e. rousseau d. ponarine y. mukharsky e.varoquaux o. avenel j.m. richomme cea-drecam service de...
TRANSCRIPT
E. Rousseau D. PonarineY. Mukharsky
E.VaroquauxO. AvenelJ.M. Richomme
CEA-DRECAMService de Physique de l’Etat CondenséCEA-SaclayFrance
To Quantum Dots and Qubitswith electrons on helium
L pool R pool
ring
Guard electrode
Confine the electrons
pool Guard electrode
550 nm40 nm
• the exact quantity of helium is added to fill the two pools and the ring.
• electrons are created by a corona discharge.
•Only electrons above pools and ring are mobile.
X axis
0.6 0.7 0.8 0.9 1.0x10-5
x axis
-0.20
-0.15
-0.10
-0.05
0.00
-V(V
olt)
SET=0.35
SET=0.2
SET=0.1
R pool
trapping
• The electrostatic trap is created by the SET itself.
Gate
R pool Gate
• Sample more or less similar to RHL one.
Counting Individual Electrons on liquid Helium .G.Papageorgiou & al. Applied physics letters 86, 153106 (2005)
Royal holloway
Sample specificity:• Ring diameter 3 m, pyramidal SET island
L pool R pool
ring
Guard electrode
The Precious
Gate
ResR
Detection
•The voltage across the SET is a periodic function of the island charge. •When an electron goes in or out of the trap the SET island charge change by q.
SET island
Q
0.47 0.48 0.49 0.50 0.51R pool potential
-0.5
0.0
0.5
1.0x10-4
SE
Tos
cill
atio
nsam
plit
ude
Q+q
Re( )sRCVf
e
Re( )sRCV qf
e e
ResR
0.47 0.48 0.49 0.50 0.51R pool potential
-0.5
0.0
0.5
1.0x10-4
SE
Tos
cill
atio
nsam
plit
ude
Detection
0.47 0.48 0.49 0.50R pool potential
-0.1
0.0
0.1
0.2
0.3
osci
llat
ions
phas
e
• We fit with a spline function a quiet part of the oscillations.• The phase of the oscillations changes then by
Charging the ring
Left and right pools
guardguard
Drawing of the potential profile
ring
0.0 0.3 0.6 0.9 1.2
-100
-98
-96
-94
-92
phase
Q/e
Right pool potential, V
One by one observation
ResR SET
0.6 0.7 0.8 0.9 1.0-95.0
-94.5
-94.0
-93.5
-93.0
-92.5
-92.0
ResR
Q/e
One by one observation
0.4e
0.4e
last jumps are around ~0.4 e, value which is reproduced by simulations.
Discharge curve
0.0 0.5 1.0 1.5right pool potential
-125
-120
-115
-110
-105
-100
-95
-90ph
ase
vari
atio
n
Zoom
Discharge curve
0.9 1.0 1.1 1.2 1.3right pool potential
-98
-96
-94
-92ph
ase
vari
atio
n
Discharge curve
0.9 1.0 1.1 1.2 1.3right pool potential
-98
-96
-94
-92ph
ase
vari
atio
n
12
5
34
0
6
89
q
Discharge curve
0 5 10 15 20 25 30electron number
0
1
2
3
4
5
6
7S
ET
isla
ndch
arge
Q/e
Density estimate• For a small number of electrons, density
can be considered as uniform. A.A.Koulakov, B.I.Shklovskii cond-mat/9705030
• The electric field is supposed to be constant on SET island.
• The electric charge on the SET island is then given by:
nSeff (1-cos(max))Qe = With max=arctan ( N
n1h
)
N=nR2 number of electronn electronic density
max
SET island
h
Electron sheetR
Seff
0 5 10 15 20 25 30
electron number
0
1
2
3
4
5
6
7S
ET
isla
ndch
arge
Q/e
Density estimate
Seff =0.34 +/- 0.07 m2
Electronic density=(1.8 +/- m-2
Sreal=0.35 m2
• The interaction between electrons is not screened by surrounding electrodes.
• From thermal fluctuations: n=1014 transition temperature Tc=2.5 K
• rs~2000 rscri~30
Coulombic interaction is dominant
• Electrons should form a Wigner crystal.
Wigner molecules
Competitionbetween the symmetry of the trap
(parabolic trap) shell ordering
and the symmetry of the Wigner crystal
triangular lattice structure
N=7
N=19
macroscopic observation
camera
No observations with electrons on helium.
Addition Spectra
Current pA
20
10
Gate voltage, V
1 2 3
4(1)
• charging energy: energy required to add
one electron
• (N) =(N)-(N-1) ~ e Vg
rightleft
gate
0.9 1.0 1.1 1.2 1.3right pool potential
-98
-96
-94
-92
phas
eva
riat
ion (1)(2)
(3)
Addition spectra
Liquid phase
• Average interaction between electrons Constant interaction model 1 particles model in a parabolic trap
• Confinement induce energy shell with magic numbers when a shell is completely filled: 2,6,12 (degeneracy due to spin)
2e
C
2e
C
Hund’s rule
Vladimir Bedanov and François PeetersPRB 49, 2667
0 5 10 15 20 25number of electrons
0.000
0.002
0.004
0.006
0.008
addi
tion
ener
gy(e
V)
“The numbers of electrons on each ring are not universal and depend on the type and strength of confinement potential.”
B.Partoens and F.PeetersJ.Phys:condens matter,9 5383 (1997)
For a parabolic trap
No magic numbers when electrons form Wigner molecules.
Simulations needed to explain addition energy plot
0 2 4 6 8 10nombre d'electron
0.00
0.02
0.04
0.06
0.08
0.10eV
Pour Vset=0.3 Vgate=0 Vground=-0.1
0 2 4 6 8 10 12 14electron number
0.00
0.02
0.04
0.06
0.08
0.10
0.12ch
emic
alpo
tent
ial
vari
atio
n Vset=Vgate=0.5 V
Monte Carlo simulations
• The modelpotential profile found with simulation simulation of the pyramidal island.
• Ground state of the configuration with N electrons is found with Monte-Carlo Simulations.
• Ground state energy vary linearly with reservoir right potential.
-0.1 0.0 0.1 0.2 0.3 0.4reservoir right potential
-5.0
-4.8
-4.6
-4.4
-4.2
-4.0
-3.8
-3.6en
ergy
(eV
)
N=19
N=20
N=21
N=22
Monte Carlo simulations
• The modelpotential profile found with simulation simulation of the pyramidal island.
• Ground state of the configuration with N electrons is found with Monte-Carlo Simulations.
• Ground state energy vary linearly with reservoir right potential.
• Criteria when the electron leaves the trap?
0.5 0.6 0.7 0.8 0.9 1.0x10-5
x
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
pote
ntia
lpr
ofil
e
Potential profile = one particule energy
1N NE E One electron leaves the trap when
-0.2 0.0 0.2 0.4 0.6 0.8 1.0reservoir right potential
-0.4
-0.3
-0.2
-0.1
0.0
0.1
(e
V)
E22-E21
E2-E1
0 5 10 15number of electrons
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14ad
diti
onen
ergy
(eV
)
experiment
simulation
Vset=0.5 Vgate=0.5
2 4 6 8 10 12 14
electron number N
0.00
0.01
0.02
0.03
0.04
0.05
Add
itio
nen
ergy
dot(N
)(m
eV)
addition spectra for different discharges
Vset=0.1 Vgate=0.2
4
6
9
Clear magic numbers!
Cannot be explain with M-C simulation
Positive impurity increase locally the density
Structural transition in a finite classical two dimensional system
G. A. Farias and F. M. Peeterssolid state communication, 100, 711 (1996)
0.6 0.9
-100
-95
ResR, V
Q
/eOne by one observation
Probability of escape
• If the barrier is thin enough, the electron can tunnel.
8.15 8.20 8.25 8.30 8.35 8.40x10-6
ResR potential
0.00140
0.00145
0.00150
0.00155
0.00160
0.00165
barr
ier
heig
ht
0.80 0.85 0.90 0.95 1.00 1.05 1.10
pulse amplitude (arbitrary unit)
0.0
0.2
0.4
0.6
0.8
1.0
prob
abil
ity
position
|0>
|1>
Potential profile
Barrier height
Quantum state evidence?
Existing to the first excited state
SETI
|0>
|1>Oscillating E
Time
Tunneling time=5.10-11 s
Potential felt by the electron
+e -e
mixs
measurement principles
1. We choose a SET current valuefrom 0 nAmp (no heating) to 50 nAmps.
2. We applied a voltage pulse to the right reservoir: the barrier height is reduce.
3. We check whether the electron is still in the trap or not.
4. 2000-3000 tries for one escape curve.
position
Potentials profiles
Barrier
?
6.50 6.55 6.60 6.65 6.70 6.75pulse amplitude
0.0
0.2
0.4
0.6
0.8
1.0
prob
abil
ity
ofex
trac
tion
p= 1-exp(-0exp(-Eb/kbT))
0 =
/2~ 30 GHz trap frequency pulse length
Eb barrier high
Eb and 0 estimated from simulations
Temperature estimate
-30 -20 -10 0 10 20 30
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Ids
Fit with numerically calculated UMultipler 33.61v
0=0.076,
0=.0052
The pulse is applied during heating
Curve width with heating current
6.50 6.55 6.60 6.65 6.70 6.75pulse amplitude
0.0
0.2
0.4
0.6
0.8
1.0pr
obab
ilit
yof
extr
acti
on
A0.5
0 200 400 600 800 10003.7
3.8
3.9
4.0
4.1
A
0.5
T, mK
Quantum tunnelingThermal activation
Crossover Temp ~ 250 mK
0.5 0.6 0.7 0.8 0.9 1.0 1.1x10-5
ResR potential
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
ener
gie
(eV
)
~ 30 GHz (before the pulse)
Cross-over temperature
~ 230 mK
the frequency of the barrier
0
2 B
hT
k
0.644 0.646 0.648 0.650 0.652 0.654
ResR potential
0.0
0.2
0.4
0.6
0.8
1.0
prob
abil
ity
extraction curve
Vsetapp=0.2598
Temp=0.235 K
Vset=0.3
Only one parameter is adjusted
Vset.
Contact potential between niobium and aluminiumthe potential on the SET is not really known
Tcell=30 mK
0 200 400 600 800 1000
2.4
2.5
2.6
2.7
2.8
2.9
Ids 0 Ids 2.3 Ids 10 Ids 0 Ids 2.3 Ids 10
A0.
5
T, mK
No change when we heat the electron!
Need to probe the coupling between the electron and its environment
1. Heating for 300 ms with 50 nAmps.
2. Wait between 2 and 100 s.
3. Applied the pulse on reservoir right.
4. Fit the curve.According to position and width of this curve get a number proportional to the temperature
Coupling with environment
position
Potential profile
Barrier
SET
100 s
-20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320200001800016000140001200010000
8000
6000
4000
2000
E
kt
s
Sep07 Sep09
Coupling with the environment
t=0 high temperaure
Even for t=2 s, temp. is low.
Heating pulse decay
50 nAmps
~ 0.4 s
Heating current
time
0.0 0.5 1.0 1.5time in micro-second
0.1825
0.1830
0.1835
0.1840
0.1845
0.1850
tem
pera
ture
a-u
0.0 0.5 1.0 1.5time in micro-second
0.1825
0.1830
0.1835
0.1840
0.1845
0.1850
tem
pera
ture
a-u
tau = 0.38 +/- 0.05 micro-s
t
taue
What can we say?
• Either the coupling with the environment is huge
Where does it come from?
Coupling with phonons
• they induce modulations of the density. So they induce modulation of the image charge.
• This coupling depends highly with the electric field on the electron.
• In our case ~ 10 s
We maybe tried the smallest electric field as we could to keep the electron in the trap!
What can we say?
• Either the coupling with the environment is huge
• Or the picture of the heating procedure is too naïve
SETI
|0>
|1>
Dynamical force?
Two wave-guids:
~ 40 GHz parrallel levels
~ 120 GHz perpendicular levels
-4 -2 0 2 4x10-7
reservoir right potential
-4
-2
0
2
4x10-7
(e
V)
circular
ellipsoïdal
Evolution with deformation
Increase of the deformation
L pool R poolring
Guard electrode
Bias and IV characteristic
PreAmpIds A
B
A-B
the SET is current bias
Uds
IV Characteristic
For C-B oscillations
-5 -4 -3 -2 -1 0 1 2 3 4-8.0x10-4
-6.0x10-4
-4.0x10-4
-2.0x10-4
0.0
2.0x10-4
4.0x10-4
6.0x10-4
UD
S,
V
IDS, nA
500 mKsample 2h
Measurement • L-in technique: 125 Hz, 6-30 V applied to the guard
L pool R poolring
Guard electrodePreAmp
125
L-in
From L-in
6V
C-B oscillations
Raw oscillations From L-in
0.07 0.08 0.09 0.10VresR
0.004929
0.004930
0.004931
0.004932
0.004933
0.004934
C-B
osci
llat
ions
Am
plit
ude
0.07 0.08 0.09 0.10VresR
-1.0
-0.5
0.0
0.5
1.0x10-4
C-B
osci
llat
ions
Am
plit
ude
Ids=2.6 nA
Some properties of this kind of quantum dots
• Classical point of view: competition between thermal fluctuations and coulombian interaction
• for n=1014 transition temperature Tc=2.5 K
• Working temperature: from 50 mK to 1K
Gas parameter• Measure the competition between
quantum fluctuations and Coulombic interaction
• For n ~ 1014 m-2 a ~n-1/2 ~ 0.1 m
• typical coulomb energy
• Typical kinetic energy (Fermi energy)
• rs~2000 rscri~30Coulombic interaction is dominant
• Semiconductors qdots rs~2
2
0
1
4c
eE
a
a
22KEma
0 2 4 6 8 10 12 14
electron number
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07ch
emic
alpo
tent
ialva
riat
ion
5
7
Vset=Vgate=0.3 V