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 ypashkin@mail.ruPhysics 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

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

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

Fabrication of metallic nanostructuresElectron-beam lithography + angle deposition

(a) (b)

(c) (d)

Tunnel Junctions

Mask

evaporation angle

Al deposition at3 angles

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

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)

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:

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

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

Quantum technologies

Quantumsensing &imaging

Quantumcomputing

Quantumcryptography

Quantummetrology

Key areas of QT

Quantumelectromechanics

Quantumcommunication

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

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

QuantumtechnologyChemistry

Physics

Biology

Engineering

Quantum technology: interdisciplinary research

Part 2

Quantum bits withsuperconducting nanostructures

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)

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)

201

E

ng

12

01

201

1

reservoir

box

Adiabatic manipulation

201

E

ng

12

01

1

reservoir

box

cost+isint1

Nonadiabatic manipulation: t = +2 k

201

E

ng

12

01

1

reservoir

box

cost+isint1

Nonadiabatic manipulation t = 2 k

201

E

ng

12

01

cost+isint1

1

reservoir

box

cost+isint1

Nonadiabatic manipulation t k

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

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)

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)

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

Observation of quantum oscillationsY. Nakamura et al., Nature 398, 786 (1999)

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)

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>

Energy bands

E0

E1

E2

E3

double degeneracy

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

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

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)

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

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

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>

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

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