2. Coulomb Staircase 3. Spectroscopy - lancaster.ac.uk · 2. Coulomb Staircase. 3. Spectroscopy. 4....
Transcript of 2. Coulomb Staircase 3. Spectroscopy - lancaster.ac.uk · 2. Coulomb Staircase. 3. Spectroscopy. 4....
Per Delsing Fig. 1
Coherent oscillations in a Single CooperCoherent oscillations in a Single Cooper--pair Boxpair Box
1.1. IntroductionIntroduction
2.2. Coulomb StaircaseCoulomb Staircase
3.3. SpectroscopySpectroscopy
4.4. Coherent oscillations
CHALMERS:Experiment:Tim DutyDavid GunarssonKevin Bladh
Theory:G. Johansson =>KarlsruheA. KäckG. Wendin
YALE:Rob SchoelkopfKonrad Lehnert =>Bolder
Coherent oscillations
Per Delsing Fig. 2
A Single CooperA Single Cooper--pair Box pair Box QubitQubitIntegrated with an RFIntegrated with an RF--SET ReadSET Read--out systemout system
RF-SET
V
singleCooper-pairbox
∆ >> EC >> EJ(B) >> T2.5K 1K 0.5-0.05K 20mK
Bouchiat et al. Physica Scripta (99)Makhlin et al. Rev. Mod. Phys. (01)Aassime, PD et al., PRL (01)
Per Delsing Fig. 3
The Single CooperThe Single Cooper--pair box (SCB)pair box (SCB)
Vg Q=n2e
C1
C2
H =Q2
2CΣ
− EJ cosθ
c.f. Hamiltonian for Bloch electronsp2
2m+U (x)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
E /
EC EJ
n g
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
<n>
ng
Bouchiat et al., Physica Scripta (98)Nakamura et al., Nature (99)Makhlin et al., Nature (00)
Per Delsing Fig. 4
The RadioThe Radio--FrequencyFrequencySingle Electron TransistorSingle Electron Transistor
3210-1
Qgate (e)
Average conductance Reflected power
Vg CSET
CQB
CCCg
SingleCooper-pair
Box
L
C
SingleElectron
Transistor
DirectionalCoupler
Mixer
SET-biasPulse line50 GHz
Tank circuit
ColdAmplifier
WarmAmplifier
~RF-source450 MHz Output
RFLO
Bias-Tee
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 5 10 15 20 25 30 35 40
Cha
rge
(e)
Time(µs)
ĘQ=0.1eBw=1MHz
Very high speed:137 MHzR.Schoelkopf, PD et al. Science (98)
Very high sensitivity:3.2 µe/√HzA.Aassime, PD et al.APL (01)
Per Delsing Fig. 5
SET IVSET IV--characteristics andcharacteristics andConductance vs. Conductance vs. VVbb and Vand Vgg
B=0.0 T B=0.4 T
Operation pointdouble JQP
-5
0
5
10
15
20
Vg
V bi
as
-0.02 0 0.02
-1
-0.5
0
0.5
1-5
0
5
10
15
20
-0.02 0 0.02
-1
-0.5
0
0.5
1
V bi
as
Vg
-20
-15
-10
-5
0
5
10
15
20
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
I (nA
)
V (mV)
RSET=44.1k½C· =370 aFCgÅ20aF
Per Delsing Fig. 6
The Sample holderThe Sample holderFabricated in oxygen free high conductivitycopper and gold plated
Inductance can be changed by changing the distance to the ground plane with a tuning screw
Inductor can be made Superconducting tominimize losses
Tank circuit : L≈400nH, Cpad≈300fF
0
5
10
15
20
25
30
35
260 280 300 320 340 360 380 400 420
P(1µA)-P(0,no Yoko)
Shot
noi
se p
ower
(nW
)
Frequency (MHz)
Q≈17.4fc=330.8 MHz
fBW=9.5MHz
Shot noise from the SET, I=1µAShot noise from the SET, I=1µA
Per Delsing Fig. 7
Improving sensitivity by adding a SQUID amplifierImproving sensitivity by adding a SQUID amplifier
Washer
Coilin
Coilend
CE
Cold HEMT amplifiers has TN≈ 2.5 K
SQUID amplifier has TN≈ 50 mKCollaboration with BerkeleyM. Mück, J.B. Kycia, and J. ClarkeAppl. Phys. Lett., 78, 967 (2001)
A transmission RF-SET would then be betterT. Fujisawa and Y. HirayamaAppl. Phys. Lett., 77, 543 (2000)
CSETCC
L
C
50 GHzQubit
manipulation
Tank circuit
Bias-Tee
HEMTAmplifier
SQUIDAmplifier
Mixer
WarmAmplifier
X~ Output
RF
LO
L
SET-bias
SingleCooper-pair
Box
C QB
C g
SingleElectron
Transistor
RF-source450 MHz
Per Delsing 8
QubitQubit measurementsmeasurements
Per Delsing Fig. 9
C· SETC· QB
CC
23aF13aF
EcQ=1.67K, 560aF 620aF, Ec=1.51K
10aF
Coupling = 1.9%
Circuit parametersCircuit parameters
RSET≈45kΩECSET≈1.51KECBOX≈1.65KEJ≈0.6KBox to SET coupling=1.9%B-field parallel to substrate fcarrier=450 MHzRF-amplitude≈-100dBmStaircase sweep frequency =141Hz
Per Delsing Fig. 10
The Coulomb blockade staircase, normal stateThe Coulomb blockade staircase, normal state
0.0
1.0
2.0
3.0
4.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
ExperimentTheory
Ave
rage
box
cha
rge
[e]
CgVg [e]
Per Delsing Fig. 11
The Coulomb blockade staircase, comparingThe Coulomb blockade staircase, comparingthe normal and thethe normal and the superconductingsuperconducting statestate
0
1
2
3
4
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Normal stateSuperconducting state: Sample 1Superconducting state: Sample 2
Box
Cha
rge
[e]
CgVg [e]
Per Delsing Fig. 12
What would you expect in theWhat would you expect in the superconductingsuperconducting statestate
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 0.5 1 1.5 2
E/E
C
ng
² ~
∆~≈∆0-kBT ln(N)
∆0≈2.4K for Al
∆~=(L-S)/(L+S)
Lafarge et al. Nature (93)
Per Delsing 13
Long Step versus Short StepLong Step versus Short Step
Per Delsing Fig. 14
Magnetic field dependence of the short stepMagnetic field dependence of the short step
0.0
2.0
4.0
6.0
8.0
10.0
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
B= 667.5 mTB= 623.0 mTB= 578.5 mTB= 534.0 mTB= 489.5 mTB= 445.0 mTB= 400.5 mTB= 356.0 mTB= 311.5 mTB= 267.0 mTB= 222.5 mTB= 178.0 mTB= 133.5 mTB= 89.0 mTB= 44.5 mT
aver
age
char
ge [e
]
CgVg [e]
Per Delsing Fig. 15
The odd even energy differenceThe odd even energy difference
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.2 0.4 0.6 0.8 1.0
Ę~ sample 1
fit values
Ę til
de [K
]
B|| [T]
2e regionsample 2
≈∆0-kBT ln(N)
∆0≈2.4K for Al
=(L-S)/(L+S)
Lafarge et al. Nature (93)
˜ ∆
˜ ∆
Extracting ˜ ∆ (B) :
Per Delsing 16
SpectroscopySpectroscopy
Per Delsing Fig. 17
Microwave irradiation of the CooperMicrowave irradiation of the Cooper--pair boxpair boxFrequency dependenceFrequency dependence
2.0
3.0
4.0
2.4 3.0 3.6
50 GHz42 GHz34 GHz30 GHz
Ave
rage
cha
rge
[e]
CgVg [e]
Limited frequency range
25-50 GHz
Two photon peaks
=> > 50 GHz
(Averaging causes broad peaks)
Per Delsing Fig. 18
Energy levels extracted from spectroscopyEnergy levels extracted from spectroscopy
0
10
20
30
40
50
60
70
0.0 0.1 0.2 0.3 0.4 0.5
EJ = maxEJ Å0, single photon peaksEJ Å0, two photon peaks
f [G
Hz]
Æn
EC=1.67 KEJ=0.6 K
Per Delsing Fig. 19
Spectroscopy Spectroscopy BB--field dependencefield dependence
Modulation of Ej with B||Irradiation by 50 GHz µ-waves1
3 0.8
0.62
<n>
0.4
0.21
0 0.9 1 1.10 0.5 1.0 1.5 2.0B|| [Telsa]Cg Vg
Per Delsing 20
Coherent oscillationsCoherent oscillations
Per Delsing Fig. 21
Nakamura, Nakamura, PashkinPashkin and Tsai (1999and Tsai (1999)
Nakamura et al., Nature (99)
Per Delsing Fig. 22
Continuous measurement with Continuous measurement with TTrr=59ns, amplitude 1e pulse train=59ns, amplitude 1e pulse train
0 1 2 3 40
1
2
3
4
5pulse train offpulse train on
<n>
CgVg [e]
Tr
Per Delsing Fig. 23
Coherent OscillationsCoherent Oscillations
][ pst∆gate charge n
g
0 0.2 0.4 0.6 0.8 1 1.2100
200
300
400
500
∆t [p
s]
0 0.2 0.4 0.6 0.8 1 1.2500
1000
1500
0 0.2 0.4 0.6 0.8 1 1.21500
2000
2500
0
0.2
0.4
0.6
0
0.2
0.4
0
0.2
0.4 Period=70 ps agrees well with Ej
Color represents difference between pulsed staircase and ”unpulsed” staircase
Per Delsing Fig. 24
Signal versus pulse durationSignal versus pulse duration
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 0.5 1 1.5 2 2.5
<n>
[e]
Ęt [ns]
Per Delsing Fig. 25
Possible sources of Possible sources of decoherencedecoherence
• Continuous measurement of course decoheres the system, pulsed measurements should improve the situation.
• Non-equilibrium quasi particles are obviously present in the system.
• Non-perfect dc pulses: the pulse is not perfectly square and thus the system is not exactly at the degeneracy point during the evolution. Therefore background charge noise couples stronger to the system
Per Delsing Fig. 26
SummarySummary
•RF-SET optimized, ∂Q=3.2 µe/√Hz achieved
•Fabrication of integrated Qubit and RF-SET
•Characterization of Cooper-pair box
– Demonstrated continuous (and pulsed) read-out of box charge.
– Observation of microwave induced transitions between |0> and |2>
– Determination of EC and EJ from spectroscopy.
– Coherent Oscillations observed (reproduced Nakamura’s results with RF-SET read-out).