1. Weak measurement of cotunneling time
Alessandro Romito (FU Berlin) 1
good afternoon
THANKS invitation,
I want to discus how weak measurement can be a quite powerful tool to access physical quantities otherwise difficult to measure
with Yuval
weak values have been nicely introduced by Belzig and are common knowledge, but in the late 80’s people had to make a point that they are different than standard ones.
Yuval Gefen (WIS)
Quy Nhon, Vietnam ,August 2013

2. Weak values – introduction for pedestrians
WV good to observe virtual states
Weak measurement of cotunneling time

3. quantum dot I
QPC=Quantum Point Contact

4. WEAK SYSTEM/DETECTOR ENTANGLEMENT
WEAK MEASUREMENT =
WEAK SYSTEM/DETECTOR ENTANGLEMENT

5. Weak measurements 2
this shows weak is different when considering post-selected ensembles / conditioanl measurments

6. Aharonov, Albert, Vaidman 1988
weak measurement  weak value:
Aharonov, Albert, Vaidman 1988
time
post selection
(eigenvalue of )
weak measuremet of
preparation

7. can be complex !

8. projective measurement
Weak measurements
projective measurement
one important thing is the weakness important
weak measurement
[Von Neumann (1932)]

9. Postselection and WV weak weak value time [Y. Aharonov et al. (1988)]
this makes a difference e.g. when looking at conditional measurements
weak
time
[Y. Aharonov et al. (1988)]

10. What for? A physical meaning for WV Foundations of quantum mechanics:
counterfactual statements
measurement of simultaneous observables
access new observables
measure wave function
violation of classical inequalities
...
Foundations of quantum mechanics:
Experimental verification
quantum optics
solid state (2013!)
Precision measurements
quantum spin Hall effect of light
spacial displacements
charge sensing
...
A physical meaning for WV
flash that it is an active interesting field
Application
quantum feedback control
state discrimination

11. WHAT ARE WEAK VALUES GOOD FOR?
Foundations of Quantum Mechanics
counterfactual correlations
simultaneous measurement of non-commuting observables
access to new observables
measure wave function
Bell-type inequalities
Precision Measurement / Amplification
small spatial displacements
charge sensing
Quantum spin-Hall effect of light
Applications
quantum feedback control
quantum state discrimination
Realizations
optics
Josephson junction / optical cavity
solid state?

12. accessing a quantum virtual state
accessing a MANY-BODY quantum virtual state

13. [D. Averin, Yu. V. Nazarov (1990)]
Cotunneling
[D. Averin, Yu. V. Nazarov (1990)]

14. [D. Averin, Yu. V. Nazarov (1990)]
Cotunneling
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?
Thouless energy
Level spacing
Charging energy
[D. Averin, Yu. V. Nazarov (1990)]

15. Sukhorukov, Ihn, Ensslin et al. (2007)]
How to detect?
Simpler case:
sequential tunneling
strong measurement
Classical probabilities
Experimentally available
Sukhorukov, Ihn, Ensslin et al. (2007)]

16. current-current correlations (self-consistent)
Simpler case:
sequential tunneling
weak measurement
current-current correlations
(self-consistent)
quantum correlations

17. cotunneling
weak measurement
microscopic model
system
detector

18. Tunneling time long-lasting question
Mac 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]....
back to simpler
different approaches, many answers
time is not an observable, we don’t have a prescription, still it is physically relevant

19. x 64 Cotunneling time <I>, elastic SIJ, elastic
<I>, elastic
with this interpretation we can compute it
heavy, most simple case gives
SIJ, elastic
x 64

20. inelastic
elastic
NOTE:

21. Summary generalizing the measurement scheme of sequential tunneling ,
the cotunneling time can be defined via weak values , 3e
The cotunneling time may deviate from the prediction of the uncertainty principle

22. THANK YOU