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Quantenelektronik
1
Experimental Investigation of Quantum Phenomena in a Persistent Current Qubit
E. Il‘ichev, N. Oukhanski, A. Izmalkov, U. Hübner, T. May, Th. Wagner, I. Zhylaev, Ya. S. Greenberg,H. E. Hoenig, H.-G MeyerInstitute for Physical High Technology, P.O. Box 100239, D-07702 Jena, Germany
M. Grajcar, W. KrechInstitute of Solid State Physics, Friedrich Schiller University, D-07743 Jena, Germany
M. H. S. Amin, A. Smirnov, Alec Maassen van den Brink, A. M. ZagoskinD-Wave System, Inc., 320-1985 West Broadway, Vancouver, B.C., Canada
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Contents
1. Introduction – single junction interferometer2. Idea of measurements:classical case3. Idea of measurements:quantum case4. Technology5. Response of the qubit to nonresonant
excitation. 6. Response of the qubit to resonant excitation. 7. Rabi spectroscopy 8. Summary and outlook
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Single-junction interferometer
Intern. flux
Extern. flux
-2
-1
1
2
3
-2 -1 0 1 2 3
β=0.8
ϕ /π
ϕext/πβ=1.5
Φ 0-Φ 0
Φ=Φext−LI
ϕ=ϕext-βsinϕ, where
β=2πLIC/Φ0
ϕ π= 20
ΦΦ
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Single-junction interferometer
-1 0 1 2 3-2
0
2
4
6
8
Magnetic flux
Ener
gy
U∝ (ϕ-ϕx)2/2-βcosϕ,
where β=2πLIc/Φ0
Intern. flux
Extern. flux
-2
-1
1
2
3
-2 -1 0 1 2 3
β=0.8
ϕ /π
ϕext/πβ=1.5
Φ 0-Φ 0
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FCEBDA
UJ
energy vs phase at different external fluxes
Idea of measurements: single-junction interferometer in classical case
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FCEBDA
UJ
energy at different external fluxes
Idea of measurements: single-junction interferometer in classical case
M
L LT CT
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FCEBDA
UJ
energy at different external fluxes
Idea of measurements: single-junction interferometer in classical case
M
L LT CT
Φ
Φe
A
D
B
E
C
F
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FCEBDA
UJ
energy at different external fluxes
Idea of measurements: single-junction interferometer in classical case
M
L LT CT
Φ
Φe
A
D
B
E
C
F
ΦdcExternal flux Φrf + Φdc
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FCEBDA
UJ
energy at different external fluxes
Idea of measurements: single-junction interferometer in classical case
M
L LT CT
Φ
Φe
A
D
B
E
C
F
ΦdcExternal flux Φrf + Φdc
Φdc
V
Voltage across the tank vs Φdc
Quantenelektronik
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FCEBDA
UJ
energy at different external fluxes
Idea of measurements: single-junction interferometer in classical case
M
L LT CT
Φ
Φe
A
D
B
E
C
F
ΦdcExternal flux Φrf + Φdc
Φdc
V
Voltage across the tank vs Φdc
Quantenelektronik
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FCEBDA
UJ
energy at different external fluxes
Idea of measurements: single-junction interferometer in classical case
M
L LT CT
Φ
Φe
A
D
B
E
C
F
ΦdcExternal flux Φrf + Φdc
Φdc
V
Voltage across the tank vs Φdc
E.Il’ichev et al. Rev. Sci. Instrum. 72, 1882, 2001
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Idea of measurements – quantum case
FCEBDA
UJ
energy at different external fluxes
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Idea of measurements – quantum case
FCEBDA
UJ
energy at different external fluxes
Φe
B E
F
C
A
D
Φ0/2
UJ
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Idea of measurements – quantum case
Φ
Φe
A
D
B
E
C
FFCEBDA
UJ
energy at different external fluxes
Φe
B E
F
C
A
D
Φ0/2
UJ
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Idea of measurements – quantum case
Φ
Φe
Φdc
Φdc
V
External flux Φrf + Φdc
Voltage across the tank vs Φdc
A
D
B
E
C
FFCEBDA
UJ
energy at different external fluxes
Φe
B E
F
C
A
D
Φ0/2
UJ
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Idea of measurements – quantum case
Φ
Φe
Φdc
Φdc
V
External flux Φrf + Φdc
Voltage across the tank vs Φdc
A
D
B
E
C
FFCEBDA
UJ
energy at different external fluxes
Φe
B E
F
C
A
D
Φ0/2
UJ
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Φ
Φe
Φdc
Φdc
V
External flux Φrf + Φdc
Voltage across the tank vs Φdc
A
D
B
E
C
F
Idea of measurements – quantum case
Ya. S. Greenberg et al. PRB 66, 214525, 2002
Ya. S. Greenberg et al. PRB 66, 224511, 2002
FCEBDA
UJ
energy at different external fluxes
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Nb technology for the coil of the tank circuit.
T. May, et al. Rev. Sci. Instrum., 74; March 2003
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•Nb coil is prepared on oxidized Si substrates lithographically.•The line width of the coil windings was 2 µm, with a 2 µm spacing. •Various square-shape coils with between 20 and 150 µm windings were designed.•We use an external capacitance CT.
Nb coil without concentrator.
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Al qubit
•Material: Aluminium, Shadow-evaporation tecnique•Two contacts ~600x200nm, (IC ≈ 600 nA), the third is smaller, so that α=EJ1 /EJ2,3 ~0.9•Inductance L ≈ 20 pH•J.E. Mooij et al., Science 285, 1036, 1999.
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Nonresonant excitation of the qubit - setup
Amp Lock In Amplifier
RF Generator5-100MHz
DC Generator0.1-10Hz
Oscilloscope
QUBIT
T=2K T=300K
Amp
T=10mK
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Tank voltage vs external flux – large Φac
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Tank voltage vs external flux near Φdc= Φ0/2 – small Φac
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Idea of Rabi spectroscopy - resonant excitation
M
L LT CT
hΩ
Ω
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Idea of Rabi spectroscopy - resonant excitation
Resonant circuit
Rabi spectra
Voltage
Frequency
ωR∼ Ahf
<Sx> ∼ sin(ωRt)sin(Ω t)
<Sy> ∼ sin(ωRt)cos(Ω t)
<Sz> ∼ cos(ωRt)
H
S
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Resonant excitation of the qubit - setup
HF Generator 0.1-3GHz
Amp Amp
DC source
QUBIT Spectrum Analyzer
T=2K T=300KT=10mK
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The voltage spectral density on the tank circuit at different microwave amplitude at 868 ± 2 MHz
2/ toclose 0ΦΦ
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0.96 0.98 1 1.02 1.04
(P/P0)1/2
0.9
1
1.1
ωR/ω
T
(b)
0.96 0.98 1 1.02 1.04
(P/P0)1/2
0
0.5
1S V
,max
/S0
(a) b
ca
bac
Decoherence time
τRabi~2.5µs
22222
2
22222
22
22
2
2
)()()()(2),(
TT
T
R
R
TRV C
LIkSγωωω
ωωωωω
ωωωεωω+−
×Γ+−
ΓΩ
=
E.Il’ichev et al., preprint , cond-mat /0303433, 2003
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Summary and outlook
Response of the single qubit to nonresonant and resonant excitation
Nonresonant response is macroscopic quantum tunneling
• Resonant response is similar to NMR for the single spin
• In contrast to quantum optics experiments, where Ω ± ωR were detected, we detected ωR
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