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Superposition Censorship
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Transcript of Superposition Censorship
AB, EPR and AC Conspiring to Preserve Causality
Avshalom C. Elitzur [email protected]
Shmuel Marcovitch [email protected]
EPR sourceWhich-path correlation
Superposition Censorship
Alice Bob
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)
SG (z)
Alice
Superposition Censorship
SG (x)
SG (z)
SG (-x)
SG (x)
Bob
EPR-Bohm sourceSpin correlation
AB-MZI
D C
Click in either C or DClick always in C
Currentsuperposed
Currentonly on left(or right)
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
“Cat State” of a Currenttoo gedankenly?
C
D
Let’s Go 2-DimensionalSuperconductor setting
Quantum mechanical flux in discrete units
0 2hce
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
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)
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
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
AC cannot help
?
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
What if interaction is adiabatic?
int
Long interference time /Weak Interaction
t EE E
E
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
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
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
3Delectron spread in long wire
fluxflux
Electron
Electron