Post on 04-Jun-2018
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
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
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:
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)
5 mm
RCMS (x4) CCMS
1 mm
Sample set-up
(Nanofab andelectronics Service )
Current line200 nm * 200 m
(Large inductance)
SQUID
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 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
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!