weak measurement of cotunneling time alessandro romito (fu berlin) quy nhon, vietnam,august 2013...
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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
