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.
Superconductors
Aluminum
1.2K
Tin
3.7K
Mercury
4.2K
Niobium
9.3K
Niobium

Tin
17.9K
Tl

Ba

Cu

oxide
125K
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
100
K
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
.
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.
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.

As long as kT < binding energy, then a current can flow without dissipation.

The BCS theory of Superconductivity states that bound photons have slightly lower
energy, which prevents lattice collisions and thus eliminates resistance.

Bound electrons behave like bosons. Their wavefunctions don’t obey
Pauli exclusion rule and thus they can all occupy the same quantum state.
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.

Thus a Josephson Junction can be used as a very sensitive voltage, current or
flux detector.

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.
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 0> and 1>.
Josephson Junction Devices II
A current

biased Josephson Junction employs
creates a “washboard” shaped potential.
Splitting in the wells indicates allows us to use
the lowest two levels as qubit states.
The higher energy state 1> can be detected because the tunneling probability
under 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.
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 “
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
Circuit Implementation Issues
Electrical measurements of circuit elements:
Classical
Quantum =
Numerical values
wavefunctions

E.g.
classical capacitor charge
superposition of positive and
negative charge
•
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
C = 10 pF
C > = a*0> + b*1>
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
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
Current Research in
Superconducting Qubits
•
Identification and reduction of sources of
decoherence
•
Improved performance of qubit
manipulation
Decoherence In Josephson Phase
Qubits from Junction Resonators
•
Microscopic two

level systems (resonators)
found within tunnel barriers
•
Affect oscillation amplitude rather than timing
Decoherence In Josephson Phase
Qubits from Junction Resonators
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
Simultaneous State Measurement of
Coupled Josephson Phase Qubits
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
Superconducting Tetrahedral
Quantum Bits
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
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