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Weak measurement of cotunneling time

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.

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Weak measurement of cotunneling time

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  1. Weak measurement of cotunneling time Yuval Gefen (WIS) • Alessandro Romito (FU Berlin) 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 MEASUREMENT = WEAK SYSTEM/DETECTOR ENTANGLEMENT

  5. Weak measurements

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

  7. can be complex !

  8. Weak measurements projective measurement weak measurement [Von Neumann (1932)]

  9. Postselection and WV time weak value weak [Y. Aharonov et al. (1988)]

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

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

  14. Charging energy 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 [D. Averin, Yu. V. Nazarov (1990)]

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

  16. 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]....

  19. Cotunneling time x 64 <I>, elastic SIJ, elastic

  20. NOTE:

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

  22. THANK YOU

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