Bomb-testing interferometers

2.7 Bomb-testing interferometers (recommended problem) The Acme Bomb Company sells a bomb triggered by the presence of silver, and claims that the trigger is so sensitive that the bomb explodes when its trigger absorbs even a single silver atom. You have heard sim-ilar extravagant claims from other manufacturers, so you’re suspicious. You purchase a dozen bombs, then shoot individual silver atoms at each in turn. The first bomb tested explodes! The trigger worked as advertised, but now it’s useless because it’s blasted to pieces. The sec-ond bomb tested doesn’t explode — the atom slips through a hole in the trigger. This confirms your suspicion that not all the triggers are as sensitive as claimed, so this bomb is useless to you as well. If you continue testing in this fashion, at the end all your good bombs will be blown up and you will be left with a stash of bad bombs. So instead, you set up the test apparatus sketched here:
itz=-1-ga r<ce a bomb with trigger
An atom with Az = +/AB enters the interferometer. If the bomb trigger has a hole, then the atom ambivates through both paths, arrives at the analyzer with lAz = +IAB, and exits the + port of the analyzer. But if the bomb trigger is good, then either (a) the atom takes path a and sets off the bomb, or else (b) the atom takes path b. a. If the bomb trigger is good, what is the probability of option (a)? Of option (b)? b. If option (b) happens, what kind of atom arrives at the analyzer? What is the probability of that atom exiting through the + port? The — port?

• • •

Sample Solution