Q UANTUM S PLITTING 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

Q UANTUM M ECHANICS : B EAM S PLITTER B EAM S PLITTER A beam splitter takes a photon and reflects it off of a half- silvered 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!

B EAM S PLITTER P ATH C ONFUSION S INGLE B EAM S PLITTER 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.

B EAM S PLITTER P ATH C ONFUSION S INGLE B EAM S PLITTER 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.

B EAM S PLITTER P ATH C ONFUSION T WO B EAM S PLITTERS 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.

B EAM S PLITTER P ATH C ONFUSION T WO B EAM S PLITTERS What appears on the image screens? 1. Interference patterns. 2. No interference patterns. 3. One screen shows a bright spot, the other -- nothing. 4. The photons get confused and ask directions.

B EAM S PLITTER P ATH C ONFUSION T WO B EAM S PLITTERS T WO B EAM S PLITTERS 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.

Q UANTUM M ECHANICS : M ACH -Z EHNDER I NTERFEROMETER M ACH -Z EHNDER I NTERFEROMETER The setup can be used to probe a sample placed in a light path.

Q UANTUM M ECHANICS : M ACH -Z EHNDER I NTERFEROMETER M ACH -Z EHNDER I NTERFEROMETER With no sample, only detector 1 detects light. o Detector 1 sees only constructive interference. o Detector 2 see only destructive interference. With a sample, each detector has a 50% chance of detecting the photon. o The sample affects the photon -- allows "which-path" information o Assumes sample is otherwise transparent. o Example: horizontal polarizer.

Q UANTUM M ECHANICS : E LITZUR -V AIDMAN BOMB - TESTER E LITZUR -V AIDMAN BOMB - TESTER

Q UANTUM M ECHANICS : E LITZUR -V AIDMAN BOMB - TESTER E LITZUR -V AIDMAN 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. Light takes both paths, interferes, and a detector lights up. 2. Light takes the top path and detector D lights up. 3. Light takes the bottom path and detector C lights up. 4. Mach and Zehnder are arrested for illicit activities.

Q UANTUM M ECHANICS : E LITZUR -V AIDMAN BOMB - TESTER E LITZUR -V AIDMAN 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.

Q UANTUM M ECHANICS : E LITZUR -V AIDMAN BOMB - TESTER E LITZUR -V AIDMAN 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.

Q UANTUM M ECHANICS : E LITZUR -V AIDMAN BOMB - TESTER E LITZUR -V AIDMAN 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!

Q UANTUM M ECHANICS : E LITZUR -V AIDMAN BOMB - TESTER E LITZUR -V AIDMAN 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.counterfactual definiteness