Josephson Circuits I. Outline 1. RCSJ Model Review 2. Response to DC and AC Drives • Voltage standard 3. The DC SQUID 4. Tunable Josephson Junction October 27, 2005 Massachusetts Institute of Technology 6.763 2005 Lecture 14 JJ RCSJ Model as Circuit Element and Image removed for copyright reasons. Please see: Figure 9.6, page 459, 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 14 Therefore, 1DC Current Drive Image removed for copyright reasons. Please see: Figure 9.6, page 459, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. A. Static Solution: B. Dynamical Solution Image removed for copyright reasons. Please see: Figure 9.10, page 464 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 9.11, page 465, 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 14 The The 0 <i> V0 Image removed for copyright reasons. Please see: Figure 9.6, page 459, 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 14 DC Voltage Drive resulting current across the JJ is ac current across the resistor is dc The voltage source is DC with v=V , so that The total current is then 2The The The Image removed for copyright reasons. Please see: Figure 9.13, page 467, 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 14 AC Voltage Drive resulting current across the JJ is current across the resistor is The voltage source The total current is then Then the guage-invariant phase is current across the capacitor is AC Voltage Drive Image removed for copyright reasons. Please see: Figure 9.13, page 467, 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 9.14, page 468, 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 14 3______________________________________ AC Voltage vs Current Drives Image removed for copyright reasons. Please see: Figure 9.13, page 467, 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 9.14, page 469, 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 9.15, page 469, 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 14 Voltage Standard Image removed for copyright reasons. Please see: NIST (public domain) http://www.boulder.nist.gov/div814/div814/whatwedo/volt/dc/JVS.html10 V conventional Josephson voltage standard chip. The chip is 1 cm x 2 cm and contains 20,208 series connected Nb-AlOx -Nb junctions. http://www.boulder.nist.gov/div814/div814/whatwedo/volt/dc/JVS.html Massachusetts Institute of Technology 6.763 2005 Lecture 14 4HYPRES: Voltage Standard Chip HYPRES is the only commercial manufacturer of the superconducting integrated circuit used in Primary Voltage Standard Systems. HYPRES chips are used in the primary voltage standards in national laboratories around the world including Italy, France, United Kingdom, Australia, China, Malaysia, Japan, England, Canada, Norway, United States, Netherlands and Mexico. The HYPRES Josephson Junction Array Voltage Standard circuits provide the ultimate accuracy for realizing and maintaining the SI Volt. Features/Specifcations • Niobium/Aluminum Oxide/Niobium, SiO2 dielectric, Niobium wiring technology. • All Niobium technology. Refractory. Impervious to moisture and thermal cycling. • 20,208 Josephson junctions (10 V chip) 3,660 Josephson junctions (1 V chip) Image removed for copyright reasons. • 18 x 38 micrometers junction area. • Installed in a FR-4 epoxy glass mount. • RF input WR-12 waveguide flange. • RF Distribution - 16 way parallel x 1263 cells in series (10 V) - 4 way parallel x 915 cells in series (1 • Designed for a frequency range of 72-78 GHz • Operating temperature of 4.2 K • Common DC terminal resistance is < 1 Ohm - typical • Approximately 10 mW operating power at the input flange for 10 V chip (2 mW for 1 V) • -11V to +11 V range for 10 V chip. • -2.5 V to + 2.5 V range for 1 V chip. • Stability time is typically 1 hour for the 10 V chip, 5 hours for the 1V chip http://www.hypres.com/ • 0.005 PPM accuracy at 10 V (10 V chip) • 0.05 PPM accuracy at 1V (1V chip) • Calibration certificate supplied with each chip. • Two (2) year warranty Massachusetts Institute of Technology 6.763 2005 Lecture 14 Parametric Inductor ( ) inductance can s 0 and I0 + Is c, 0 ~ Ic sin φ, so that Image removed for copyright reasons. Please see: Figure 9.6, page 459, 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 14 Take the time derivative of the currents, and for the Josephson term: The parameteric time-dependent be defined as *On the zero-voltage branch, for I << I << I then I5Inductance along V=0 branch L[ Φ O ]2π IC | Φ [in Φο ] Massachusetts Institute of Technology 6.763 2005 Lecture 14 The DC SQUID (damped) Image removed for copyright reasons. Please see: Figure 9.16, page 471, from Orlando, T., and K. Delin. Foundations of Applied Superconductivity. Reading, MA: Addison-Wesley, 1991. ISBN: 0201183234. Our goal is to show that the DC SQUID circuit in (a) is equivalent to the circuit for a single junction with an effective Iand an effective c resistance. The