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

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