Josephson Junctions, What are they?

kitefleaUrban and Civil

Nov 15, 2013 (3 years and 6 months ago)

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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.

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