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Problem%20Set%204%202008.1

# Problem%20Set%204%202008.1 - light into the upper beam by...

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Problem Set #4 (Due Apr. 25 12:00pm) 1. Chap 2, 18 2. Chap 2, 19 3. Chap 2, 23 4. Chap 2, 36 5. A single-particle interferometer (Mach-Zehnder interferometer) consists of an arrangement of two beam splitters, B 1 and B 2 , two mirrors, M 1 and M 2 , and two detectors D 0 and D 1 as illustrated in the figure below. Note that the reflective side (in black with higher reflective index than the glass in gray) of B 1 is down and right and that of B 2 is up and left. Ignore the thickness of the glass in the beam-splitters and assume that they reflect 50% of the beam and transmit 50%. A phase shifter is inserted into the upper beam and this shifts the phase of the
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Unformatted text preview: light into the upper beam by φ . This amounts to > >→ > >→ 1 | 1 | | | ϕ i e (a) Suppose that a photon is incident in the beam represented by |0>. Determine the probability with which it arrives at detector D and the probability with which it arrives at D 1 . (Hint: Write the photon state after the beam splitter 1 and 2. Be careful about the phase change at the splitters and mirrors). (b) What would be the answer in (a) if the photon is incident in the beam represented by |1>? D 1 B 2 M 1 |1> |0> Phase Shifter M 2 D B 1...
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