dc-squid for measurements on a josephson persistent-current qubit applied physics quantum transport...
TRANSCRIPT
![Page 1: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/1.jpg)
DC-squid for measurements on aJosephson persistent-current qubit
Applied PhysicsQuantum Transport Group
Alexander ter HaarMay 2000
Supervisors:Ir. C.H. van der WalProf. dr. ir. J.E. Mooij
![Page 2: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/2.jpg)
Introduction
3 m
![Page 3: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/3.jpg)
Introduction
Superconductor
Superconductor
Insulator
1 m
![Page 4: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/4.jpg)
Introduction Quantum mechanics
State of the system: Left OR Right
Classical mechanics:
Quantum mechanics:
State of the system: Left AND Right
![Page 5: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/5.jpg)
|||||0|1>
|0
|1
Introduction
Two level system:
Two level systems
Two currents in opposite directioncreating an opposite magnetic flux:
E1
E0
3 m
![Page 6: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/6.jpg)
Cou
nts
-1.0 -0.5 0.0 0.5 1.00
50
100
150
Introduction
I sw
(nA
)Flux (0)
The squid as a magnetometer
100 120 140 160 1800
1000
2000
2000
100 120 140 160 180Isw (nA)
0
I bias
(n
A)
V (V)0 400
0
100
Switching point
![Page 7: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/7.jpg)
Motivation
• Study dynamical behavior of a quantum mechanical 2-level system using a dc-squid.
• Use dynamics of this quantum 2-level system for quantum computing.
![Page 8: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/8.jpg)
Introduction
Factorize large numbers into integers.
![Page 9: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/9.jpg)
Goal of this research
Understand the dc-squid as a device for Understand the dc-squid as a device for measuring the small magnetic flux measuring the small magnetic flux signal of a quantum system.signal of a quantum system.
![Page 10: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/10.jpg)
Outline
•Introduction to Josephson junction structures•Analysis of the dc-squid
•Measurements on a single junction•Measurements on the dc-squid
•Application of the dc-squid•The qubit system•Measurements on the qubit system
![Page 11: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/11.jpg)
Josephson junction structures
E
Ibias = 0
0<Ibias < Ic
Ibias = Ic
Ibias
Introduction
m Cx
I bias
(n
A)
V (V)0 400
0
100
Switching point
C
![Page 12: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/12.jpg)
Josephson junction structures
Statistical escape mechanisms from the zero voltage state:
• Hopping over the barrier• Quantum tunneling through the barrier
Escape mechanisms
100 120 140 160 1800
1000
2000
Isw (nA)100 120 140 160 180
2000
Cou
nts
0E
![Page 13: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/13.jpg)
Josephson junction structures
Tunneling from higher levels within the potential well.
Escape mechanisms
E
![Page 14: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/14.jpg)
Measurements on the single junction
0
2000
0
2000
0
2000
0
2000
40 50 60 700
2000
T=30mK
T=40mK
T=60mK
T=80mK
T=120mK
40 60Isw (nA)
Cou
nts
We can use the histograms to calculate the escape rates from the zero voltage state.
![Page 15: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/15.jpg)
Measurements on the single junction
Isw (nA)
Cou
nts
40 50 60 70103
104
105
0
1000
2000
(1
/s)
![Page 16: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/16.jpg)
Measurements on the single junction
(1
/s)
103
104
105
106
103
104
105
106
103
104
105
106
103
104
105
106
50 60 70
103
104
105
106
Isw (nA)50 60 70
T=30mK
T=40mK
T=60mK
T=80mK
T=120mK
106
104
106
104
106
104
106
104
106
104
![Page 17: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/17.jpg)
The dc-squid
f
Ibias
introduction
bias = 0.5 ( cir = 0.5 ( f
C
Icir
100 m
![Page 18: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/18.jpg)
The dc-squid The internal degree of freedom
E
cirbias
EL
Eind J
2
022cos( )
![Page 19: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/19.jpg)
The dc-squid Quantum fluctuations
Quantum fluctuations in the flux through the squid loop:
Qubit signal:prod 0.001 0
<
![Page 20: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/20.jpg)
0
100
0 1000
4
Measurements on the dc-squid Comparing<
I sw>
(n
A)
(
nA)
T (mK)
Interpolated datafor the squid.Single Junction.
![Page 21: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/21.jpg)
0
2000
0
2000
0
2000
0
2000
0
2000
0 10 20 30 400
2000
C
ount
s
T = 20 mK
T = 40 mK
T = 80 mK
T = 160 mK
T = 640 mK
T = 320 mK
Iswitch (nA)
Measurements on the dc-squid
Histograms of the small test squid versus temperature
The test squid
![Page 22: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/22.jpg)
Measurements on the dc-squid The dc-squid
100 120 140 160 180 200102
103
104
105
106
0
1000
2000
3000
C= 2pF
C= 0.2pF
C=0.02pF
100 150 200
106
105
104
103
102
3000
2000
1000
T=30 mK
(1
/s)
Iswitch (nA)
![Page 23: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/23.jpg)
Measurements on the dc-squid Comparing
Conclusions:
• Quantum fluctuations in the internal degree of freedom play an important role in widening the histograms.
• Quantum fluctuations in the internal degree of freedom are much larger than the qubit signal.
![Page 24: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/24.jpg)
The qubit system
I cir
(I
c )
fqubit (
fqubit (
E
(E
J)f
3 m
0.48 0.50 0.521.5
2.0
E
0.48 0.50 0.52
-0.5
0.0
0.5
![Page 25: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/25.jpg)
Measurements on the qubit system
-1.0 -0.5 0.0 0.5 1.00
50
100
150
I sw
(nA
)
fsquid<
I sw>
(n
A)
0.48 0.50 0.52
90
100
110
fqubit
![Page 26: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/26.jpg)
0.48 0.50 0.52-1.0
-0.5
0.0
0.5
<I sw
>-
line
ar tr
end
(nA
)
Measurements on the qubit system
fqubit
![Page 27: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/27.jpg)
Measurements on the qubit system
0.496 0.500 0.504
-0.5
0.0
0.5
<I sw
>-
line
ar tr
end
(nA
)
fqubit
![Page 28: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/28.jpg)
Measurements on the qubit system
0.498 0.500 0.502
<I sw
>-
linea
r tr
end
(0.
4 nA
/div
isio
n)
9.711 GHz 8.650 GHz
6.985 GHz
5.895 GHz
4.344 GHz
3.208 GHz
2.013 GHz
1.437 GHz
1.120 GHz
0.850 GHz
0.498 0.5 0.502fqubit
![Page 29: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/29.jpg)
Measurements on the qubit system
0 1x10-3 2x10-3 3x10-30
2
4
6
8
10
0
2
0 5x10-4
f
Fre
quen
cy (
Ghz
)
0.48 0.50 0.521.5
2.0
fqubit (
E
(E
J)
![Page 30: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/30.jpg)
Conclusions
• Quantum fluctuations in the internal degree of freedom of the dc-squid play an important role in widening the histograms of the dc-squid.
• Spectroscopy measurements show the existence of an energy gap at a frustration of half a flux quantum indicating the two energy levels repel at that point.
dc-squid measurements
![Page 31: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/31.jpg)
Questions
?
![Page 32: DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir](https://reader035.vdocument.in/reader035/viewer/2022062803/56649f3b5503460f94c58f0a/html5/thumbnails/32.jpg)
Outline