hideaki takayanagi ntt basic research laboratories, ntt corporation, japan
DESCRIPTION
Superconducting Flux Qubit as a Macroscopic Artificial Atom. Hideaki Takayanagi NTT Basic Research Laboratories, NTT Corporation, Japan. NTT 物性科学基礎研究所. 髙 柳 英 明. Outline. Quantum Information Research at NTT Fux Qubit Single-Shot Measurement Multi-Photon Absorption Rabi Oscillation - PowerPoint PPT PresentationTRANSCRIPT
Hideaki Takayanagi NTT Basic Research Laboratories, NTT Corporation, Japan
NTTNTT 物性科学基礎研究所物性科学基礎研究所
髙 柳 英 明髙 柳 英 明
Superconducting Flux Qubit as a Macroscopic Artificial Atom
Outline
1. Quantum Information Research at NTT2. Fux Qubit3. Single-Shot Measurement4. Multi-Photon Absorption5. Rabi Oscillation6. Conclusions
Head: H. Takayanagi
About 20 researchers participate to the projectwhich consists of five sub-projects.
Four qubit-research projects and a quantum cryptography one.
QIT Project in NTT Basic Research Laboratories
SQUID
Coupled QDs(artificial molecule) Exciton in QDs
Quantum gate operationRabi oscillationSingle-shot measurementMulti-photon absorptionRabi oscillation
Four Kinds of Qubit
Atom Chip
cooled atom
Solid-State Qubits
Quantum cryptography with a single photon
電気光学変調器
AmpGene-rator
時間間隔解析器
時間間隔解析器
AliceBob
HeliumCryostat
Quantumdot
lens
Pin-holeLens
Single-modefiber Grating
Space filter
BeamSplitter
Half-wavelength ¼ wavelength
Splitter
50%-50%BeamSplitter
Detector 1
Detector 2
Detector 3
Detector 4
waveguide
Counter Photon 0
Mirror Attenuator
Titanium-Sapphire Laser
Lens
BeamSplitter
Testing
Nature, 420 (2002) 762
0 2.5 5 7.5 10 12.5 15 17.5
0
2.5
5
7.5
10
12.5
15
17.5
Josephson persistent current QubitJosephson persistent current Qubit
Josephson Energy : cos( 2 a -+= EJU ) )cos (a- --1 cos- 2 2 f 1
2
Phase difference
+ + 2 f = 1 2
3q =
)( 2
1 p
1 2
)(2
1 m 1
2
qubit = f 0
EJ
1
2
p
m
=0.6
mp
U
=0.8
U
mp
=1.0
m p
U
=0.6
mp
U
=0.8
U
mp
=1.0
m p
U
=0.6
mp
U
=0.8
U
mp
=1.0
m p
U
=0.6
mp
U
=0.8
U
mp
=0.8
U
p
m
J. E. Mooij et al.,Science 285, 1036 (1999).
f = qubit / 0
f = qubit / 0 = 0.5
B
EJ
EJ
Schematic qubit energy spectrum Schematic qubit energy spectrum
0.49 0.50 0.51
-10
-5
0
5
10
15
Ene
rgy
(GH
z)qubit /
0.4 0.5 0.6-100
0
100
Ene
rgy
(GH
z)
qubit/
)(
)(
2
1
f
f
5.00qubit f
Three-Josephson-junction Loop:Description
)2cos(coscos2 2121 fE
U
J
Josephson Energy:f 2321
• Flux quantization:
)cos1( JJ EU
• Josephson Energy (1 junction):
• Coupling energy (1 junction):
EC = e2/ 2C EJ
C
EJ ; C
ext= f 0
3
1 2 EJ
C
J.E. Mooij 、 et al (1999)
<1.0
Three-Josephson-junction Loop:Energy Diagram
)(2
1
)(2
1
21
21
m
p
2 minima in each unit cell.
m
p
p
U
m
Top View
f=0.5
Three-Josephson-junction Loop: Dependence of the Potential
=0.6 =0.8
=1.0
pm
U
m m pp
UU
If increases, the barrier height :• increases between the two minima of one unit cell• decreases between the minima of adjacent cells
f=0.5
Three-Josephson-junction Loop:Flux Dependence of the States
Classical states = persistent currents of
opposite sign. Degenerated at f = 0.5
Quantum tunnelling “anti-crossing”
Symmetric and antisymmetric superposition of the macroscopic
persistent currents Quantum ground state |0> Classical states
Quantum first excited state |1>
<Iq>/Ip
E0 (1) E Level splitting
/0
Sample FabricationSample Fabrication
Qubit and a detector dc-SQUID
NTT Atsugi
Josephson junctionsAl / Al2O3 / Al
Junction areaSQUID : 0.1 x 0.08 m2
Qubit : 0.1 x L m2, ( = 0.8 ) L = 2 ~ 0.2
Loop size SQUID ~ 7 x 7 m2
Qubit ~ 5 x 5 m2
Mutual inductance M ~ 7 pH
• e-beam lithography
• Shadow evaporation
• Lift-off
e-beam lithographye-beam lithography
suspended-bridge & shadow evapolation suspended-bridge & shadow evapolation
Thermometer
Cavity
Ibias lineVm line
Microwave line
To mixing chamber
A loop
Samples
Sample and Cavity
NTT Atsugi
DC measurement
R.T.
4.2K
1.2K
0.8K
0.4K
10mK
1 2 3 4 5
Twisted Constantan wire
100
HP 10dB
200
connectors
Heat anchor for outer shield
Sample box
•No on-chip capacitor and resistor •No on-chip control line•Change twisted wires to thin coaxial
cables to introduce dc-pulse
V
2.4mm connectors
Flexible coaxial cable
200 200
Loop antenna~ 1mm above the sample
HP 20dB
RF lineVII
10 nF
Through capacitor
attenuator
resistance
DC measurement
I b
t
Vm
t
0
70 ~ 100 μsec
0
~ 100 nA
Readout through a dc-SQUIDReadout through a dc-SQUID
Vth(~30μV)
4~6 nA
Sweep Ib ( 140 Hz )
Tilt SQUID potential
Record each switching
when Vm = Vth~ 30 V
as a function of Isw
VmI b
qubit
IswIsw
Isw
Isw
~ 7 ms
DC measurement
Readout with a dc-SQUIDReadout with a dc-SQUID
)cos(20
extcsw II
-1000
-500
0
500
1000
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Voltage (mV)
Cur
rent
(nA)
Current is swept
I(V) curve
Isw(/ 0) curve
Magnetic field is swept
DC measurement
Qubit step in the SQUID IQubit step in the SQUID Iswsw
Qubit switches its current sign
Flux in SQUID changes through M
SQUID Isw changes
Step on the Isw(/ 0)
M
dc-SQUID
Qubit
Φ
qubit / 0
DC measurement
Josephson junctions : Al / Al2O3 / Al
Junction area : SQUID 0.2 x 0.2 m2
qubit 0.2 x L m2, L=0.3, 0.5, 1.0
SQUID
QubitI
Loop size : Lqubit = 5.1, 9.7, 19.0
(m) LSQUID = 6.3, 10.9, 20.2
LSQUIDLqubit
Parameter dependence of the qubit step
( , Ej, Ec )
Two energy scale Ec, ETwo energy scale Ec, EJJ
H = H = EEcc - - EEJJ cos cos - - IIexex [n, [n,]=i]=i
Josephson energy : Josephson energy : EEJJ
charging energy : charging energy : EEcc =(2ne) =(2ne)22/(2C/(2CJ J ))
kkBBT << T << EEJJ <<<< E Ecc < < → charge qubit
kkBBT << T << EEcc <<<< E EJJ < < → phase 、 flux qubit
energy energy
Phase difference
-Number of
tunneled pair n
Pair tunneling
superconductor superconduct
orTunnel barrier
QB# 5Junction area = 0.1 m2
Loop size : Lqubit = 9.7 m LSQUID = 10.9 m
QB# 8Junction area = 0.1 m2
Loop size : Lqubit = 19.0 m LSQUID = 20.2 m
~ 0.4GHz ~ kBT )
kBT~25mK
QB# 4Junction area = 0.06 m2
Loop size : Lqubit = 9.7 m LSQUID = 10.9 m
QB# 7Junction area = 0.06 m2
Loop size : Lqubit = 19.0 m LSQUID = 20.2 m
~ 2GHz > kBT )
QB# 6Junction area = 0.2 m2
Loop size : Lqubit = 9.7 m LSQUID = 10.9 m
QB# 3Junction area = 0.2 m2
Loop size : Lqubit = 5.1 m LSQUID = 6.3 m
~ 2MHz << kBT )
Qubit energy splitting
qubit / 0
qubit / 0qubit / 0qubit / 0
qubit / 0qubit / 0
Calculated qubit energy level
Ej=544 GHzEc=1.6 GHzEj/Ec=338
Ej=280 GHzEc=3.2 GHzEj/Ec=87
Ej=130 GHzEc=5.4 GHzEj/Ec=24
=2 GHz
=0.4 GHz
=2 MHz
Optimal operation point for SQUIDQubit signals appear at half-integer
Sensitivity of dc-SQUIDdepends on magnetic fields
We can achieve excellentresolution at f = 1.5
↓
↑
Spectroscopy
EJ = 312 GHz, EC = 3.8, = 0.7
83CJ EE
= 2.6 GHz
after averaging
w/o averaging0.001M 2.4 GHz
Qubit signals at different SQUID modulationQubit signals at different SQUID modulation
S/N depends on SQUID Isw
qubit and SQUID to be crossed
at small Isw
|>|>
|>
|>
design
T = 25 mK
DC measurement
H 1
2
, ( f 0.5) , f ext /0
E0(1) () 2 2 , E 2 2
0 a L b R
1 b * L a* R
ˆ I p L L R R I p
I p 0 0 | ˆ I p | 0
( a2 b
2)I p
2 2I p
I p 1 1 | ˆ I p | 1
(a2 b
2)I p
2 2I p
L
R
Quantum ground state |0> Classical states
Quantum first excited state |1>
<Iq>/Ip
E0 (1) E Level splitting
/0
f=
TkI
ee
Ie
IeII
Bp
Ep
E
pE
p
thermalp
E
2tanh
1
1
22
22
2222
10
Quantum ground state |0>
Classical states
Quantum first excited state |1>
<Iq>/Ip
E0 (1) E Level splitting
/0
Boltzman Distribution
Schematic qubit energy spectrum Schematic qubit energy spectrum
0.49 0.50 0.51
-10
-5
0
5
10
15
Ene
rgy
(GH
z)qubit /
0.4 0.5 0.6-100
0
100
Ene
rgy
(GH
z)
qubit/
)(
)(
2
1
f
f
5.00qubit f
SpectroscopySpectroscopy
ground state
excited state
DC measurement
Pulse measurement
Readout without averaging
Single shot measurement into { l0>, l1> } bases
The <Iq> step shape does not change.
Only the population changes.
qubit / 0
DC measurement
Close-up of Isw, T=25 mK
f f = 1.50102
Histogram is well separated !
0.001M 2.4 GHz
counts
counts
qubit / 0
DC measurement
Readout after averaging
Expected Current
( canonical ensemble average )
qubit / 0
DC measurement
Experimental setupExperimental setupR.T.
4.2K
1.2K
0.8K
0.4K
29mK
1 2 3 4 5
Thin coaxial cable 0.33 mm
HP 10dB
Samplecavity
Flexible coaxial cable
Terminator50
RF lineSLP-1.9
Weinschell10dB
On-chip strip line
Meanderfilters
VVII
V + V -I +I -
RF in
Sample cavity
RFin : 2 attenuatorsRFout : terminator
+ attenuatorDC : LP filter + Meander filter
RF in
Pulse measurement
Multi-photon transition betweenMulti-photon transition between superposition of macroscopic quantum states superposition of macroscopic quantum states
E 0
(1)
1.5101.5051.5001.4951.490
qubit
/
h
< I
P >
T
1.5101.5051.5001.4951.490
qubit
/
1 1
1
12
3
32
233
2
2h
+
ー
( ) /√2 ground state
( ) /√2 1st excited state
Multi-photon transition
Multi-photon spectroscopyMulti-photon spectroscopy
SQUID readout
-2
-1
0
1
2
d I
SW (
nA
)
1.5041.5021.5001.4981.496
qubit /
0
RF : 3.8 GHz
-10 dBm
1
12
23
2
1
0
-1
-2
d I
SW (
nA
)
1.5041.5021.5001.4981.496
qubit /
0
RF : 3.8 GHz
0 dBm
1
1 2
2
3
=0.86GHz
1-photon
2 -photon
Multi-photon transition
110
100
90
80
70
I SW [n
A]
1.49121.4905 1.49421.4935
qubit / 0
1.49721.4965
data fitting
Multiphoton absorption at 9.1 GHz
single
off
10 dBm12 dBm
0 dBmPRF =- 21 dBm
12 dBm
off
off
9.6 dBm
13.2 dBm
doubletriple
RF Power dependence
20[dBm]]dBm[RF
RF10PI
500
400
300
200
100
0
HW
HM
[M
Hz]
43210IRF (arb. units)
singledoubletriple
3.0
2.0
1.0
0.0
amp
litu
de
[nA
]
43210IRF (arb. units)
9100MHz
212
212
2
1222
1-
2
1222
1Amp
2
1][s HWHM
][rad/s HWHM
TT
TT
T
TT
T
TT
n
n
nn
nn
20rf
rf
rf10
)(P
nn
I
IsJ
power microwave : [dBm]
constant coupling :
point degeneracy at the splittingenergy : [MHz]5602[rad/s]
timedephasing : [s]
timerelaxation : [s]
dipth -n of ampletude : Amp
dipth -n of maxima halfat width half : ][s HWHM
rf
2
1
-1
P
s
T
Tn
n
----- (3)
------------------ (4)
)( rf00 IsJ
Multi-photon transition
Peak width vs MW intensityPeak width vs MW intensity
Bloch Kinetic Equation
180 ns ~1μs
resonant microwave
Ib DC pulse
time
Pulse measurement schemePulse measurement schemerepetition: 3kHz ( 333 s)
SQUID switch
Non-switching
Pulse measurement
h
E ext )(
ext
I bias
Vout +
Ibias + SQUID Ibias -
Vout -
MW discrimination of the switching event
Non-switching event Switching event
V th
Switchingevents
Non-switchingevents
55
50
45
40
35
30
25
Pro
bab
ilit
y [%
]
210
Delay Time [ s]
T1 = 1.6 s
data exp-fit
Relaxation time TRelaxation time T11
9.1 GHz 1 s pulse
030304_1 (1,2)FQB2
Ib pulse height 1.474 V, Trailing height ratio 0.6
1 s
500 ns3 s
delay time
0.49 0.50 0.51
-10
-5
0
5
10
15
Ene
rgy
(GH
z)
qubit /
Ground state
1st excited sate
MW
Pulse measurement
Trailing height ratio 0.7
600 s
150 ns
Resonant MW pulse width
11.4 GHz
Quantum Oscillation : Rabi oscillationsQuantum Oscillation : Rabi oscillations
pulse width ( ns )
sw
itc
hin
g p
rob
ab
ilit
y (
% )
MW amplitude (a.u.)
R
ab
i fr
eq
ue
nc
y
( M
Hz
)
Dephasing time ~ 30 ns
Pulse measurement
NTT Atsugi
SummarySummary
Future planFuture plan
• Spectroscopy of MQ artificial 2-level systemSpectroscopy of MQ artificial 2-level system• Qubit readout without averaging (DC)Qubit readout without averaging (DC)• Multi-photon transition between superposed MQ statesMulti-photon transition between superposed MQ states• Coherent quantum oscillation ( Rabi oscillation )Coherent quantum oscillation ( Rabi oscillation )
• TT11 ~1.6 ~1.6 s, Ts, T22 RabiRabi ~ 30 ns ~ 30 ns
• Ramsey, Spin echo Ramsey, Spin echo • Two qubit fabrication and operation Two qubit fabrication and operation • MQC with single shot resolutionMQC with single shot resolution
NTT Basic Research Laboratories Hirotaka TanakaShiro SaitoHayato NakanoFrank DeppeTakayoshi MenoKouich Semba
Tokyo Institute of TechnologyMasahito Ueda
Yokohama National UniversityYoshihiro ShimazuTomoo Yokoyama
Tokyo Science UniversityTakuya MouriTatsuya Kutsuzawa
collaborators collaborators
エネルギー固有状態を one-shot measurement で見た。
RL qubit
の時、
を測っている。12222
z)(1
2p
)(12 p
を測っているのではない。これを測ると、
0.50/
と の superposition は、生きている。
L R
LL 0 と の間のsuperposition は死んでいる。
LL 1
0.5
time domain で真ん中に出る理由Qubit の磁場の量子力学的平均値を取っているからQubit の磁場は z のはず( projection) 。
intSQUIDqubit HHHH を使って、 time-dependent な Schrödinger方程式を解き、 SQUID の switching currentを求めると、 EJ/EC が小さくなると、ピークは1つ、反対に EJ/EC が大きくなると、ピークは2つになる。
0.5
ピーク1つ
ピーク2つ