superposition censorship

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AB, EPR and AC Conspiring to Preserve Causality Avshalom C. Elitzur [email protected] Shmuel Marcovitch [email protected]

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AB, EPR and AC Conspiring to Preserve Causality Avshalom C. Elitzur [email protected] Shmuel Marcovitch [email protected]. Superposition Censorship. Bob. Alice. EPR source Which-path correlation. Interference in Terms of Spin Using Stern-Gehrlach Devices. SG (- x ). - PowerPoint PPT Presentation

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Page 1: Superposition Censorship

AB, EPR and AC Conspiring to Preserve Causality

Avshalom C. Elitzur [email protected]

Shmuel Marcovitch [email protected]

Page 2: Superposition Censorship

EPR sourceWhich-path correlation

Superposition Censorship

Alice Bob

Page 3: Superposition Censorship

Interference in Terms of SpinUsing Stern-Gehrlach Devices

D C

Eigenstate of z-spin enters

SG (x)

SG (z)

SG (-x) (Erasure of the x-spin measurement)

Interference key: z-spin

zzAharonov and Vardi, PRD 20, 3213 (1979)

Page 4: Superposition Censorship

SG (z)

Alice

Superposition Censorship

SG (x)

SG (z)

SG (-x)

SG (x)

Bob

EPR-Bohm sourceSpin correlation

Page 5: Superposition Censorship

AB-MZI

D C

Click in either C or DClick always in C

Currentsuperposed

Currentonly on left(or right)

Page 6: Superposition Censorship

D C

Alice Bobdoes nothing

Click in either C or D

measures x spin

Click in C

Currentsuperposed

Currentonly on left(or right)

EPR-Bohm source

AB+EPR

We neglect any phases due to interaction of the spin with the magnetic fields in the SG devices throughout

Page 7: Superposition Censorship

“Cat State” of a Currenttoo gedankenly?

C

D

Page 8: Superposition Censorship

Let’s Go 2-DimensionalSuperconductor setting

Quantum mechanical flux in discrete units

0 2hce

Page 9: Superposition Censorship

Flux Interference Josephson Arrays, Elion et. al, PRL 71, 2311, 1993

BobAlice x xxx

= fluxon

x x x x

does nothingParticle acquires 0 or AB phase, thus breaking the fluxon’s interference

measures spin xParticle does not measure the fluxon, which stays in superposition

= electron

Page 10: Superposition Censorship

Resolution: Aharonov-Casher effect 25 years retrodiction..

BobAlice x xxx

measures spin xFluxon acquires 0 or AC phase, in accordance with Bob’s particle’s location

AC effect: It is the fluxon interference which shifts!D C

In any case, clicks may equally appear in D

x x x x

Aharonov and Casher, PRL 53, 319 (1984)

Page 11: Superposition Censorship

012

112

tunnling coupling in JJE

2D: Solenoid SQUID

Macroscopic current ~A

Josephson Junction removes degeneracy

ext 012

Experimental setting:

Superposition of Macroscopic Clockwise/Anticlockwise Currents

Van der Wal el. al, Science, 206, 773 (2000)Friedman et. al. Nature, 406, 43 (2000)

System is in ground state

Page 12: Superposition Censorship

Superconducting layer

BobAlice x xxx

does nothingParticle acquires /2 or -/2 AB phase, breaking the fluxon’s superposition.measures spin xFluxon is not effected by the electron and stays in superposition.

Superposition of Macroscopic Clockwise/Anticlockwise Currents

x x x x

xe

x

z

z

Induced magnetic field?

ext 012

Penetrating flux

topological effect – electron can be very far!

superposition remains

Page 13: Superposition Censorship

AC cannot help

?

Page 14: Superposition Censorship

Strong Impulsive Interaction→ Back-reaction

Furry and Ramsey, Phys. Rev. 118, 623 (1960)

Bob cannot distinguish between Alice’s two choices

Bob’s particle changes the state of the flux even when not interfering

int 0H H

electron near and fast

No paradox

Page 15: Superposition Censorship

What if interaction is adiabatic?

int

Long interference time /Weak Interaction

t EE E

E

Page 16: Superposition Censorship

Enter Protective Measurement 16 years retrodiction.. Aharonov, Anandan and Vaidman, PRA 47, 4616 (1993)

11

1 22

E

1 2

int

interaction is adiabatic /t E

E E

Electron in superposition

0.5e 0.5e

Classic trajectory!

Strong measurement

01

1 22

Protective Measurement

Measuring chargee

Page 17: Superposition Censorship

This is just what we have:Protective AB setting

measuring the flux’s expectation value:

Flux remains superposed

Even if Alice does nothing, Bob’s particle remains unentangled with flux,

0

No AB phase

No paradox

Page 18: Superposition Censorship

Conclusions

AB bears on QM fundamentals: causality, nonlocality, adiabaticy

Flux Interference: Causality protected by AB+ACelectrons and fluxons interact topologically

Flux Superposition: Causality protected by

Flux expectation value – when measurement becomes protectiveBack-reaction – when interaction is strong

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3Delectron spread in long wire

fluxflux

Electron

Electron