to irreversible interaction with
  environment,
• destroys superposition of states
• -       change capacitor dielectric constant
• - low frequency parts of noise cause
• resonance to wobble
• ?diphase oscillation in circuit
• - noise with frequency of transition will
  cause transition between states ?energy
  relaxation

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More Problems

• Unwanted transitions possible
• Can engineer energy difference between states to
  avoid this
• Spurious resonance states
• Example spurious microwave resonators inside
  Josephson tunnel barrier coupling destroys
  coherence by decreasing amplitude of
  oscillations
• Measurement Crosstalk entanglement of different
  qubits
• Measuring 1 qubit affects state of other qubits
• solve with single shot measurement of all qubits
• 2 qubits done, but multiple will be a challenge

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Current Research in Superconducting Qubits

• Identification and reduction of sources of
  decoherence
• Improved performance of qubit manipulation

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Decoherence In Josephson Phase Qubits from
Junction Resonators

• Microscopic two-level systems (resonators) found
  within tunnel barriers
• Affect oscillation amplitude rather than timing

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Decoherence In Josephson Phase Qubits from
Junction Resonators
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Simultaneous State Measurement of Coupled
Josephson Phase Qubits

• Previous studies rely on separate measurements of
  each qubit
• Need simultaneous measurement to establish
  entanglement
• Crosstalk necessitates faster measurement schemes

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Simultaneous State Measurement of Coupled
Josephson Phase Qubits
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Faster Qubit Measurement Scheme

• Allows for study of 2-qubit dynamics
• 2-4ns measurement scheme is an order of
  magnitude faster than previous ones
• Short bias current pulse reduces well depth

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Superconducting Tetrahedral Quantum Bits
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Superconducting Tetrahedral Quantum Bits

• Enhanced quantum fluctuations allow junctions of
  higher capacitances
• Quadratic susceptibility to flux, charge noise
• Variety of manipulation schemes using magnetic or
  electric bias