Hideaki Takayanagi

1
Superconducting Flux Qubit as a Macroscopic
Artificial Atom
Hideaki Takayanagi NTT Basic Research
Laboratories, NTT Corporation, Japan
NTT?????????
? ? ? ?
Outline

1. Quantum Information Research at NTT
2. Fux Qubit
3. Single-Shot Measurement
4. Multi-Photon Absorption
5. Rabi Oscillation
6. Conclusions

2
QIT Project in NTT Basic Research Laboratories
Head H. Takayanagi
About 20 researchers participate to the
project which consists of five sub-projects.
Four qubit-research projects and a quantum
cryptography one.
3
Solid-State Qubits
Four Kinds of Qubit
Coupled QDs (artificial molecule)
Exciton in QDs
SQUID
Rabi oscillation
Single-shot measurement Multi-photon
absorption Rabi oscillation
Quantum gate operation
cooled atom
Atom Chip
4
Quantum cryptography with a single photon
Nature, 420 (2002) 762
5
Josephson persistent current Qubit
J. E. Mooij et al.,Science 285, 1036 (1999).
Phase difference
Fqubit f F0
B
f Fqubit / F0
f Fqubit / F0 0.5
6
Schematic qubit energy spectrum


15
100
10
5
Energy (GHz)
Energy (GHz)
0


0
-5
-10
-100
0.4
0.5
0.6
0.49
0.50
0.51
F
/
F
qubit
0
Fqubit
/
F0
7
Three-Josephson-junction LoopDescription
0lt? lt1.0
Josephson Energy
J.E. Mooij?et al (1999)
8
Three-Josephson-junction LoopEnergy Diagram
f0.5
2 minima in each unit cell.
Top View
9
Three-Josephson-junction Loop? Dependence of
the Potential
f0.5
U
U
U
?0.6
? 0.8
? 1.0

• If ? increases, the barrier height
• increases between the two minima of one unit
  cell
• decreases between the minima of adjacent cells

10
Three-Josephson-junction LoopFlux Dependence of
the States
11
Sample Fabrication

• e-beam lithography
• Shadow evaporation
• Lift-off

Josephson junctions Al / Al2O3 / Al Junction
area SQUID 0.1 x 0.08 ?m2 Qubit 0.1 x L ?m2,
( a 0.8 ) L 2 0.2 Loop size SQUID 7 x
7 ?m2 Qubit 5 x 5 ?m2 Mutual inductance M 7
pH
Qubit and a detector dc-SQUID
NTT Atsugi
12
e-beam lithography
suspended-bridge shadow evapolation
13
Sample and Cavity
DC measurement
To mixing chamber
Microwave line
Thermometer
Vm line
Ibias line
Samples
A loop
Cavity
14
DC measurement
RF line
1
2
3
4
5
10 nF
connectors
HP 20dB
R.T.
2.4mm connectors
4.2K
Through capacitor
Flexible coaxial cable
HP 10dB
1.2K
attenuator
0.8K
resistance
0.4K
10mK
Heat anchor for outer shield
Twisted Constantan wire 100 ?

• No on-chip capacitor and resistor
• No on-chip control line
• Change twisted wires to thin coaxial cables to
  introduce dc-pulse

200 ?
200 ?
200 ?
Sample box
Loop antenna 1mm above the sample
15
DC measurement
Readout through a dc-SQUID
Record each switching when Vm Vth 30 mV as a
function of Isw
Sweep Ib ( 140 Hz ) Tilt SQUID potential
I b
100 nA
Isw
Isw
Isw
46 nA
Isw
t
0
70 100 µsec
Vm
7 ms
Vth(30µV)
t
0
16
Readout with a dc-SQUID
DC measurement
17
Qubit step in the SQUID Isw
DC measurement
Fqubit / F0
18
Parameter dependence of the qubit step
( D, Ej, Ec )
SQUID
I
LSQUID
Lqubit
Qubit
Josephson junctions Al / Al2O3 / Al Junction
area SQUID 0.2 x 0.2 ?m2 qubit 0.2 x L ?m2,
L0.3, 0.5, 1.0
Loop size Lqubit 5.1, 9.7, 19.0 (?m)
LSQUID 6.3, 10.9, 20.2
19
Two energy scale Ec, EJ
energy
energy
Pair tunneling
superconductor
p
-p
superconductor
Phase difference
Number of tunneled pair n
Tunnel barrier
H Ec - EJ cos g - Iex g
n,gi Josephson
energy EJ charging energy
Ec (2ne)2/(2CJ ) kBT ltlt
EJ ltlt Ec lt D ? charge qubit
kBT ltlt Ec ltlt EJ lt D ? phase?flux qubit
20
QB 5 Junction area 0.1 ?m2 Loop size Lqubit
9.7 ?m LSQUID 10.9 ?m
QB 4 Junction area 0.06 ?m2 Loop size Lqubit
9.7 ?m LSQUID 10.9 ?m
QB 6 Junction area 0.2 ?m2 Loop size Lqubit
9.7 ?m LSQUID 10.9 ?m
( D 2GHz gt kBT )
( D 0.4GHz kBT )
( D 2MHz ltlt kBT )
Fqubit / F0
Fqubit / F0
Fqubit / F0
QB 8 Junction area 0.1 ?m2 Loop size Lqubit
19.0 ?m LSQUID 20.2 ?m
QB 7 Junction area 0.06 ?m2 Loop size
Lqubit 19.0 ?m LSQUID 20.2 ?m
QB 3 Junction area 0.2 ?m2 Loop size Lqubit
5.1 ?m LSQUID 6.3 ?m
Fqubit / F0
Fqubit / F0
Fqubit / F0
D
Qubit energy splitting
kBT25mK
21
Calculated qubit energy level
D0.4 GHz
D2 GHz
D2 MHz
Ej280 GHz Ec3.2 GHz Ej/Ec87
Ej130 GHz Ec5.4 GHz Ej/Ec24
Ej544 GHz Ec1.6 GHz Ej/Ec338
22
Optimal operation point for SQUID
Qubit signals appear at half-integer
Sensitivity of dc-SQUID depends on magnetic fields
We can achieve excellent resolution at f 1.5
???
???
23
Spectroscopy
EJ 312 GHz, EC 3.8, a 0.7
D 2.6 GHz
after averaging
w/o averaging
0.001 F0 M 2.4 GHz
24
Qubit signals at different SQUID modulation
DC measurement
S/N depends on SQUID Isw
design
qubit and SQUID to be crossed at small Isw
?gt
?gt
?gt
?gt
T 25 mK
25
f
26
Boltzman Distribution
27
Schematic qubit energy spectrum


15
100
10
5
Energy (GHz)
Energy (GHz)
0


0
-5
-10
-100
0.4
0.5
0.6
0.49
0.50
0.51
F
/
F
qubit
0
Fqubit
/
F0
28
Spectroscopy
DC measurement
Pulse measurement
excited state
ground state
29
Readout without averaging
DC measurement
Single shot measurement into l0gt, l1gt bases
The ltIqgt step shape does not change. Only the
population changes.
Fqubit / F0
30
Close-up of Isw, T25 mK
DC measurement
Histogram is well separated !
counts
counts
f
Fqubit / F0
0.001 F0 M 2.4 GHz
f 1.50102
31
Readout after averaging
DC measurement
Expected Current ( canonical ensemble average )
Fqubit / F0
32
Experimental setup
Pulse measurement
1
2
3
4
5
RF line
SLP-1.9
R.T.
4.2K
RFin 2 attenuators RFout terminator
attenuator DC LP filter Meander filter
Flexible coaxial cable
HP 10dB
1.2K
0.8K
0.4K
V
V -
I
I -
29mK
Weinschell 10dB
Thin coaxial cable f 0.33 mm
Meander filters
Sample cavity
RF in
RF in
Terminator 50 W
Sample cavity
On-chip strip line
33
Multi-photon transition
Multi-photon transition between superposition of
macroscopic quantum states
?
( ) /v2 1st excited state

( ) /v2 ground state
3
3
2
2
1
1
3
1
2
2
3
1
34
Multi-photon transition
Multi-photon spectroscopy
SQUID readout
D0.86GHz
1-photon
2 -photon
35
Multiphoton absorption at 9.1 GHz
RF Power dependence
double
single
triple
off
off
off
PRF - 21 dBm
0 dBm
9.6 dBm
13.2 dBm
10 dBm
12 dBm
12 dBm
36
Multi-photon transition
Peak width vs MW intensity
Bloch Kinetic Equation
9100MHz
----- (3)
------------------ (4)
37
Pulse measurement
Pulse measurement scheme
repetition 3kHz ( 333 ms)
180 ns
1µs
SQUID switch
Ib DC pulse
Non-switching
time
resonant microwave
MW
discrimination of the switching event
Vout
Vout -
V th
I bias
Fext
Non-switching events
Switching events
Ibias
Ibias -
SQUID
Non-switching event Switching event
38
030304_1 (1,2)FQB2
Pulse measurement
Relaxation time T1
15
9.1 GHz 1 ms pulse
10
data
MW
5
exp-fit
Energy (GHz)
0
m
T
1.6
s
1
-5
Ground state

-10
0.49
0.50
0.51
Fqubit
/
F0
500 ns
0
3 ms
m
Delay Time

s
1 ms
delay time
Ib pulse height 1.474 V, Trailing height ratio
0.6
39
Pulse measurement
Quantum Oscillation Rabi oscillations
11.4 GHz
Dephasing time 30 ns
150 ns
600 s
Trailing height ratio 0.7
Resonant MW pulse width
NTT Atsugi
40
Summary

• Spectroscopy of MQ artificial 2-level system
• Qubit readout without averaging (DC)
• Multi-photon transition between superposed MQ
  states
• Coherent quantum oscillation ( Rabi oscillation
  )
• T1 1.6 ms, T2 Rabi 30 ns

Future plan

• Ramsey, Spin echo
• Two qubit fabrication and operation
• MQC with single shot resolution

41
collaborators
NTT Basic Research Laboratories Hirotaka
Tanaka Shiro Saito Hayato Nakano Frank
Deppe Takayoshi Meno Kouich Semba Tokyo
Institute of Technology Masahito Ueda Yokohama
National University Yoshihiro Shimazu Tomoo
Yokoyama Tokyo Science University Takuya
Mouri Tatsuya Kutsuzawa
42
??????????one-shot measurement????
??? ???????
???????????? ???????
0.5
? ?superposition????????
? ???superposition???????
43
0.5
time domain ????????? Qubit???????????????????? Qu
bit????sz???(projection)?
?????time-dependent?Schrödinger ???????SQUID?switc
hing current ??????EJ/EC???????????? 1?????EJ/EC??
?????????? 2?????
???1?
???2?
0.5