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

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

quantum dot I QPC=Quantum Point Contact

WEAK SYSTEM/DETECTOR ENTANGLEMENT WEAK MEASUREMENT = WEAK SYSTEM/DETECTOR ENTANGLEMENT

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

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

can be complex !

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

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)]

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

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?

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

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

[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)]

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)]

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

cotunneling weak measurement microscopic model system detector

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

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

inelastic elastic NOTE:

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

THANK YOU