Null weak values in quantum dots and beyond OZ , Alessandro Romito, - PowerPoint PPT Presentation

Null weak values in quantum dots and beyond OZ , Alessandro Romito, and Yuval Gefen and Experiment: OZ , Alessandro Romito, D. J. Starling, G. A. Howland, J. C. Howell , and Yuval Gefen arXiv:1205:3877 Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Outline • (Null) Weak values • Realistic implementations Amplified quantum state discrimination • Optical analogue => Experimental manisfestation

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Motivation Weak Values why ? • Elucidates fundamentals & paradoxes of quantum mechanics • Non-destructive measurement of (classically forbidden) virtual states • Hyper-precision measurements • Amplified quantum state discrimination

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Measuring a qubit system • How to measure | β 0 | 2 ? | 0 > | 1 > | 1 > | 0 > Charge qubit | 0 > Josephson phase Spin qubit qubit | 1 > Which-path qubit Polarization of light

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Measuring a charge qubit (strongly) Couple a quantum point contact to one of the quantum dots | 0 > | 1 > I 1 I I 0 | β 0 | 2 | α 0 | 2 P( Q ) Q Q 1 Q 0

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Measuring a charge qubit (weakly) Couple a quantum point contact to one of the quantum dots | 0 > | 1 > I | β 0 | 2 | α 0 | 2 P( Q ) Q Q 1 Q 0

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Weak Value Protocol • Preparation | i > Detector | 0 > • Weak measurement of | 1 > • (later) Strong measurement of on final state | f > I Weak value P( Q ) Q Q 1 Q 0 Y. Aharonov, D. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988)

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Null Weak Value Protocol • Preparation | i > Detector | 0 > • Weak measurement of • Strong measurement of with small probability p<<1 | 1 > • (later) Strong measurement of p on final state | f > Detector

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Null Weak Value Protocol • Preparation | i > Detector | 0 > • Strong measurement of with small probability p<<1 | 1 > • (later) Strong measurement of p on final state | f > Detector X 0 p | β 0 | 2 X X 1 | i >

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Null Weak Value Protocol • Preparation | i > Detector | 0 > • Strong measurement of with small probability p<<1 | 1 > • (later) Strong measurement of p on final state | f > Detector X 0 p | β 0 | 2 X X 1 | i > |< f | i p >| 2 | f > 1-p | β 0 | 2 | i p > | f > |< f | i p >| 2 | i p > = N [ α 0 | 0 > + (1- p ) 1/2 β 0 | 1 > ]

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Josephson phase qubit X 0 p | β 0 | 2 X X 1 | i > |< f | i p >| 2 | f > 1-p | β 0 | 2 | i p > | f > |< f | i p >| 2 N. Katz et al., Science 312, 1498 (2006); L. P. Pryadko and A. N. Korotkov, Phys. Rev. B 76, 100503 (2007).

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 What is it good for? • Amplified quantum state discrimination Option 1 Option 2 Compare Null Weak Values Measure strongly SNR std =| | β δ | 2 - | β 0 | 2 | cond – P 0 cond | SNR NWV =| P δ cond ) N < N | β δ | 2 (1- | β δ | 2 ) cond (1- P δ P δ

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 What is it good for? • Amplified quantum state discrimination

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Optical experiment • Amplified quantum state discrimination | f > H V V | H > ~ | 0 > ; | V > ~ | 1 > | i > = α 0 | H > + β 0 | V > NWV (scheme B) | i p > = N [ α 0 | H > + (1- p ) 1/2 β 0 | V > ] Null weak value = # W / (# W + # p ) NWV (scheme A) State preparation Standard method (crossed polarizers) O. Zilberberg , A. Romito, D. J. Starling, G. A. Howland, J. C. Howell, and Y. Gefen, arXiv: 1205.3877 (2012)

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012 Summary • Correlated measurements (and HOW you measure) => new observables • Novel protocol: partial collapse + strong measurement ( ≠ Weak value protocol) • Amplified quantum state discrimination (+ experiment) Thank you!