Superconducting electronics from Josephson effects to quantum computing

Superconducting electronics -from Josephson effects to quantum computing -by Pascal Febvre and Paul Seidel

Superconducting electronics – Part 2 Josephson junctions, arrays and SQUIDs

Josephson devices � Mainly thin film technology � Different types (SIS, SNS, SINIS, SFS, …) � Josephson � Complex junctions as active devices (e. g. mixers) superconducting circuits (e. g. RSFQ) � Different sensors (SQUIDs, SQUIFs, radiation detectors) 3

Thin film preparation methods [R. Wördenweber]

Patterning of films by lithography and etching

Arrays of Josephson junctions

Serial arrays for voltage standard [wikipedia]

[ J. Niemeier ] 9

SQUIDs Superconducting quantum interference devices �RF-SQUID �DC-SQUID �(D)ROS-SQUID �Digital SQUIDs �Π-SQUID �Supercond. Quantum interference filter (SQIF)

[Gallop]

RF-SQUID �non-linear inductance of Josephson junction gives a periodic modulation of the resonance frequency of the tank circuit �these changes follow the amplitude of the rf current for a given working frequency �response variies with Φ 0 = h/2 e = 2, 07 10 -15 Vs �advantage: no electrical contacts �disadvantage: noise of tank curcuit and amplifier large than intrinsic SQUID noise

RF-SQUID �Total flux Φ = Φex + LIC sin φ �Phase φ = 2 π Φ / Φ 0 �Φ = Φex + LIC sin (2 π Φ / Φ 0 ) �SQUID-Parameter ßrf = 2 π LIC / Φ 0

Characteristic of r. f. SQUID ßrf =0. 6 ßrf > 1

LIC = 1. 25 Φ 0 k = 0 ↔ k =1 [Ruggiero, Rudman]

Voltage of tank circuit (without noise) Q = RT/ωrf LT M = K (LLT)½ ωrf 20 MHz … 1 GHz Transfer function V Φ = ωrf LT / M

Transfer function �K can not be choosen too small ! �Irf has to cut the step for all flux values �for LIC ≈ Φ 0 follows K 2 Q ≥ π / 4 (≈ 1) �with K ≈ Q -1/2 results

With thermal noise

Noise of RF-SQUIDs �Intrinsic flux noise �Final step slope (thermal noise)

Energy resolution �Amplifier at room temperature and capacitive contributions of current lines result in an effective noise temperature

Parameter [SQUID Handbook]

Bulk (Zimmermann)SQUIDs

Transition to films [SQUID Handbook]

Zimmermann-SQUID IPTT Tschernogolovka/ FSU Jena about 1970 Niobium bulk Zimmermann-SQUID IPTM Tschernogolovka about 1975 Thin film –bulk hybrid technique [Meyer]

HTS-RF-SQUID [FZ Jülich]

Step-edge junction

HTS-RF-SQUID Resonator

Comparison of noise

Noise characteristics

Planar microwave SQUID

DC-SQUID

Interference of the ring currents �Current splitting �Ring current J → I = I 1 + I 2 I 1 = +J I 2 = � Josephson currents I 1 = Icsinφ1 I 2 = Icsinφ2 -J

1. ) for Ic 1 = Ic 2 = Ic (symmetrical) � Flux is external Flux plus self field by ring current Φ = Φex + LJ � Phase difference is 2π-periodical φ2 – φ1 = 2 π Φ / Φ 0 = 2 π (Φex + LJ) / Φ 0

2. ) Approximation without flux contribution of the ring current ( this current is in general J < Ic thus LJ < LIc → should be << Φ 0 /2, i. e. << 1 Inductance (Ring) Parameter

With this assumption it is Φ = Φex and thus follows I = Ic [sinφ1 + sin (φ1 + 2πΦex/Φ 0)] with δ = φ1 + π Φex/Φ 0 and simple transformatios for sin functions results in I = 2 Ic sinδ cos (πΦex /Φ 0)

SQUID Modulation

Integer values of flux Φex = n · Φ 0 cos = 1 Maximum value Is, max = 2 Ic obtained Ring current disappears (sinφ1 = sinφ2 = 1)

Half integer values of flux �Φex = (n+1/2) Φ 0, n = 0, ± 1, ± 2, … �Is, max = 0 �Ring current reaches maximum (± Ic)

DC-SQUID Modulation

Asymmetric case �Is, max = Ic 1 + Ic 2 �but Is, max (Φ) nearer to the maximum �Modulation amplitude becomes smaller �Dependence on βL �optimum βL~ 1 (Limit for Aeff at fixed L)

Inductance parameter ßL ßL = 2 LIC / Φ 0

Influence of asymmetry

SQUID and junction modulation

Energy resolution

FFL-Electronics (flux locked loop)

Flux modulation

[Drung]

Direct electronics with AFP (additional positive feedback) [Drung]

bias reversal

Gradiometer types

Wire incoupling structures [ J. Clarke ]

Multi channel gradiometer [ Biomagnetisches Zentrum der FSU Jena ]

LTS-SQUIDs

The Jena SQUID UJ 111

UJ 111 (with lead shield) FSU Jena 1984 Nb-Pb thin film technology

Niobium 8 layers YBCO 1 layer Grain boundary

Planar DC-SQUID Gradiometer Superconducting antenna I 2 FSQ I 1 -I 2 B 1 B 2 Magnetic flux within SQUID

F. Schmidl, A. Zakasarenko, E. Il`ichev, P. Seidel

HTS DC-SQUID Gradiometer

Flux transformer

Pi-SQUIDs

[Chesca]

Comparison

Relaxation Oszillation SQUIDs

Digital SQUIDs

Quantum interference filter (SQIF) 30 JJ SQIF and a simple SQUID of same size [Oppenländer, Schopohl]

Serial SQIF [Schultze]

2 p. T / √ Hz [IPHT Jena]}

2 D- SQIF array [R. Fagaly]

Bi-SQUID [R. Fagaly]