QUANTUM SPLITTING
by
Robert Nemiroff
Michigan Technological University
Physics X: About This Course
• Officially "Extraordinary Concepts in Physics"
• Being taught for credit at Michigan Tech
o Light on math, heavy on concepts
o Anyone anywhere is welcome
• No textbook required
o Wikipedia, web links, and lectures only
o Find all the lectures with Google at:
 "Starship Asterisk" then "Physics X"
o
http://bb.nightskylive.net/asterisk/viewforum.php?f=39
QUANTUM MECHANICS:
BEAM SPLITTER
A beam splitter takes a photon and reflects it off of a halfsilvered mirror. The beam splitter can be tuned so that there is
a 50% chance that the photon will go right through unaffected,
and 50% that the photon will be reflected at a right
angle. Oddly, these two paths can interfere!
BEAM SPLITTER PATH CONFUSION
SINGLE BEAM SPLITTER
Suppose a light is directed toward a beam splitter so that light can take
either of two paths around a rectangle. Two image screens are placed
at the opposite corner of the rectangle from the beam splitter, one facing
horizontally, one facing vertically. What appears on the image screens?
1. Interference patterns.
2. No interference patterns.
3. Black light that only be seen in the dark.
BEAM SPLITTER PATH CONFUSION
SINGLE BEAM SPLITTER
2. No interference patterns.
The path of each photon -- "which path" information, can be found for
each photon just by noting which direction it was going as it left the
rectangular apparatus. Therefore no interference patterns will appear.
BEAM SPLITTER PATH CONFUSION
TWO BEAM SPLITTERS
Once again, suppose that a light is directed toward a beam splitter so
that light can take either of two paths around a rectangle. A second
beam splitter is now placed at the opposite corner of the rectangle from
the beam splitter, allowing half the light to proceed horizontally, half
vertically. The two image screens still remain.
BEAM SPLITTER PATH CONFUSION
TWO BEAM SPLITTERS
What appears on the image screens?
1.
2.
3.
4.
Interference patterns.
No interference patterns.
One screen shows a bright spot, the other -- nothing.
The photons get confused and ask directions.
BEAM SPLITTER PATH CONFUSION
TWO BEAM SPLITTERS
1. Interference patterns &
3. One screen shows a bright spot, the other -- nothing.
The second beam splitter makes it so that "which-path" information is
erased. Each photon that strikes either image screen could have arrived there
taking either path. Therefore, the paths interfere. It could be considered that each
photon took "both paths" simultaneously, and interference patterns
remain. Strangely enough, one path can show total constructive interference and
hence a bright spot, while the other path total destructive interference, and hence
nothing.
QUANTUM MECHANICS:
MACH-ZEHNDER INTERFEROMETER
The setup can be used to probe a sample placed in a light path.
QUANTUM MECHANICS:
MACH-ZEHNDER INTERFEROMETER
•
With no sample, only detector 1 detects light.
o
o
•
Detector 1 sees only constructive interference.
Detector 2 see only destructive interference.
With a sample, each detector has a 50% chance of detecting the
photon.
o
o
o
The sample affects the photon -- allows "which-path" information
Assumes sample is otherwise transparent.
Example: horizontal polarizer.
QUANTUM MECHANICS:
ELITZUR-VAIDMAN BOMB-TESTER
QUANTUM MECHANICS:
ELITZUR-VAIDMAN BOMB-TESTER
A bomb is placed in a Mach-Zehnder Interferometer. The bomb is
designed to be light sensitive -- if illuminated it will explode. The bomb
might be a dud, though, and if so will just let the light pass. A photon is
released by A.
What happens if the bomb is a dud?
1.
2.
3.
4.
Light takes both paths, interferes, and a detector lights up.
Light takes the top path and detector D lights up.
Light takes the bottom path and detector C lights up.
Mach and Zehnder are arrested for illicit activities.
QUANTUM MECHANICS:
ELITZUR-VAIDMAN BOMB-TESTER
1. Light takes both paths, interferes, and a detector lights up.
Since the bomb is a dud, it does not affect the light (a precondition of
the experiment) and the interferometer acts as if there is no obstruction
at all. Therefore, photons take both the top and bottom paths, even if
somebody is standing inside the interferometer, and C or D detects the
photon.
QUANTUM MECHANICS:
ELITZUR-VAIDMAN BOMB-TESTER
A bomb is placed in a Mach-Zehnder Interferometer. The bomb is
supposed to be light sensitive -- if illuminated it will explode. The bomb
might be a dud, though, and if so will just let the light pass. A photon is
released by A.
What happens if the bomb is real and primed?
1. Light takes both paths, interferes, and a detector lights up.
2. Light takes the bottom path and the bomb explodes.
3. Light takes the top path, detector D lights up, and the bomb does not
explode.
4. Hilarity ensues when the butler throws the whole thing in the trash.
QUANTUM MECHANICS:
ELITZUR-VAIDMAN BOMB-TESTER
2. Light takes the bottom path and the bomb explodes. OR
3. Light takes the top path, detector D lights up, and the bomb does not
explode.
So half the time the bomb explodes, but half the time it does
not. Therefore, if detector C lights up, the bomb is a dud. If detector D
lights up, either the bomb is a dud or the bomb is live. So if D lights up,
you only know with 50% certainty that the bomb is alive. Still, that is
better than detonating it!
QUANTUM MECHANICS:
ELITZUR-VAIDMAN BOMB-TESTER
There is no classical way of testing the bomb without exploding it.
This 50/50 quantum way is therefore a clear improvement.
This is another example of counterfactual definiteness -- determining
something definite with QM by actually measuring it.