Daniel Rohrlich, Yakov Neiman, Yonathan Japha, and , Yonathan Japha, and Ron FolmanRon Folman

Department of Physics and Ilze Katz Center forDepartment of Physics and Ilze Katz Center for Meso- and Nanoscale Science, BGU,Meso- and Nanoscale Science, BGU, Israel Israel

Two-path Interference with a Single Quantum Slit or Mirror

BGU

Two path interferenceTwo path interference

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Single particle superposition

A single particle in a A single particle in a superposition of two superposition of two locations is prepared inlocations is prepared ina double well potentiala double well potentialand then the potentialand then the potentialis turned off.is turned off.

The wavepackets expand The wavepackets expand and overlap after t=and overlap after t=Mdw/h Mdw/h

Initial state of probe+Initial state of probe+Target:Target:

Condition for interference: loss of orthogonality of target states

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After scattering:After scattering:Final state:Final state:

It final target states (left and right) remain orthogonal then thereIt final target states (left and right) remain orthogonal then thereIs no interference! Is no interference! Final state is an entangled state.Final state is an entangled state.The phase The phase have no effect. have no effect.

1D example: One-mirror Fabry-Perot

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In the special case M=m: pfin=Pin

Transfer of orthogonality from target to probe

General solution for the 1D problem

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Suppression of visibility

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If the initial probe momentum has a spread pin

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The probe induces an effective coherence length on the The probe induces an effective coherence length on the target. target.

One-slit Young interference

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Transfer of orthogonality

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Condition for full interferenceCondition for full interference infin

in

MP

mp sin/

/

Angular spectrum of scattering

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45

2

1

in

m

M

Visibility as a function of M/m

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Visibility as a function of pin

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Summary and conclusions

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• Two-path interference by scattering off a single free quantum particle in a superposition of two locations is possible.

• Interference is suppressed by initial momentum spread of the probe particle or by measurement precision.

• Double slit interference from a single slit is possible when the mass of the target is comparable to the mass of the probe (or smaller).

• The condition for interference is loss of orthogonality of the target states or equivalently purity of the probe state.