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

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

May 28, 2023 356 likes •521 views

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,

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Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

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

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Outline

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

  • (Null) Weak values
  • Realistic implementations

Amplified quantum state discrimination

  • Optical analogue =>

Experimental manisfestation

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Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

  • Elucidates fundamentals & paradoxes of

quantum mechanics

  • Non-destructive measurement of

(classically forbidden) virtual states

  • Hyper-precision measurements

Motivation Weak Values why ?

  • Amplified quantum state discrimination
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SLIDE 4
  • How to measure |β0|2 ?

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Measuring a qubit system

| 1 > | 0 >

Josephson phase qubit Charge qubit Polarization of light

| 0 > | 1 >

Which-path qubit

| 0 > | 1 >

Spin qubit

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SLIDE 5

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Measuring a charge qubit (strongly)

|α0 |2 Q1 Q0 |β0 |2

Couple a quantum point contact to one

  • f the quantum dots

| 0 > | 1 >

I0 I1 I Q P(Q)

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SLIDE 6

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Measuring a charge qubit (weakly)

Q1 Q0

Couple a quantum point contact to one

  • f the quantum dots

I

| 0 > | 1 >

|α0 |2 |β0 |2 Q P(Q)

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SLIDE 7

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Weak Value Protocol

Q1 Q0

  • Preparation | i >
  • Weak measurement of
  • (later) Strong measurement of
  • n final state | f >

| 0 > | 1 >

I Q P(Q)

  • Y. Aharonov, D. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988)

Detector Weak value

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SLIDE 8
  • Preparation | i >
  • Weak measurement of
  • (later) Strong measurement of
  • n final state | f >
  • Strong measurement of

with small probability p<<1

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Null Weak Value Protocol

| 0 > | 1 >

Detector p Detector

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SLIDE 9
  • Preparation | i >
  • (later) Strong measurement of
  • n final state | f >
  • Strong measurement of

with small probability p<<1

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Null Weak Value Protocol

| 0 > | 1 >

Detector p

| i > p|β0 |2 X X X 1

Detector

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SLIDE 10
  • Preparation | i >
  • (later) Strong measurement of
  • n final state | f >
  • Strong measurement of

with small probability p<<1

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Null Weak Value Protocol

| 0 > | 1 >

Detector p

| i > p|β0 |2 X X X 1 1-p|β0 |2 | ip> | ip> = N [ α0| 0 > + (1-p)1/2 β0| 1 > ] | f >

|< f | ip >|2 Detector

| f >

|< f | ip >|2

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SLIDE 11

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

Josephson phase qubit

| i > p|β0 |2 X X X 1 1-p|β0 |2 | ip> | f >

|< f | ip >|2

| f >

|< f | ip >|2

  • N. Katz et al., Science 312, 1498 (2006); L. P. Pryadko and A. N. Korotkov, Phys. Rev. B 76, 100503 (2007).
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Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

  • Amplified quantum state discrimination

Option 1 Measure strongly

What is it good for?

Option 2 Compare Null Weak Values

<

SNRstd=| |βδ |2 - |β0 |2 | |βδ |2 (1- |βδ |2) N SNRNWV=| Pδ

cond – P0 cond |

Pδ

cond (1- Pδ cond ) N

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SLIDE 13

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

  • Amplified quantum state discrimination

What is it good for?

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SLIDE 14

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

  • Amplified quantum state discrimination

Optical experiment

  • O. Zilberberg , A. Romito, D. J. Starling, G. A. Howland, J. C. Howell, and Y. Gefen, arXiv: 1205.3877 (2012)

State preparation Standard method (crossed polarizers) NWV (scheme B) NWV (scheme A)

| i > = α0| H > + β0| V >

H V V

| H > ~ | 0 > ; | V > ~ | 1 > | ip> = N [ α0| H > + (1-p)1/2 β0| V > ] | f >

Null weak value = #W / (#W + #p )

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SLIDE 15

Oded Zilberberg - QD2012, Landau Institute, Chernogolovka, 9/13/2012

  • Correlated measurements (and HOW you measure)

=> new observables

  • Novel protocol: partial collapse + strong measurement

( ≠ Weak value protocol)

  • Amplified quantum state discrimination

(+ experiment)

Summary

Thank you!