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Transcript
BGU
Two-path Interference with a Single
Quantum Slit or Mirror
Daniel Rohrlich, Yakov Neiman, Yonathan Japha, and
Ron Folman
Department of Physics and Ilze Katz Center for
Meso- and Nanoscale Science, BGU, Israel
Two path interference
2
Single particle superposition
A single particle in a
superposition of two
locations is prepared in
a double well potential
and then the potential
is turned off.
The wavepackets expand
and overlap after t=pMdw/h
Initial state of probe+
Target:
3
Condition for interference: loss of
orthogonality of target states
After scattering:
Final state:
It final target states (left and right) remain orthogonal then there
Is no interference!
Final state is an entangled state.
The phase a have no effect.
4
1D example: One-mirror Fabry-Perot
In the special case M=m: pfin=Pin
Transfer of orthogonality from target to probe
5
General solution for the 1D problem
6
Suppression of visibility
If the initial probe momentum has a spread pin
2
The probe induces an effective coherence length on the
target.
7
One-slit Young interference
8
Transfer of orthogonality
Condition for full interference
9
pin / m
 sin  in
Pfin / M
Angular spectrum of scattering
M 1

m 2
 in  45
10
Visibility as a function of M/m
11
Visibility as a function of pin
12
Summary and conclusions
• 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.
13