Superconductive Electronics

1
Superconductive Electronics
2
Lecture Overview

• Superconductors - basic principles
• Josephson junctions
• Rapid Single-Flux Quantum (RSFQ) circuits
• Reversible parametric quantron
• Superconducting quantum computers

3
Principles of Superconductivity

• Fermions Bosons
• Coherent bosonic systems
• Cooper pairs BCS theory

4
Particle Exchange

• Consider a quantum state of two identical
  particles in single-particle states x and y,
  respectively.
• Amplitude given by wavefunction ?(x,y)
• Imagine any physical process (descibed by a
  unitary matrix U) whose effect is just to
  exchange the locations of the two particles.
• Because two such swaps gives the identical
  quantum state, UU1 (identity operation),
• One swap U must multiply the state vector by
  .
• There are only two square roots of 1 Namely, 1
  and ?1.
• Now, what happens if xy?

5
Fermions Bosons

• Fermions are simply those particles such that,
  when they are swapped, the state vector is
  multiplied by ?1.
• ? ?(y,x) ??(x,y), so if xy then ?(y,x) ?(x,x)
  ??(x,x)
• But ?(x,x)???(x,x) unless ?(x,x)0,
• so, there is always 0 probability for two
  fermions to be in the same state x. (Pauli
  exclusion principle.)
• Examples of some fundamental fermions
• Electrons, Quarks, Neutrinos
• Bosons are those particles that when swapped,
  multiply the state vector by 1.
• The quantum statistics of Bosons turns out
  actually to give a statistical preference for
  them to occupy the same state.
• Examples of some fundamental bosons
• Photons, W bosons, Gluons

6
Compound Bosons

• Note that exchanging two identical pairs of
  fermions multiplies the state vector by (?1)2
  1.
• ? Two identical systems that each contain an even
  number of fermions behave like bosons.
• If they contain an odd number of fermions, they
  behave like fermions.
• Protons, Neutrons (3 quarks each) are fermions
• Atoms w. an even number of neutrons are bosons
• n protons n electrons 2k neutrons even of
  fermions boson

7
Coherent Bosonic Condensates

• Large numbers of bosons can occupy the same
  quantum state and form a large, many-particle
  system having a definite quantum state.
• Three (more or less) familiar examples
• Laser beams - Bosonic condensates of photons.
• Supercurrents - Bosonic condensates of Cooper
  pairs of conduction electrons.
• Bose-Einstein condensates - E.g. In 1995 Cornell
  Wieman cooled large numbers of 87Rb atoms (37
  protons 50 neutrons 37 electrons boson) to
  a single quantum state at a temperature of 20 nK.

8
History of Superconductivity

• Discovered by Kammerlingh-Onnes in 1911 In solid
  mercury below 4.2 K resistance is 0!
• Superconducting loop currents can persist for
  years.
• Meissner Oschenfeld discovered in 1933 that
  superconductors exclude magnetic fields.
• Induced countercurrent sets up an opposing field.
• Electron-atom interactions shown to be involved
  in 1950.
• Bardeen, Cooper, Schrieffer proposed a working
  theory of superconductivity in 1957
• BCS theory.

9
Electron-Lattice Interactions

• Electron moving throughlattice exerts an
  attractiveforce on nearby ions.
• Causes a lattice deformation local
  concentration of charge.
• Positively charged phonon (quantum of lattice
  distortion)propagates as particle/wavein wake
  of electron.
• Later, phonon may be absorbedby a 2nd electron.

10
Cooper Pairs

• Two electrons exert a netattractive force on
  eachother due to the exchangeof phonons to
  which theyare both attracted.
• Repulsive below some distance.
• Typical separation 1 ?m
• Binding energy of pair 3kBTc
• Tc is critical superconducting temperature
• Note that phonon exchange doesnt change
  totalmomentum of pair.

11
Multiple overlapping pairs

• The lowest-energy state is wheneach electron is
  paired with themaximum number of neighbors.
• Most favored when all pairs have same total
  momentum. - Wavefunctions in phase
• As a result, each electrons momentum is locked
  to its neighbors.
• All of the pairs move together.
• 3kBTc energy to break a given Cooper pair.
• This energy not thermally available if TltltTc.

12
Josephson Junctions
Insulator (thin)

• Structure very simple
• Thin insulator betweentwo superconductors.
• Current-controlled switch
• Cooper pair wavefunctionstunnel
  ballisticallythrough the barrier.
• below critical current Ic
• Hysteretic I-V curve
• After current exceeds Ic,resistance stays high
• Till I drops back to 0.

10Å
Superconductive metal
I
Device hasbuilt-inmemory
Ic
V
1.5 ps switching speed
13
Leftovers from Last Lecture

• Most superconducting devices require very low
  (lt5K temperatures).
• However, high-temperature superconductors were
  discovered in the 1980s
• Tc ranging from 90-130 K (compare 0C 273 K).
• Electron pairing mechanism not well understood
• High-temperature Josephson junctions have also
  been proposed
• 77K, liquid-N temp. deemed feasible (Braginski
  1991)
• Discussion of BCS mechanism was very
  oversimplified
• see van Duzer Turner for details

14
Microstrip Transmission Lines

• Nice features
• Short (ps) waveforms
• Near c speeds
• Low attenuation dispersion
• Dense layout with low crosstalk
• JJs can be impedance-matched w. TLs
• avoids wave reflection off of junction
• permits ballistic wave transfer
• 10 ? can be obtained, w. V lt 3 mV
• Resistive state P V2/R lt 1 ?W.
• 100 Mjunctions ? 100 W?

15
Overview of JJ Logics

• Voltage-state logics
• IBM project in 1970s
• primarily dealt with magnetically-coupled gates
• Resistor-junction logic families (Japan, 1980s)
• RCJL (Resistor-Coupled Josephson Logic)
• 4JL (four-junction logic)
• MVTL (Modified Variable Threshold Logic)
• also used inductors magnetic coupling
• These technologies not found to be practical...
• Better Single-Flux-Quantum (SFQ) logics
• Encode bits using single quanta of magnetic
  flux! ?0 ? h/2qe 2 mVps

16
A Simple Element Current Latch

• Bias current Ib slightly less than JJ critical Ic
• Incoming current pulse Iin(t)
• pushes JJ current over Ic, JJ switches to off
  state
• Part of bias current shunted into output TL
• JJ hysteresis means Iout is latched in high state

Ib lt Ic
current
Iout
Iin
Iout
Iin
(Ic)
time
How to turn JJ back on?
17
Overdamped Josephson Junctions

• Place resistor in parallel w. JJ
• Brings junction current back below Icwhen input
  pulse goes away
• Restores junction back to on statewaiting for
  another pulse
• Iout becomes another pulse similar toinput pulse
• Switching speeds up to 770GHz have been
  measured!
• Voltage-state JJ logics werelimited to 1 GHz
• Were not competitive with modern CMOS

current
Iout
Iin
time
18
Problems w. superconductors

• Typical logic gates complex, hard to understand
• Simpler gates might yet be discovered
• Low temperatures increase total free-energy loss
  for a given signal energy dissipated
• E.g. T5 K 60x worse than _at_ 300 K
• Superconducting effect may go away in nanoscale
  wires (10 nm or less)
• Cooper pairs too big to fit
• Seems true for metal-based superconductors
• But, other nanoscale structures may take over!
• Superconductivity has been shown _at_lt20K in carbon
  nanotubes (Sheng, Tang et al. 01)
• Low temperatures imply lower maximum clock
  frequencies, by Margolus-Levitin bound.
• E.g., 5 K circuits limited to a 300 GHz average
  frequency of nbops