Josephson Josephson Junctions,Junctions,

What are they?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 insulatingGap.

-This is the very basic form of quantum coherence. The wavefunction in one branch is coherent with the wavefunction of the second branch. Thus ifwe manipulate the state it will be continuous across the boundary with a onlyphase difference.

SuperconductorsSuperconductors

AluminumAluminum 1.2K1.2K

TinTin 3.7K3.7K

MercuryMercury 4.2K4.2K

NiobiumNiobium 9.3K9.3K

Niobium-TinNiobium-Tin 17.9K17.9K

Tl-Ba-Cu-Tl-Ba-Cu-oxide oxide

125K125K

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

MetalMetal Critical T(K)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 thusA 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 obeyPauli exclusion rule and thus they can all occupy the same quantum state.

Cooper PairsCooper Pairs-Cooper pairs can tunnel together through the insulating layer of Josephson Junction.

-This process is identical to that of quantum barrierpenetration in quantum mechanics.

-Because of the superconducting nature (no resistance) and the fact that Cooper pairs can jointly tunnel through an insulator we canmaintain 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 Josephson Junction DevicesDevices

-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 Josephson Junction Devices IIDevices 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 |1> 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.

WhyWhy Josephson Junctions? Josephson Junctions? Microscopic implementationsMicroscopic implementations::

based on electron spins, nuclei spins, or other microscopic based on electron spins, nuclei spins, or other microscopic propertiesproperties

(+)decohere slowly as naturally distinguishable from environment(+)decohere slowly as naturally distinguishable from environment (+)single ions can be manipulated with high precision(+)single ions can be manipulated with high precision (-)hard to apply to many qubits(-)hard to apply to many qubits (-)difficult to implement with devices(-)difficult to implement with devices

Macroscopic Implementations: Solid StateMacroscopic Implementations: Solid State- Semiconductors: quantum dots, single donor systemsSemiconductors: quantum dots, single donor systems- Superconductors: Josephson Junctions: Superconductors: Josephson Junctions:

- more success so farmore success so far- Josephson tunnel junction is “the only non-dissipative, strongly Josephson tunnel junction is “the only non-dissipative, strongly

non-linear circuit element available at low temperature “non-linear circuit element available at low temperature “

Benefits of Josephson Benefits of Josephson JunctionsJunctions

- Low temperatures of superconductorLow temperatures of superconductor::- no dissipation of energyno dissipation of energyno resistanceno resistanceno electron-no electron-

electron interactions(due to energy gap of Cooper pairs)electron interactions(due to energy gap of Cooper pairs)- low noise levelslow noise levels

- PrecisePrecise manipulation of qubits possible manipulation of qubits possible- ScalableScalable theoretically for large numbers of qubits theoretically for large numbers of qubits- Efficient use of resourcesEfficient use of resources: circuit implementation : circuit implementation

using existing integrated circuit fabrication technology using existing integrated circuit fabrication technology - Nonlinear Circuit Element Nonlinear Circuit Element

- Needed for quantum signal processingNeeded for quantum signal processing- ““easy” to analyze electrodynamics of circuiteasy” to analyze electrodynamics of circuit

Current versus flux across Josephson Junction

Circuit Implementation Circuit Implementation IssuesIssues

Electrical measurements of circuit elements:Electrical measurements of circuit elements: ClassicalClassical Quantum = Quantum = Numerical values Numerical values wavefunctionswavefunctions

- - E.g. E.g. classical capacitor charge classical capacitor charge superposition of superposition of positive and negative chargepositive 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>

ProblemsProblems Intrinsic decoherenceIntrinsic decoherence due to entanglement due to entanglement

Statistical variations inherent in fabrication Statistical variations inherent in fabrication transition frequencies transition frequencies and coupling strength determined and taken into account in algorithmsand coupling strength determined and taken into account in algorithms

Noise from environmentNoise from environment causes time dependent causes time dependent decoherence and relaxationdecoherence and relaxation

relaxation: bloch sphere latitude diffusing, state mixing-relaxation: bloch sphere latitude diffusing, state mixing- decoherence: bloch sphere longtitude diffusing, dephasing -decoherence: bloch sphere longtitude diffusing, dephasing -

Due to irreversible interaction with environment, Due to irreversible interaction with environment, destroys superposition of statesdestroys superposition of states--       change capacitor dielectric constant       change capacitor dielectric constant-- low frequency parts of noise cause low frequency parts of noise cause

resonance to wobbleresonance to wobblediphase oscillation in circuitdiphase oscillation in circuit-- noise with frequency of transition will cause noise with frequency of transition will cause transition transition between states between states energy relaxationenergy relaxation

More ProblemsMore Problems Unwanted transitions possibleUnwanted transitions possible

Can engineer energy difference between states to avoid thisCan engineer energy difference between states to avoid this Spurious resonance states:Spurious resonance states:

Example: spurious microwave resonators inside Josephson tunnel Example: spurious microwave resonators inside Josephson tunnel barrier coupling destroys coherence by decreasing amplitude of barrier coupling destroys coherence by decreasing amplitude of oscillationsoscillations

Measurement CrosstalkMeasurement Crosstalk: entanglement of different : entanglement of different qubitsqubits Measuring 1 qubit affects state of other qubitsMeasuring 1 qubit affects state of other qubits solve with single shot measurement of all qubitssolve with single shot measurement of all qubits

2 qubits done, but multiple will be a challenge2 qubits done, but multiple will be a challenge

Current Research Current Research in in

Superconducting Superconducting QubitsQubits•Identification and reduction of Identification and reduction of

sources of sources of decoherencedecoherence•Improved performance of qubit Improved performance of qubit

manipulationmanipulation

Decoherence In Josephson Decoherence In Josephson Phase Qubits from Junction Phase Qubits from Junction

ResonatorsResonators• Microscopic two-level systems Microscopic two-level systems

(resonators) found within tunnel (resonators) found within tunnel barriersbarriers

• Affect oscillation amplitude rather Affect oscillation amplitude rather than timingthan timing

Decoherence In Josephson Decoherence In Josephson Phase Qubits from Junction Phase Qubits from Junction

ResonatorsResonators

Simultaneous State Simultaneous State Measurement of Coupled Measurement of Coupled Josephson Phase QubitsJosephson Phase Qubits

• Previous studies rely on separate Previous studies rely on separate measurements of each qubitmeasurements of each qubit

• Need simultaneous measurement to Need simultaneous measurement to establish entanglementestablish entanglement

• Crosstalk necessitates faster Crosstalk necessitates faster measurement schemesmeasurement schemes

Simultaneous State Simultaneous State Measurement of Coupled Measurement of Coupled Josephson Phase QubitsJosephson Phase Qubits

Faster Qubit Measurement Faster Qubit Measurement SchemeScheme

• Allows for study of 2-qubit dynamicsAllows for study of 2-qubit dynamics• ~2-4ns measurement scheme is an ~2-4ns measurement scheme is an

order of magnitude faster than order of magnitude faster than previous onesprevious ones

• Short bias current pulse reduces Short bias current pulse reduces well depthwell depth

Superconducting Superconducting Tetrahedral Quantum BitsTetrahedral Quantum Bits

Superconducting Superconducting Tetrahedral Quantum BitsTetrahedral Quantum Bits

• Enhanced quantum fluctuations Enhanced quantum fluctuations allow junctions of higher allow junctions of higher capacitancescapacitances

• Quadratic susceptibility to flux, Quadratic susceptibility to flux, charge noisecharge noise

• Variety of manipulation schemes Variety of manipulation schemes using magnetic or electric biasusing magnetic or electric bias