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Applied Superconductivity
Josephson Effects, Superconducting Electronics,
and Quantum Circuits
Lecture Notes Summer Semester 2013
R. Gross and F. Deppe
© Walther-Meißner-Institut
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Intro - 2
General Remarks on the Courses to the Field
Superconductivity and Low Temperature Physics
The following lectures are offered on a regular basis: 1. Superconductivity and Low Temperature Physics I
Foundations of Superconductivity
2. Superconductivity and Low Temperature Physics II (SS 2013: Thu., 12:30h, HS 3) Foundations of Low Temperature Physics and Techniques
3. Applied Superconductivity Josephson-Effects, Superconducting Electronics, Quantum Circuits
4. Several Seminars (see announcements)
Documents and Hints: http://www.wmi.badw.de Teaching (announcement of lectures) Lecture Notes (download of scripts, handouts, etc.)
Seminars (announcement of seminars)
SS 2013: - Advances in Solid-State Physics Tue. 10:15 – 11:30h Seminar room 143, WMI - Superconducting Quantum Circuits Tue. 14:30 – 16:00h Library, WMI
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Intro - 3
Applied Superconductivity Superconductivity and Low Temperature Physics II
Spin Electronics
Sum
mer
Sem
este
r 2
01
3
VO, ÜB,
Skript
Seminar: Superconducting Quantum Circuits
Tue., 14.30 – 16.00 h, Seminar room, WMI
Seminar: Advances in Solid State Physics
Tue., 10.15 – 11.45 h, Seminar room, WMI
Seminar: Spin Mechanics and Spin Dynamics
Wed., 10.15 – 11.45 h Seminar room, WMI
Mon. and Wed., 14.15 – 15.45 h Seminar room, WMI
Tue, 13.30 – 15.00 h Seminar room, WMI
VO, ÜB,
Skript
VO, ÜB,
Skript
Rudolf Gross Frank Deppe
Thu, 12.30 – 14.00 h Physics Department, HS3
Hans Hübl
S. Gönnenwein
Walther-Meißner-Institut (www.wmi.badw.de)
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Intro - 5
I Foundations of the Josephson Effect
1 Macroscopic Quantum Phenomena 1.1 The Macroscopic Quantum Model of Superconductivity 1.2 Fluxoid/Flux Quantization 1.3 Josephson Effect
2 JJs: The Zero Voltage State 2.1 Basic Properties of Lumped Josephson 2.2 Short Josephson Junctions 2.3 Long Josephson Junctions
3 JJs: The Voltage State 3.1 The Basic Equation of the Lumped Josephson Junction 3.2 The Resistively and Capacitively Shunted Junction Model 3.3 Response to Driving Sources 3.4 Additional Topic: Effect of Thermal Fluctuations 3.5 Secondary Quantum Macroscopic Effects 3.6 Voltage State of Extended Josephson Junctions
Contents of Lecture
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Intro - 6
Contents of Lecture
II Applications of the Josephson Effect
4 SQUIDs
4.1 The dc-SQUID 4.2 The rf-SQUID 4.3 Additional Topic: Other SQUID Configurations 4.4 Instruments Based on SQUIDs 4.5 Applications of SQUIDs
5 Digital Electronics
5.1 Superconductivity and Digital Electronics 5.2 Voltage State Josephson Logic 5.3 RSFQ Logic 5.4 Analog-to-Digital Converters
6 The Josephson Voltage Standard
6.1 Voltage Standards 6.2 The Josephson Voltage Standard 6.3 Programmable Josephson Voltage Standard
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Intro - 7
7 Superconducting Photon and Particle Detectors 7.1 Superconducting Microwave Detectors: Heterodyne 7.2 Superconducting Microwave Detectors: Direct Detectors 7.3 Thermal Detectors 7.4 Superconducting Particle and Single Photon Detectors 7.5 Other Detectors
8 Microwave Applications
8.1 High Frequency Properties of Superconductors 8.2 Superconducting Resonators and Filters 8.3 Superconducting Microwave Sources
Contents of Lecture
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Intro - 8
III Superconducting Quantum Circuits
Contents of Lecture
9 Superconducting Quantum Bits 9.1 Quantum Bits and Quantum Computers 9.2 Implementation of Quantum Bits 9.3 Why Superconducting Qubits
10 Superconducting Circuit Quantum Electrodynamics (circuit-QED) 10.1 Light-matter interaction 10.2 Cavity vs. Circuit QED 10.3 Ultra-strong coupling
11 Quantum Microwaves 11.1 Dual-path tomography of propagating quantum microwaves 11.2 Planck spectroscopy 11.3 Path entanglement of continuous-variable quantum microwaves
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Intro - 9
Werner Buckel, Reinhold Kleiner, Supraleitung – Grundlagen und Anwendungen, VCH-Verlag, Weinheim (2012).
R. Gross, A. Marx Festkörperphysik, Oldenbourg-Verlag (2012).
M. Tinkham, Introduction to Superconductivity, McGraw-Hill, New York (1975).
K. K. Likharev, Dynamics of Josephson Junctions and Circuits, Gordon and Breach Science Publishers, New York (1986).
T. P. Orlando, K. A. Delin, Foundations of Applied Superconductivity, Addison-Wesley, New York (1991).
Vorlesungsskript: R. Gross, A. Marx, http://www.wmi.badw.de/teaching/Lecturenotes/index.html
Bibliography
Introduction
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Intro - 11
Temperature Scale
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
tem
per
atu
re (
K)
same amount of new physics on every decade of log T scale
center of hottest stars
center of the sun, nuclear energies
electronic energies, chemical bonding
surface of sun, highest boiling temperatures
organic life
liquid air
liquid 4He universe
superfluid 3He
lowest temperatures of condensed matter
elec
tro
nic
m
ag
net
ism
nu
clea
r-
ma
gn
etis
m
sup
erco
nd
uct
ivit
y
low
te
mp
era
ture
re
se
arc
h
lowest temperature in nuclear spin system achieved by adiabatic demagnetization of Rhodium nuclei: ≈ 100 pK
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Intro - 13
Carl Paul Gottfried von Linde * 11. Juni 1842 in Berndorf, Oberfranken
† 16. November 1934 in Munich
Low Temperature Technology in Germany
1868 offer of chair at the Polytechnische Schule München (now TUM)
1873 development of cooling machine allowing the temperature stabilization in beer brewing
21. 6. 1879 foundation of „Gesellschaft für Linde’s Eismaschinen AG“ together with two beer brewers and three other co-founders
1892 - 1910 re-establishment of professorship
12.5.1903 patent application: „Lindesches Gegenstrom- verfahren“ liquefaction of oxygen (-182°C = 90 K)
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Intro - 14
• Helium liquefaction: 1908 • discovery of superconductivity: 1911 H. K. Onnes, Comm. Leiden 120b (1911)
Nobel Price in Physics 1913
Discovery of Superconductivity (1911)
choice of name:
infinite electrical conductivity
He
ike
Kam
me
rlin
gh O
nn
es
(18
53
-19
26
)
superconductivity
Universität Leiden (1911)
Tc = - 269°C
Hg
Temperatur (K) W
ider
stan
d
(W)
<
"for his investigations on the properties of matter at low temperatures which led, inter alia to the production of liquid helium"
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Intro - 16
Kammerlingh Onnes and van der Waals
Kammerlingh Onnes and technician Flim
Discovery of Superconductivity (1911)
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Intro - 17
path dependent final state of the perfect conductor
perfect conductor in magnetic field
increase Bext
increase
Bext
decrease T
decrease T
C
C PC
PC PC
conductor
perfect conductor PC
PC
switch off Bext
Perfect conductor in magnetic field
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Intro - 18
perfect diamagnetism
Walther Meißner (1882 – 1974)
Discovery of the Meißner-Ochsenfeld Effect (1933)
Robert Ochsenfeld (1901 – 1993)
W. Meißner, R. Ochsenfeld, Ein neuer Effekt bei Eintritt der Supraleitfähigkeit, Naturwissenschaften 21, 787 (1933).
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Intro - 19
Wa
lth
er M
eiß
ner
(1
88
2 –
19
74
)
superconductors perfectly expel magnetic field
ideal diamagnetism, c = – 1
0 1 exin BB c
choice of name for perfect diamagnetism:
Meißner-Ochsenfeld Effect
superconductor
T > TC T < TC
B B
(c = magnetic susceptibility
Discovery of the Meißner-Ochsenfeld Effect (1933)
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Intro - 20
superconductor in magnetic field
Meißner-Ochsenfeld- Effect
or
perfect diamagnetism
super- conductor
C
C
SC SC
SC
increase
Bext
decrease T
increase Bext
decrease T
switch off Bext
SC
SC conductor
path independent final state of the superconductor
superconducting state is a
thermodynamic phase
Superconductor in magnetic field
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Intro - 21
Walther Meißner * 16. Dezember 1882 in Berlin
† 15. November 1974 in Munich
1913 – 1934 building and heading of low temperature laboratory at the Physikalisch-Technischen- Reichsanstalt, liquefaction of H2 (20K)
7.3.1925 first liquefaction of He in Germany (4.2 K, 200 ml), 3rd system world-wide besides Leiden and Toronto
1933 discovery of perfect diamagnetism of superconductors together with Ochsenfeld Meißner-Ochsenfeld Effect
1934 offer of chair at the Technische Hochschule München (now TUM)
1946 – 1950 president of the Bayerischen Akademie der Wissenschaften
1946 foundation of the commission for Low Temperature Research Walther-Meißner-Institut
Walther Meißner (1882 – 1974)
Walther Meißner - der Mann, mit dem die Kälte kam W. Buck, D. Einzel, R. Gross, Physik Journal, Mai 2013
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Intro - 25
1935 Fritz and Heinz London
first „quantum mechanical“
theory of superconductivity
(phenomenological)
macroscopic wave function
London equations
Fritz London (1900 – 1954)
Theory of Superconductivity
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Intro - 27
Alexei Abrikosov Lev Landau Vitaly Ginzburg
Nobel Prize 2003 Nobel Prize 2003 Nobel Prize 1962
Ginzburg-Landau Theory (1952)
"for his pioneering theories for condensed matter, especially liquid helium"
Nobel Prize in Physics 1962
Lev Davidovich Landau
“for their pioneering contributions to the theory of superconductors and superfluids”
Vitaly Ginzburg, Alexei Abrikosov
Nobel Prize in Physics 2003
(together with Anthony Leggett)
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Intro - 29
Tag der Physik 07. 07. 2000
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Intro - 30
J. Bardeen L. N. Cooper R. Schrieffer
Microscopic (BCS) Theory (1957)
Nobel Prize in Physics 1972
"for their jointly developed theory of superconductivity, usually called the BCS-theory"
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Intro - 31
Flux Quantization (1961)
R. Doll M. Näbauer
B.S. Deaver W.M. Fairbank
• Robert Doll Martin Näbauer (Wather-Meißner-Institut)
• Bascom S. Deaver William Martin Fairbanks (Stanford University)
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Intro - 32
Flux Quantization
(a) (b)
-0.1 0.0 0.1 0.2 0.3 0.4-1
0
1
2
3
4
reso
na
nce
am
plitu
de
(m
m/G
au
ss)
Bcool
(Gauss)
0.0 0.1 0.2 0.3 0.40
1
2
3
4
tra
pp
ed
ma
gn
etic f
lux (
h/2
e)
Bcool
(Gauss)
F0
prediction by Fritz London: h/e first experimental evidence for the existence of Cooper pairs
Paarweise im Fluss D. Einzel, R. Gross, Physik Journal 10, No. 6, 45-48 (2011)
R. Doll, M. Näbauer Phys. Rev. Lett. 7, 51 (1961)
B.S. Deaver, W.M. Fairbank Phys. Rev. Lett. 7, 43 (1961)
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Intro - 34
Brian David Josephson (geb. 04. 01. 1940)
Prediction of the Josephson Effect (1962)
(together with Leo Esaki and Ivar Giaever)
Nobel Prize in Physics 1973
"for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects"
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Intro - 35
Johannes Georg Bednorz * 16. Mai 1950 in Neuenkirchen im Kreis Steinfurt
Karl Alexander Müller * 20. April 1927 in Basel)
Discovery of the High Tc Superconductivity (1986)
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Intro - 36
Discovery of the High Tc Superconductivity (1986)
J. Georg Bednorz (b. 1950) K. Alexander Müller (b. 1927)
"for their important break-through in the discovery of superconductivity in ceramic materials"
Nobel Prize in Physics 1987
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Intro - 37
Energy Technology Generators, motors
Trasnformers Fault current Limiters
Magnetic energy storage Cables
Applications of Superconductivity
Electronics Sensors (e.g. SQUIDs)
RSFQ Logic Quantum Computing
Medical Technology Magnetic Resonance Imaging
Magneto-encephalography Magneto-cardiography
Traffic Ship motors
Superconducting levitation trains
Processing Separation of ore Water treatment
Microwave Technology Filters, Antennas
Cavities Mixers, Sources,
Receivers
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Intro - 39
Superconducting Wires, Tapes, and Cables
Superconducting Wires: NbTi, Nb3Sn in Cu-matrix
HTS tapes
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Intro - 41
Applications of superconductivity
• power applications (transport and storage
of energy energy storage (2 MJ)
current limiter
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Intro - 42
Fault Current Limiters
(Source: Physik Journal 6, 2011)
superconducting fault current limiter in the power station Boxberg of Vattenfall
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Intro - 43
Generators
(Source: Physik Journal 6, 2011)
superconducting rotor for hydroelectric power station
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Intro - 44
Superconducting Magnets
(So
urc
e: P
hys
ik J
ou
rnal
6, 2
01
1)
production of superconducting solenoids for MRI systems at Siemens, Erlangen
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Intro - 45
• transportation systems and traffic
maximum velocity:
581 km/h (02. 12. 2003)
Jap. Yamanashi MAGLEV-System
MLX01
(42.8 km long test track between Sakaigawa and Akiyama, Japan)
Applications of superconductivity
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Intro - 46
Atlas detector
high energy physics • superconducting magnets
MRI systems
fusion
Applications of superconductivity
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Intro - 48
high-field MRI system (for whole-body tomography)
MAGNETOM® AERA 1.5T
integrated MRI-PET system Siemens Biograph-mMR, 3 T
Applications of superconductivity
MRI Systems
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Intro - 49
Electronics Applications
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Intro - 50
• sensors and detectors
microwave receivers
Quantum interference detectors
Applications of superconductivity
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Intro - 52
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
B (Tesla)
earth magnetic field
urban noise
car @ 50m
screw driver @ 2m
transistor, IC chip @ 2m
single transistor @ 1m
car @ 2km
lung particle
human heart muscles
foetal heart human eye human brain (a)
human brain (stimulated) foetal brain
biomagnetic signals environmental noise signals
Biomagnetism
Superconducting Quantum Interference
Detector (SQUID)
sensitivity: a few fT/√Hz
1 mm PTB Berlin
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Intro - 53
Biomagnetism
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Intro - 54
Source: K. K. Likharev, SUNY Stony Brook
Josephson Computer
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Intro - 55
________________________
Stony Brook ____________________________________________
PetaFLOPS Scale Computing:
Speed and Power Scales (Year 2006)
Semiconductors (CMOS)
Performance: > 105 chips @ 10 GFLOPS each Power: ≈ 150 W per chip total > 15 MW
Footprint: >30 x 30 m2 latency > 3 ms
Superconductors (RSFQ)
Performance: 4·103 processors @ 256 GFLOPS each Power: ≈ 0.05 W per PE node total 250 W @ 5 K (100 kW @ 300 K) Footprint: 1 x 1 m2 latency 20 ns
Source: K. K. Likharev, SUNY
Rapid Single Flux Quantum (RSFQ) Logic
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Intro - 56
Intel dual-core 45 nm
(2007)
first transistor (1947)
Bardeen, Brattain, & Shockley
vacuum tubes
ENIAC (1946)
Enigma (1940)
physics
technology
superconducting Qubit
20 µm
WMI
From mechanical to quantum mechanical IP
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Flux Qubit
coplanar waveguide resonator 1.25 GHz
Q > 105
hybrid ring S23 = - 3 dB S31 = - 50 dB
Superconducting Quantum Circuits
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The Nobel Prize in Physics 2012
David J. Wineland Serge Haroche
The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"
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study of light – matter interaction on a fundamental quantum level
Light-matter interaction
• consequences of quantum nature of light on light-matter interaction
• quantum mechanical control and manipulation of light and matter
basis for quantum information technology
Cavity QED
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why artificial atoms?
- tunability of (by design & in experiment)
• transition frequency
• selection rules / symmetry
- (ultra) strong coupling to resonator modes
Light-matter interaction
T. Niemczyk et al., Nature Physics 6, 772 (2010)
F. Deppe et al. , Nature Physics 4, 686 (2008) T. Niemczyk et al., arXiv:1107.0810v1
Circuit QED
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Prospects of Circuit QED systems
fundamental quantum
experiments
solid state quantum technology &
quantum sensors
quantum information &
communication
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Collaborative Research Center 631: Solid State Quantum Information Processing
spokesman: R. Gross
Quantum Information Processing
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Cluster of Excellence Nanosystems Initiative Munich (NIM)
spokesman: J. Feldmann coordinator of RA I -Quantum Nanophysics: R. Gross
Nanosystems
