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Quantum experiments in superconducting nano-circuits

Olivier BuissonInstitut Néel

Equipe Cohérence Quantique

PrésentationOlivier Buisson47 ansDirecteur de recherches à l’Institut Néel-CNRS-UJF-INP

Parcours scientifique:Ingénieur physicien de l’INPG de 1984 -1987“Master” Physique de la Matière et du Rayonnement

Thèse en 1990 (CRTBT-CNRS et CNET Grenoble)

Post-doctorat (coopération) à Rio de Janeiro (1990-1991)

Embauche au CRTBT (1991)De 1991 à 1999, études des modes plasma 2D et 1D dans les

supraconducteurs

En 1999, Projet sur les circuits quantiques supraconducteurs

Activités actuelles

Responsable d’un projet scientifique:- définir et réaliser de nouvelles expériences de recherches- encadrement d’étudiants, thèsards et post-doc- rédaction de publications, séminaires, conférences- projet pour financer les études scientifiques

- CNRS (salaires, gros équipements, soutiens techniques,…)- RTRA (gros équipements, bourses)- ANR (ministère) (équipements, fonctionnements, missions,…)- CEE (équipements, fonctionnements, missions, bourses…)

Administration:- responsable d’une équipe de dix chercheurs- comité de pilotage de la Fondation Nanosciences- participation à la vie de l’Institut- jury de theses, évaluation des publications

Enseignement:- master énergétique-physique (2004-2008)- …

Quantum experiments in superconducting nano-circuits

PhD students :B. DelsolE. DumurT. Weissl

Past PhD students:F. Lecocq (2011) Post-doc in USAA. Fay (2008) Post-doc in HelsinkiJ. Claudon(2005) Researcher in CEAF. Balestro (2003) Asssitant Prof. UJF

Permanent researchers :W. GuichardF.W.J. HekkingR. KramerL. LévyC. NaudO. BuissonB. Pannetier

Post-doc:A. FeofanovI. MateiG. Rastelli

Out-line

- Motivation to study quantum electrons properties and quantum transport

- Introduction to superconductivity

- Superconducting Josephson junction circuits

- Realisation of quantum experiments

- Conclusion

10µm

New physics in the nano-circuitsElectronics circuits are smaller and smaller

Quantum phenomena appear!

Quantum phenomena a new physics for electrons inside a circuit

substratchannel

V Gate

source

Field Effect Transistor

drainI

Description of the electrons by waves

Quantum noise due to small current (electron one by one)

Single electron effects (Coulomb blockade,…)

Quantum tunnelling between gate and channel

10µm

New nano-electronics device

Nanowire transport:Molecule transport:

Quantum mechanics is the basis of these new device

Nanotube

500 nmW. Wernsdorfer et al. (Neel Institute)

F. Balestro, et al (Neel Institute)

V. Bouchiat, C. Naud, et al (Neel Institute)

Nano- transistor:

X. Jelh et al (INAC)

Graphene transport:

10µm

New engineering domain

Current engineering - destroy the quantum effects- avoid its perturbation

(high dielectric, losses, …)

Take advantage of quantum effects to build new electronics

- single electron transistor- interference device- high sensitive detectors- current standard (metrology)- …- artificial atom

Quantum engineering:

Single electron transistor

0.5 mVg

Vg

Single electron quantum box

n=0 n=2n=1 n=3

Energy

Vg

C2/e)(E 2c n

Quantum Coherence of the electrons

Scattering Centers

Incident electron

Constructive interferences

B

-12000 -11000 -10000

-8

-4

0

4

8

B (G)

square 3*105

BSe

Ahronov-Bohm oscillations

R(1

0-5

)

L. Saminadayar and C. Bauerle, et al (Neel Institute)

Interference effects of theelectronic wavefunction !

Quantum Coherence of the electrons

Scattering Centers

Incident electron

Destructive interferences

B

-12000 -11000 -10000

-8

-4

0

4

8

B (G)

square 3*105

BSe

Ahronov-Bohm oscillations

R(1

0-5

)

Inelastic or dephasing scattering

Open questions: - electron-electron interaction- electron-spin (magnetic impurities interaction (Kondo effects)- electron-photon interaction

Superconductivity

Introduction of the superconducting state

G ( r)=ns (r)1/2 ei(r)

2e

e

The Cooper pairs or superconducting electrons are described by a macroscopic |G > quantum ground state- the phase ( r) is very well defined- ns ( r)1/2 Cooper pair density

Normal electron

New properties because of the phase of the wave function

T<Tc R=0 at 10-19

H. K. Onnes (1911)

Superconductor: many metals (Pb, Nb, Al, …) but not Cu, Au, Pt, …- YBaCuO, HgSrCaCuO (Tc ~150K)- recently MgB2 , FeCuSrBaYCuO, ….

|G > is a very stable because no excitations below the gap

Ib

)/cos(2)( 0max cII

Superconducting Quantum Interfermoeter Device: SQUID

Interferometry experiments with the superconducting electrons!!!

I max

(A

)

B

Is1 Is2

Max (Is1 +Is2 ) depends on

2150 10 07.22 Tme

h where

0/22 BSe

B=0

H

B=0 (H+M)=0M=-H!

Perfect diamagnetism+ Expulsion of magnetic field(Meissner effect)

B>0

Superconductivity in presence of a magnetic field

High magnetic fieldLow magnetic field

Magnetic flux:

0 nBSFlux quantization

K. Hasselbach (Néel)

Observation of flux quantization (vortex)

Superconductivity in presence of a magnetic field

Levitation experiments:

Thanks to P. F. Sibeud and F. Lévy-Bertrand (CRETA-NEEL-CNRS)

Beyond the ground state physics?

Intermediate conclusion

Electrons in nano-circuit:- charge quantization- single electron transistor- interference effects

Superconducting circuits:- macroscopic quantum states- vortex - flux quantization

Quantum properties of the ground state

Quantum states:artificial atoms

Nanofabrication:confined electrons

e-i(E1-E0)t/h

E0

E1

0.5 m

e 2e

Spins

Artificial atoms

T. Meunier, et al (Neel Institute)X. Jehl (INAC)

Semiconducting qubitSuperconducting qubits

W. Guichard and O.B. (Neel Institute)M. Hofheinz (INAC)

Cooper pair transistor Josephson junction

Quantum coherence scales

Nanoscale: a=10-100nm

2

2

2

2

12

2

aCeavma

F

HzKJouleE 1023 10110

Dilution fridge Microwave techniques

Quantum experiments:

Quantized energy levels: small sizeQuantum limit: very low temperature

Interaction artificial atom and photon: high frequency

Energy scales:

Nanofabrication

Current compromise:

Common techniques!

a: the size

Josephson junctions fabrication

The Josephson junctionCoupling between two superconductors : a tunnel barrier

ns

Tunnel barrierx

n1e i 1

Supra 1 Supra 2n 2 e i 2

AlAl

AlOx

Si

SiO

200nm

The Controlled Undercut Technique

LowDose

After development:E-beam exposure

Florent Lecocq Thesis

NanoFab

The Controlled Undercut Technique

1st evaporation

b)

max

min

SS

2nd evaporationOxydation

Florent Lecocq Thesis

The Controlled Undercut Technique

max

min

SS

After removing resist

Florent Lecocq Thesis

b)

View cut:

The Controlled Undercut Technique

max

min

SS

After removing resist

Superconducting nano-circuitsdynamics

The Josephson junction

For I<Ic , R=0 : superconducting current through an insulator!!!

I

2e

Ic

RnV

Cooper pair tunneling

Josephson equations :Is Ic sin( )

V 0

2ddt

Ic

2eRn

where 21

Is

V

n1e i 1

Supra 1 Supra 2n 2 e i 2

Cooper pair tunnelling:

Linear approximation: dtdI

IVII s

ccs 2

0

Inductance behaviour !

The capacitive Josephson junction

Id

V

n1e i 1

Supra 1 Supra 2n 2 e i 2

Ib = Id + Is

Current conservation:

C dVdt

Ib Ic sin

V

Ib

C

Id Is

sin

220

2

220

c

bc

III

dtdC

21

Mechanical analogy

sin

220

2

220

c

bc

III

dtdC

dU( )

dmass: m

A fictitious particle of mass m in a potential U()

V

Ib

C

Id Is

U

)cos(22)( 00 cb IIU

where

force:

Ib : the slope

Linear approximation

Equivalent to an harmonic oscillator!

V

Ib

C

IdLJ

Is

U (Ib ,)

p (Ib )

V

Ib

C

Id Is

p (Ib )

2221 ~~ QH p

Quantum harmonic oscillator

Properties:

p (Ib )

Is =Ic sinQ

iQ ]~,~[

ˆ Q and ˆ are conjugate variables-- eigenstates |0>, |1>, |2>, …- energy level quantification:

- zero point quantum fluctuationspn nE )2

1(

U (Ib )

H 1

2 p˜ P 2 ˜ X 2 p

˜ X 3

- energy level quantification:- non equidistant level- tunnel effect of the ground state- quantum state manipulation

En (n 1

2) p 154

2(n 12)2 p

Quantum anharmonic oscillator

New Properties:

p (Ib )

Since <<1, perturbation theory

Tilted washboard potentialCharging energy

ˆ H ˆ Q 22C Ic cos( ˆ ) Ib ˆ

Hamiltonian of the circuit:

MW

,1

p (Ib ,b )

U (Ib ,b )

bias point (Ib ,b )shape of the

anharmonic well

MW current MW (t)excitation

b

Ib +IMW (t)

JJ1

JJ2

m

12 p

˜ P 2 ˜ X 2 p˜ X 3

1 cos(2t) 2 ˜ X

Quantum state manipulation

I

Quantum measurements

|0>|1>

|2>

Optimized flux pulse amplitude

Pro

babi

lity

ofes

cape

Nanosecond flux pulse amplitude (0 )

Flux pulse

Escape measurements

Currentbiased

0

Ib

Read out<V>

t

tescape

t

U()?

Pesc 1 et

0

0.2

0.4

0.6

0.8

1

8.7 8.8 8.9 9 9.1

ExpérienceThéorie

IDC (µA)

306mK267mK

146mK

22mK

IC = 9.426ACJ = 0.44pFLenv = 2.5nHt = 50s

Esca

pe P

roba

bilit

y

Ib (A)

-9

-6

-3

0

3

6

9

-500 -250 0 250 500

I p

V (V)

I b(

A)

Realisation of the quantum experiments

at very low temperature

5 mm

RCMS (x4) CCMS

1 mm

Sample set-up

(Nanofab andelectronics Service )

Current line200 nm * 200 m

(Large inductance)

SQUID

Measurement scheme

T=40mK

Quantummeasurement

Escapemeasurement

Quantummanipulation

Experiments

40 cm

1.5K

800mKStill

<30mKMixing chamber

300KA dilution stick is inserted inside the dewar(Cryogenics facility)

Sample holder & Dilution fridge

6cm

100mKHeat exchange

Sample holder

Spectroscopy of the artificial atom

Spectroscopy measurements

Resonant transition of different quantum states

Ip =0 ADC /0 =0.45

TRF

Tmes

measurementIRF (t)

RF

0

1

2

Microwave0

0,02

0,04

0,06

0,08

0,1

8 8,02 8,04 8,06 8,08 8,1

Esc

ape

Pro

babi

lity

Frequency (GHz)

FWHM = 4MHz

3

b /0

Freq

uenc

y(G

Hz)

0

0,02

0,04

0,06

0,08

0,1

8 8,02 8,04 8,06 8,08 8,1

Esc

ape

Pro

babi

lity

Frequency (GHz)

Energy spectrum of an artificial atom!

Spectroscopy

|1// ,0

>

|3// ,0

>|2// ,0

>

|0// ,1

>

b /0

Freq

uenc

y(G

Hz)

Energy spectrum of an artificial atom!

Longitudinal mode

Transverse mode

Manipulation of the quantum states

0

0,5

1

0 0,2 0,4 0,6 0,8 1

P 1

TRF

(U.A.)

|1>

|0> |0>

|1>

Coherent control: Rabi oscillations

0

1

00

Probability to be in 1

state

TRF

Tmes

Initial state: 0 Final state ?

Microwavefield

)10(2

1 )10(2

1

Microwaveduration

IMW (t)

Two possible quantum state: |0> or |1> A quantum bit!Coherent superposition:

T1 = 200ns

Experiments on Rabi oscillations

|0>

|1>

|1>

|1>

|0>|0>

TRF

Tmes

Initial state: 0 Final state ?

0.2

0.3

0.4

0.5

0.6

0.7

0 40 80 120 160

Quantum state manipulation...

Tmw (ns)

Pes

c |1>

By adjusting the MW duration : |0>|0>|1>

|1>

but also :

NOT

|0>|1> NOT

|1>

|0>|0>

)10(2

1

)10(2

1

)10(2

1 )10(2

1

TRF

Tmes

Initial state0

TMW

IMW (t)

Conclusion

Les circuits supraconducteurs présentent des comportements quantiques- effet tunnel macroscopique- niveaux d’énergie quantifiés- manipulation des états quantiques quantiques

Système modèle pour la physique quantique de l’électronet la nano-électronique quantique

- Une nouvelle informatique pour demain?- Developpements de nouveaux détecteurs quantiques- Quantum simuation

Des expériences très variées!!!de nouvelles idées apparaissent en permanence…

PerspectivesArtificial crystal

Prof. Wiebke Guichard

Josephson junction chains

Fundamental research: - collective behavior in a system

with multiple degrees of freedom- Quantum Phase-Slips

1 µm

Interaction between articial atom and microwave photons

Fluorescence-like effects!

Wiebke Guichard, Bernard, Pannetier, Frank Hekking, Laurent Lévy, Cécile Naud,Ioan Pop, Iulian Matei, Florent Lecocq, Zihui Peng, Alexei Feofanov, Thomas Weissl, and Quantum Coherence group

Projects:ANR QUNATJO