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
Introduction
3 m
Introduction
Superconductor
Superconductor
Insulator
1 m
Introduction Quantum mechanics
State of the system: Left OR Right
Classical mechanics:
Quantum mechanics:
State of the system: Left AND Right
|||||0|1>
|0
|1
Introduction
Two level system:
Two level systems
Two currents in opposite directioncreating an opposite magnetic flux:
E1
E0
3 m
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
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.
Introduction
Factorize large numbers into integers.
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.
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
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
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
Josephson junction structures
Tunneling from higher levels within the potential well.
Escape mechanisms
E
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.
Measurements on the single junction
Isw (nA)
Cou
nts
40 50 60 70103
104
105
0
1000
2000
(1
/s)
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
The dc-squid
f
Ibias
introduction
bias = 0.5 ( cir = 0.5 ( f
C
Icir
100 m
The dc-squid The internal degree of freedom
E
cirbias
EL
Eind J
2
022cos( )
The dc-squid Quantum fluctuations
Quantum fluctuations in the flux through the squid loop:
Qubit signal:prod 0.001 0
<
0
100
0 1000
4
Measurements on the dc-squid Comparing<
I sw>
(n
A)
(
nA)
T (mK)
Interpolated datafor the squid.Single Junction.
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
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)
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.
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
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
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
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
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
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)
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
Questions
?
Outline
