Page 1
Y. Nakamura, O. Astafiev, T. Yamamoto, S. Kafanov, J. S. Tsai
J.P. Pekola, O.-P. Saira, M.M. Möttönen (Aalto U)
A. Kemppinen, V.F. Maisi (MIKES)
F. Hoehne (TU Munich)
D.V. Averin (SUNY)
Yuri Pashkin [email protected] Department, Lancaster University, UK
NEC Smart Energy Research Laboratoriesand RIKEN Advanced Science Institute, Japan
Until 2007: Fundamental Research LaboratoriesUntil 2010: Nano Electronics Research Labs.Until 2012; Green Innovation Research Labs.
Tsukuba, Ibaraki, Japan
Superconducting nanostructuresfor quantum technologies
Windsor Summer School – 15 August 2012
Page 2
This presentation (2 talks)
1. Introduction
2. Quantum bits with superconducting nanostructures
A. Single charge qubit
B. Coupled charge qubits (quantum beatings)
3. Charge pumping with Coulomb blockade devices
A. Incoherent charge pumping
B. Coherent charge pumping
Page 3
Tsukuba history 1997 - 2012
Al tunnel-junction nanoelectronic devices
1stdeposition
~ 15 nm
2nd deposition~ 6 nm
Single-electron transistors
Charge qubits
single qubitcoupled qubits
С-transistor suspended C-transistor
Electron pumps
Al/AlOx/Altunnel
junctions
Cr gate
Al island
200 nm
R-transistor
Page 4
Fabrication of metallic nanostructuresElectron-beam lithography + angle deposition
(a) (b)
(c) (d)
Tunnel Junctions
Mask
evaporation angle
Al deposition at3 angles
Page 5
Coulomb blockade
e
E Ec = e2/2C
C (F) 0.8х10-15 0.8х10-16 0.8х10-17 0.8х10-18
Ec 100 eV 1 meV 10 meV 0.1 eVEc/kB (К) 1 10 100 1000
Page 6
E = q2/2C
CgU/e
C
U
Cg
CgU - ne
n = -1 n = 0 n = 1 n = 2
210-1
Ec/4
n
0-1
12
Ec >> kBT
Ec << kBT
Single-electron box
Saclay group, 1991)
Page 7
Single-electron transistor (SET)
V
Vg
NN+1
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
-0.06
-0.03
0.00
0.03
0.06
0.09
CgVg = e/2
CgVg = eT = 4.2 K
Cur
rent
(nA
)
Voltage (V)
Conditions: kBT << Ec e2/2CR >> RQ h/4e2 6.5 k
source drain
gateCg
C1 C2
e e
Averin, Likharev (1986) theoryFulton, Dolan (1987) exp.
Coulomb blockadee-periodic modulation on Qg
Coulomb staircaseCharge sensitivity 10-3 e/Hz1/2 in dc
10-5 e/Hz1/2 in rf
Features:
Page 8
Lancaster history 2012
Research on solid-state quantum nanostructures looking for novel physical phenomena
developing high-end instrumentation
Three major fields: quantum superconducting circuits
quantum metrology
quantum nanoelectromechanics
LU Quantum Technology Centre
Newly built class 100 cleanroom: Electron-beam writer JEOL JBX-5500FS
deposition and etching machines
Cryogenic and measurement facilities
Page 9
What is quantum technology?
Build and control quantum systems for practical purposes
Control = - tune energy levels- prepare a system in a well-defined initial state- manipulate the system- do measurement
Page 10
Quantum technologies
Quantumsensing &imaging
Quantumcomputing
Quantumcryptography
Quantummetrology
Key areas of QT
Quantumelectromechanics
Quantumcommunication
Page 11
The second quantum revolution
Jonathan P. Dowling, Gerard J. Milburn (2002)
- use the rules to develop new technologies/applications
The first quantum revolution
- understand new rules that govern physical reality
Page 12
Two generations of quantum technologies“Quantum technologies: an old new story”, Physics World , May 2012
Iulla Georgescu and Franco Nori
1st-generation quantum technologies
2nd-generation quantum technologies
Concept Technology
spin
tunneling
superposition and
entanglement
• NMR, ESR• GMR (hard discs, MRAM)• STM• tunneling diodes• Josephson junction, SQUIDs
• quantum computing• quantum simulation• quantum communication• quantum random number generation• quantum imaging
Page 13
QuantumtechnologyChemistry
Physics
Biology
Engineering
Quantum technology: interdisciplinary research
Page 14
Part 2
Quantum bits withsuperconducting nanostructures
Page 15
E = q2/2C
CgVg/2e
C
Vg
Cg
CgVg - 2ne
n = -1 n = 0 n = 1 n = 2
210-1
Ec
n
0-1
12
Ec >> EJ, kBT
Ec << EJ, kBT
EJ
Cooper pair box
Two-level system
M. Büttiker (1987)V. Bouchiat et al. (1995)
Page 16
gate
++++
reservoirisland = Cooper-pair box
- - - -
• two-level system• ~108 conduction electrons
n
kTEEE
JC
C
4
n=0 1
Cooper-pairtunneling
E = (CgVg – 2ne)2/2C
Charge qubit
1
0
21
21
EE
EEH
J
J
0 1
0
1
21
20
2/1
2/0
eQEE
eQEE
gc
gc
V. Bouchiat et al. (1995)
Page 17
201
E
ng
12
01
201
1
reservoir
box
Adiabatic manipulation
Page 18
201
E
ng
12
01
1
reservoir
box
cost+isint1
Nonadiabatic manipulation: t = +2 k
Page 19
201
E
ng
12
01
1
reservoir
box
cost+isint1
Nonadiabatic manipulation t = 2 k
Page 20
201
E
ng
12
01
cost+isint1
1
reservoir
box
cost+isint1
Nonadiabatic manipulation t k
Page 21
Josephson-quasiparticle cycle (Fulton et al., 1989)
2e
Cooper-pair box
JE
qp1 JE• detection of state• initialization to the initial state
10
CC EeVE 322
ee
qp1
qp2
+ probe
Final state readout
Page 22
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
Dc sweep + pulses (1)
Page 23
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
0.40 0.45 0.50 0.55 0.60 0.65
2
3
4
5
6
7
8
9
10
C
urre
nt (p
A)
Gate voltage (V)
Imax = 2e/Tr = 5 pA
2.5 pA
Dc sweep + pulses (2)
Page 24
dc JQP peakpulse-inducedoscillations
70.00
0.005.00
10.0015.0020.0025.0030.0035.0040.0045.0050.0055.0060.0065.00
0.680.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66
t = 80 ps
t = 1 ns
Dc sweep + pulses (3)
tnon-adiabaticpulse
Page 25
Observation of quantum oscillationsY. Nakamura et al., Nature 398, 786 (1999)
Page 26
Coupled charge qubits
gate 2gate 1
probe 1probe 2
reservoir 2
qubit 2
reservoir 1
qubit 1
1 m
cross-section
capacitive coupling
остров 2 остров 1
I1 and I2 give info aboutcharge states
I2 I1
Vb2 Vb1
Vp Vg1Vg2
pulsegate
Yu.A. Pashkin et al., Nature 421, 823 (2003)
Page 27
HamiltonianCharge basis
En1n2 = Ec1(ng1–n1)² + Ec2(ng2–n2)² + Em(ng1–n1)(ng2–n2)
Ec1,2 = 4e²CΣ2,1/2(CΣ1,2CΣ2,1 – Cm²) 4e²/2CΣ1,2
ng1,2 = (Cg1,2Vg1,2 + CpVp)/2e
Em = 4e²Cm/(CΣ1CΣ2 – Cm2)
1112
1012
2101
2100
21
210
210
21
210
21
021
21
EEE
EEE
EEE
EEE
H
JJ
JJ
JJ
JJ
I00> I10> I01> I11>
I00>
I10>
I01>
I11>
initial state
EJ1,2 ~ Em < Ec1,2
I00>
Page 28
Energy bands
E0
E1
E2
E3
double degeneracy
Page 29
Quantum evolution at double degeneracy
pulsegate
gate 1gate 2
10.50
10.
50
n g2
ng1
0,0
0,1
1,0
1,1
ng1 (= ng2)
врем
я
superposition of four states
I1I2
X
0,1
1,0
0,0
1,1
11011000)( 4321 cccct
E00 = E11E10 = E01
Page 30
Quantum beatings
))cos()1())cos()1(241
)1( 24
2322
tt
ccpI
operation point
ng1 (= ng2)0.50.45
p1
p2
time, ps0 1000
+
-
2f
+ 2
-
2
00exp)(
Htit
11011000)( 4321 cccct
Page 31
Quantum beatings: experiment
Expected from the modelEJ1 = 13.4 GHzEJ2 = 9.1 GHzEm = 15.7 GHz
10.50
10.
50
n g2
ng1
0,0
0,1
1,0
1,1
L RX
- +
0.6 нс
2.5 нс
EJ1
EJ2
01234
01234
01234
0.0 0.2 0.4 0.6 0.8 1.001234
0 10 20 30
I 1 (p
A)
I 2 (p
A)
I 1 (p
A)
I 2 (p
A)
t (ns)
13.4 GHz
9.1 GHz
f (GHz)
Page 32
EJ1 dependence of frequencies
Em2
effect of coupling!
Em = 14.5 GHzdc measurement:Em = 15.7 GHz
EJ2 = 9.1 GHz
max EJ1 = 13.4 GHz
0 2 4 6 8 10 12 140
5
10
15
1st qubit
EJ1/hfr
eque
ncy
(GH
z)
EJ1 (GHz)
EJ2/h
fit2nd qubit
Page 33
Analogy with two coupled classical oscillators
1 2 2
1
2
1
21
2 112
with coupling
Difference?
oscillation of:C.: physical parameter xQ.: probability p(x) to be in 0 or 1
L
C
M
1 2
without coupling
Page 34
Entanglement of two coupled qubits
Entangled qubits: BA
11011000 4321 cccc If
11002
1
01102
1
maximallyentangledstates, E = 1
Entropy of entanglement:
BBAA TrTrE 22 loglog
our qubits EJ1 = 9.1 GHzEJ2 = 9.1 GHzEm = 14.5 GHz
0 500 10000.0
0.5
1.0
Ent
ropy
of e
ntan
glem
ent
Time (ps)
0 500 10000.0
0.5
1.0
Abs
[ci]
Time (ps)
“almost”maximally entangled state
I00>
I10> and I01>
I11>
Page 35
artificial atoms
on Si chips
Chalmers
TU Delft
Superconducting circuits with quantum coherence
2 m
NEC
charge qubitsYale, JPL
flux qubitsNTT, Jena
phase qubitsKansas,Maryland,UCSB
Saclay
quantronium
NECfirst solid-state qubit
1m
NIST
fluxoniumYale
transmonYale,ETH
Page 36
Solid-state quantum computing
Proof-of-principles phase passed
- single qubits demonstrated
- interqubit coupling
- quantum logic gates
- decoherence sources identified
Remaining issues
- increase coherence time
- switchable interqubit coupling