Weak measurement of cotunneling time
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Weak measurement of cotunneling time Alessandro Romito (FU Berlin) Quy Nhon, Vietnam ,August 2013 Yuval Gefen (WIS)
description
Weak measurement of cotunneling time. Yuval Gefen (WIS). Alessandro Romito (FU Berlin). Quy Nhon, Vietnam ,August 2013. Weak values – introduction for pedestrians WV good to observe virtual states Weak measurement of cotunneling time. quantum dot. I. - PowerPoint PPT Presentation
Transcript of Weak measurement of cotunneling time
Weak measurement of cotunneling time
Alessandro Romito (FU Berlin)
Quy Nhon, Vietnam ,August 2013
Yuval Gefen (WIS)
Weak values – introduction for pedestrians WV good to observe virtual states
Weak measurement of cotunneling time
I
QPC=Quantum Point Contact
quantum dot
WEAK MEASUREMENT = WEAK SYSTEM/DETECTOR ENTANGLEMENT
FQMC13Weak
measurements
weak measurement weak value:
time
post selection(eigenvalue of )
weak measuremet of
preparation
A
B
ˆ ˆ[ , ] 0A B
Aharonov, Albert, Vaidman 1988
0
preselected state
post-selected state
weakly measur
ˆ ed observable
in
fin
B
0
0
ˆ| |ˆ
|
fin in
weakfin in
BB
can be complex !
FQMC13
[Von Neumann (1932)]
projective measurement
weak measurement
Weak measurements
FQMC13
time
weak value
weak
[Y. Aharonov et al. (1988)]
Postselection and WV
CQOX - QIM
counterfactual statementsmeasurement of simultaneous observablesaccess new observablesmeasure wave functionviolation of classical inequalities...
Foundations of quantum mechanics:
What for?
Experimental verificationquantum opticssolid state (2013!)
Precision measurementsquantum spin Hall effect of lightspacial displacementscharge sensing...
Applicationquantum feedback controlstate discrimination
A physical meaning for WV
WHAT ARE WEAK VALUES GOOD FOR?
Foundations of Quantum Mechanicscounterfactual correlationssimultaneous measurement of non-commuting observablesaccess to new observablesmeasure wave functionBell-type inequalitiesPrecision Measurement / Amplificationsmall spatial displacementscharge sensingQuantum spin-Hall effect of light Applicationsquantum feedback controlquantum state discriminationRealizationsoptics Josephson junction / optical cavity solid state?
accessing a quantum virtual state
accessing a MANY-BODY quantum virtual state
Cotunneling
[D. Averin, Yu. V. Nazarov (1990)]
Cotunneling
[D. Averin, Yu. V. Nazarov (1990)]
Thouless energy
Level spacing
Charging energy
Can you detect the extra charge in the dot?
For how long there is an extra charge in the dot in a successful cotunneling event?
How to detect?Simpler case:
sequential tunneling
strong measurement
Classical probabilities
Sukhorukov, Ihn, Ensslin et al. (2007)]
Experimentally available
Simpler case:
sequential tunneling
weak measurement
current-current correlations(self-consistent)
quantum correlations
(0)
(1) 0 0(1) (0)
( )[ ( ) ] ( )
lim( )
T t
seq T
dt ds P s J t s J I t
T I J J
cotunneling weak measurement
microscopic model
system
detector
1
change in transmission of QPC:
( )
N N
Amplitude Amplitude iu
FQMC13Tunneling timelong-lasting questionMac Coll (1932), Condon (1933), Wigner (1955) [delay time]..., Smith (1960) [dwell time],,,, Baz’ (1966) [Larmor precession]..., Buttiker & Landauer (1982) [time dep. modulation], Sokolovski & Connor (1993) [path integral], Steinberg (1995) [weak values]....
/E CE
FQMC13Cotunneling time
<I>, elastic
SIJ, elastic
x 64
inelastic 0
elastic
0
0
0
Re{ }WV dwell cotIm{ }WV
Th CE E
/ CE
cot / CE NOTE:
1/
2 CE 2
2
| |
2
ThTh C
S D
L EE E
X X
d
2
2
| |
2
ThTh C
S D
L EE E
X X
d
/ CE
21
2
3ln ( )
2 | |Th
C S D C
L E
E X X E
FQMC13Summary
ageneralizing the measurement scheme of sequential tunneling
,
athe cotunneling time can be defined via weak values
,
3eThe cotunneling time may deviate from the prediction of the uncertainty principle
