Lecture 12: Superconducting Quantum Interference Devices OUTLINE 1. Superconducting Quantum Interference 2. SQUIDs • SQUID Equations • SQUID Magnetometers • Josephson loop vs SQUID Loop 3. Distributed Josephson Junctions • Short Josephson Junctions • Josephson Phasors (pendula) • Long Josephson Junctions October 20, 2005 Massachusetts Institute of Technology 6.763 2005 Lecture 12 Superconducting Quantum Interference Image removed for copyright reasons. Please see: Figure 8.8, page 411, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 1Phase difference around the loop From the definition of the gauge invariant phase Adding them Image removed for copyright reasons. Please see: Figure 8.8, page 411, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 In the superconductor the supercurrent equation gives together gives SQUID Equations J = 0, in Image removed for copyright reasons. Please see: Figure 8.8, page 411, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 Often the contour can be taken where this case The total current can be written then as The flux in the contour is The circulating current is given by The total flux can then be written as 2Method of Solution Image removed for copyright reasons. Please see: Figure 8.8, page 411, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. For a given external flux, there is a range of i and Φ that satisfy these equations. One wants to determine the maximum i that can be put through the SQUID and still have zero voltage. (For larger I the current will be shown to create a voltage). Massachusetts Institute of Technology 6.763 2005 Lecture 12 SQUID without self inductance And, Image removed for copyright reasons. Please see: Figure 8.9, page 414, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Image removed for copyright reasons. Please see: Figure 8.9, page 414, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 In this case therefore, The extremum occurs when , that is, when Therefore, 3SQUID with self inductance Image removed for copyright reasons. Please see: Figure 8.10, page 416, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Image removed for copyright reasons. Please see: Figure 8.11, page 417, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 SQUID Magnetometers 1pF µmµm Φ 1.11.1I+ V+ I-V-20 µm Φ0 LDC SQUID Shunt capacitors ~ 1pF Jct. Size ~ 1.1µm Loop size ~20x20µm2 SQUID ~ 50pH I~10 & 20µAcMassachusetts Institute of Technology 6.763 2005 Lecture 12 4Josephson Loop vs. Superconducting Loop I+ V+ βL>> 1 I-V-Image removed for copyright reasons. Please see: Figure 5.3, page 249, from Orlando, T., and K. Delin.Image removed for copyright reasons. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234.Please see: Figure 5.3, page 249, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 Distributed Josephson Junction 0 as ∆z 0 heff solved Law Also, Image removed for copyright reasons. Please see: Figure 8.14, page 421, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 Therefore, Likewise, for the y-directions In general this must be self-consistently with Ampere’s 5Short Josephson Junction B = Bo iy,then Jc is Image removed for copyright reasons. Please see: Figure 8.14, page 421, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 Let the self fields generated by the currents be negligible, and That can be integrated directly, The total current with constantFlux through the junction Critical current of the junction Short Josephson Junction: “single-slit interference” Image removed for copyright reasons. Please see: Figure 8.14, page 421, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Image removed for copyright reasons. Flux through the junction Please see: Figure 8.15, page 424, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Critical current of the junction Massachusetts Institute of Technology 6.763 2005 Lecture 12 6Vortices in Short Junctions Image removed for copyright reasons. Please see: Figure 8.16, page 425, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Image removed for copyright reasons. Please see: Figure 8.15, page 424, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Massachusetts Institute of Technology 6.763 2005 Lecture 12 Vortices in Short Junctions a 2π phase Image removed for copyright reasons. Please see: Figure 8.16c, page 425, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Image removed for copyright reasons. Please see: Figure 8.17, page 426, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Image removed for copyright reasons. Please see: Figure 8.15, page 424, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: