Single-gate non- adiabatic quantized charge pumps International Conference on Quantum Metrology, Poznań, Poland, May 13 th , 2011 Datorzinātnes lietojumi un tās saiknes ar kvantu fiziku Vyacheslavs (Slava) Kashcheyevs University of Latvia, Riga, Latvia Collaboration: Bernd Kästner PTB, Braunschweig, Germany
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International Conference on Quantum Metrology, Poznań, Poland, May 13 th, 2011 Datorzinātnes lietojumi un tās saiknes ar kvantu fiziku Vyacheslavs (Slava)
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Single-gate non-adiabatic quantized charge pumps
International Conference on Quantum Metrology, Poznań, Poland, May 13th , 2011
Datorzinātnes lietojumi un tās saiknes ar kvantu fiziku
Vyacheslavs (Slava) Kashcheyevs University of Latvia, Riga, Latvia
Collaboration:Bernd Kästner
PTB, Braunschweig, Germany
Single-gate pumps in metrology context
A particular class of “quantized pumps” Aim at low, predictable error rate Motivated by…
ometrology needs o basic physics
I
V2
1 e per cycle
I = e f
Outline
Introduction (phenomenological) Message I: constructive non-adiabaticity Message II: universality of decay cascade Outlook for metrological applications
Outline
Introduction (phenomenological) Message I: constructive non-adiabaticity Message II: universality of decay cascade Outlook for metrological applications
Animation: A. Müller
Quantum dot
V1(t)
V2
V1(t) = V1DC + V1
AC cos t
Quantum dot
~ 250 nm
V1DC
mV
mV
V2
V1AC
f
Data: F. Luckas (U.of Hannover)
Outline
Introduction (phenomenological) Message I: constructive non-adiabaticity Message II: universality of decay cascade Outlook for metrological applications
Double-barrier quantum dot~ 250 nm
Source
Quantum dot
Current IDrain
V2
V1
Charge stability diagram
Coulomb blockadefor
Resonance lines
V1
V2
2
1
0
Bottom energy
3
Left
Right
V1
2
1
0
Bottom energy
3
Left
Right
Adiabatic paradigm for pumps
Stay close to equilibrium Well-established
SET technology At least two
phase-shifted parameters Increasing frequency
increases error rateV2
LOAD
UNLOAD
Mapping of charge carrier type: Buitelaar, VK et al, Phys. Rev. Lett. 101, 126803 (2008)
First quantized pump: Pothier et al, Eur.Phys.Lett., 17, 249 (1992)
Blumenthal et al, Nature Physics 3, 343 (2007)Kaestner, VK et al, Phys. Rev. B 77, 153301 (2008)
Moskalets-Büttiker (2002) “no-go theorem” :adiabatic single-parameter modulation cannot produce current
Outline
Introduction (phenomenological) Message I: constructive non-adiabaticity Message II: universality of decay cascade Outlook for metrological applications
Universal limit: decay cascade regime
V
V (mV)C
urr
ent
(e·f
)
VK and B.Kaestner, Phys. Rev. Lett. 104, 186805 (2010)
decreasing escape rate escape rate to maintain equilibrium essential non-equilibrium for If then the initial condition is forgotten!
Happy families are all alike; every unhappy family is unhappy in its own way.Leo Tolstoy, Anna Karenina, Chapter 1, first line
Raise faster than decouple!
1-step line shape
Backtunneling to empty space
Survival probability:
Escape rate ansatz:
Kaestner et al,Appl. Phys. Lett. 94, 012106 (2009) Fujiwara et al. Appl.Phys.Lett. 92, 042102 (2008)
n
Γ(t)
Universal shape in rescaled coordinates
Data: PTB group, unpublished
Rescaled voltage
Data from B.Kaestner et al,Appl. Phys. Lett. 94, 012106 (2009)
f=50 MHzT=40 mK
Single-step fitting
I=ef=8 pA• Plot on double-log scale• Look for straight line
Many-step line shape
• Define (dimensionless):
• If there is scale separation…
• …then the solution is
Data from B.Kaestner et al,Appl. Phys. Lett. 94, 012106 (2009)
f=50 MHzT=40 mK
Two-step fitting δ2 is the figure of merit
I=ef=8 pA
Fitting parameters!
Universality of the decay cascade
VK and B.Kaestner, arXiv (2009); PRL (2010)
Device “fingerprint”
αV/ δ
a. Si nanowire dots, pulsed , T=20KFujiwara et al. APL (2008)
b. GaAs/AlGaAs etched, B=3 TKaestner et al APL (2009)
c. Surface-acoustic-wave-drivenJanssen & Hartland (2001)
d. Classical simulation, Robinson & Barnes, PRB (2001)
δ2
δ3
δ4
δ5
Theory prediction:
δ2 is the figure of merit
Outline
Introduction (phenomenological) Message I: constructive non-adiabaticity Message II: universality of decay cascade Outlook for metrological applications
-0.22 -0.20 -0.18
0
20
40
60
IP (pA)
VGD
(V)
Sample A Fit A1 Sample B Fit B
-0.198 -0.192 -0.186
54.464
54.468
54.472
54.476
Sample A Run 1 Fit A1 Run 2 Fit A2
IP (pA)
VGD
(V)
-200
-100
0
n×106
S.Giblin et al., New J. Phys. 12 073013 (2010)
f=340 MHz
Traceable measurement (NPL)
d2=15.2 (Fit A1)
d2=17.1 (Fit A2)
Outlook for metrological applications
Advantages:o Optimal frequencies in 100 MHz ÷ 1 GHz rangeo Stability against voltage bias negligible leakageo Single ac driving signal parallelizationo Robustness one gate per pump to tune
Optimization directions:o barrier selectivity optimizationo serial operation with error detection and correction(Wulf & Zorin, arXiv:0811.3927)