1 / 18

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

laurel
Download Presentation

Superconductive Electronics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related