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Superconductive Electronics

Superconductive Electronics. Lecture Overview. Superconductors - basic principles Josephson junctions Rapid Single-Flux Quantum (RSFQ) circuits Reversible parametric quantron Superconducting quantum computers. Principles of Superconductivity. Fermions & Bosons Coherent bosonic systems

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Superconductive Electronics

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  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, UU=1 (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 x=y?

  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 x=y 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 doesn’t 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 electron’s 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 T<<Tc.

  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-in“memory” Ic V 1.5 ps switching speed

  13. Leftovers from Last Lecture • Most superconducting devices require very low (<5K temperatures). • However, “high-temperature” superconductors were discovered in the 1980’s • Tc ranging from ~90-130 K (compare 0°C = ~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 < 3 mV • Resistive state P = V2/R < 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 mV·ps

  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 < 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. T=5 K: 60x worse than @ 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 @<20K 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

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