Sluices, pumps and phase-slip: the outlook for a quantum current standard

1
Sluices, pumps and phase-slip the outlook for a
quantum current standard
Low Temperatures 2008, Espoo, Finland 28-30 March
2008

• S. P. Giblin

2

• The metrological triangle - what information will
  it provide?
• Triangle closure experiments currently underway
  or planned
• Candidate single electron pump technologies
• Semiconductor pumps
• Hybrid turnstile
• Quantum phase-slip

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The metrological triangle
f
Josephson Effect
Single Electron Transport
V/fJ n/KJ
I/fS nSQS
V
I
Quantum Hall Effect
V/I RK/i
K. K. Kikharev, A. B. Zorin, J. Low Temp. Phys.
59, 347 (1985)
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Include error terms

• KJ (1 eJ) ? 2e/h
• RK (1 eK) ? h/e2
• QS (1 eS) ? e

triangle experiment measures eJ eK eS

• Reasons for believing eJ eK 0 (assumed by
  CODATA)
• Theoretical arguments (topology in case of QHE,
  gauge invariance etc in case of JJ).
• Experimental absence of material dependence to KJ
  or RK (universality).

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What does all the available data say about the
error terms?
Relax conditions in CODATA least-squares
determination
KJ
Input Data
RK
Observational Equations
h
e
eK (0.020 0.018) ? 10-6 eJ (-0.077 0.080)
? 10-6
Include only non-discrepant data
eJ (0.238 0.720) ? 10-6
P. Mohr, B. Taylor and D. Newell, report to the
18th CCU, 11-13 June 2007, also arXiv08010028
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Direct metrological triangle using Cryogenic
Current Comparator (CCC)
Integration time set by CCC current noise ? 104 s
to reach 1 part in 107
F. Piquemal, G. Geneves, Metrologia 37, 207
(2000) J.Flowers, Science 306, 1324 (2005)
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Direct metrological triangle using high-value
resistor and BOT
RK/i
100 pA
2.4 nV/?Hz _at_ 0.1 K
I1NQxf2
Vn1f1/KJ
1 MO
100 µV
I2
BOT, measures I1-I2 1 fA/?Hz
Integration time set by Johnson noise ? 5?104 s
to reach 1 part in 107
H. Seppa et al, CPEM digest 2004
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Indirect metrological triangle
nQx
1 pF, 6.25 Me
1 pA for 1 s
0.01 e/?Hz
C
RRK/i
1 V
Vn1f1/KJ
Accuracy limited by measurement of C in terms of
RK to ?2 parts in 108 Frequency dependence of C
0.01 Hz - 1 kHz ??
M. Keller et al, Science 285, 1706 (1999)
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Triangle experiments - hardest problems

• Direct via CCC - making a stable, high
  turns-ratio CCC (mostly solved by LNE)
• Direct via BOT and resistor - making a high value
  cryogenic resistor with low temperature
  co-efficient, then comparing with RK (In progress
  - MIKES)

Need SET current gt 100 pA

• Indirect via Capacitor - Understanding
  f-dependence of C from 0.01 Hz to 1 kHz

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Result of single QMT experiment done to date
Indirect triangle, charging capacitor with 1 pA
current from 7-junction Al / AlOx pump

• C0/CQ - 1 (-0.10 0.92) ? 106

eK (0.020 0.018) ? 10-6 eJ (0.238 0.720)
? 10-6
M. Keller et al, Science 285, 1706 (1999) M.
Keller, Metrologia 45, 102 (2008)
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Basic SET physics
V/2
EC e2/2C gtgt kBT C 1 fF (micron-size)
requires T lt 100 mK Number of electrons on island
stable against thermal fluctuations RTgtgtRK Wavefun
ction of extra electrons localised on island
N
N1
N2
N-1
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Conventional fixed-barrier pumps
Al / AlOx junctions
A 3-junction electron pump
VB
I
V/2
-V/2
VG1
VG2
VG1G
VG
1
2

1. Electron from source onto first island
E
2. Electron onto second island

• f ltlt 1/RTCT ? 10 MHz

1/f
t
3. Electron from second island into drain
M. Devoret, D. Esteve, C. Urbina, Nature 360, 547
(1992)
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NIST 7-j pump - unresolved questions
At lowest temperatures theory predicts a much
lower error rate than is experimentally observed
in a shuttle experiment
Theory includes cotunnelling but not PAT
1012
Experiment includes a measurement of all pump R,
C and pump temperature.
R. Kautz, M. Keller, J. Martinis, PRB 60, 8199
(1999)
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Cause of rare errors in 7-j pump - substrate
noise ?
QN (e/Hz1/2)
10-3
Measured in SET transistors
104
106
108
1010
102
F (Hz)
10-7
Magnitude of 1/f noise required to explain
observed error rate (somewhat schematic)
10-9
M. Covington, M. Keller, R. Kautz, J. Martinis,
PRL 84, 5192 (2000)
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Tuneable-barrier pumps
Allow tunneling with low RT, Enforce quantisation
with high RT.
M. D. Blumenthal at al, Nature Physics 3, 343
(2007)
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Tuneable-barrier pumps - best result so far
f 547 MHz
88 pA
0.01
87 pA
M. D. Blumenthal at al, Nature Physics 3, 343
(2007)
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Non-adiabatic theory (1)
Consider how occupation of dot changes as barrier
is raised rapidly
N undefined
N electrons
V(t) V0 exp (-t/t)
10-7
I
Ng
K. Flensberg et al, PRB 60, R16291 (1999)
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Non-adiabatic theory (2)
N / cycle
800 kHz
80 MHz
8 GHz
10-8 (with right params.)
B. Kaestner, V. Kashcheyevs, S. Amakawa, L. Li,
M. D. Blumenthal, T. J. B. M. Janssen, G. Hein,
K. Pierz, T. Weimann, U. Siegner, H. W.
Schumacher, Cont-Mat arXiv0707.0993v1
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Hybrid turnstile
S
N
S
Vg
Vb/2
Vb/2
EC/? 4, 30 pA accurate to 10-8
J. Pekola al, Nature Physics 4, 120 (2008) D.
Averin and J. Pekola, arXiv0802.1364 (2008)
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Quantum Phase Slip
A possibility of a possibility - H. Mooij
Charge and phase are conjugate variables
J. E. Mooij and Yu. V. Nazarov, Nature Physics 2,
169 (2006)
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Quantum phase - slip
Josephson junction with large EJ planar
geometry. PSJ with large ES long thin geometry.
a few µm
lead
lead
80 nm
8 µm
w ltlt ?
High-ohmic resistors RgtgtRK up to ES/h
Heating in resistors could limit current to ? 1 nA
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Studies on QPS so far have focussed on fitting
R(T) and I(V) of thin SC wires to theoretical
models. Observation of I(V) steps would be
conclusive proof of coherent QPS
Altomare et al, PRL 97, 017001 (2006)
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Partners in EMRP project REUNIAM
PTB
R-pumps, QPS fab, indirect triangle
LNE
R-pumps, direct triangle (CCC route)
METAS
indirect triangle
MIKES
Direct triangle (BOT route)
NMI
F-dependence of capacitor
NPL
Tuneable-barrier pump, QPS meas.
HTU
Hybrid turnstile
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Post-doc positions

• PTB (Germany) - fabrication of QPS devices
• LNE (France) - CCC development
• NPL / Cambridge (UK) - GaAs pump fabrication and
  measurement