Beam Splitter Physics: |45>,-|45> State Output

In summary, if two identical photons enter a beam splitter from different sides with the states |45> and -|45>, the output will be -i|45>(l)|45>(l) - i|45>(r)|45>(r) - |45>(l)|45>(r) where the third term is both reflected and the fourth term is both transmitted. The Hong-Ou-Mandel effect states that identical photons entering different ports of a beam splitter will always exit via the same port. The i in the middle of the ket for the third term is a typo and should be i|45>.
  • #1
StevieTNZ
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If we have a beam splitter, and we fire two photons from either side towards it (both meeting and interfering at the same time):

If the state of the photon coming in from the left is |45>, and the one coming in from the right is -|45>, would the output be:

-i|45>(l)|45>(l) - i|45>(r)|45>(r) - i|45>(l)|i45>(r) - |45>(l)|45>(r)

Where the 3rd term is both reflected, the last term both transmitted, and the first two where they exit on the same side of the beam splitter output.

The attached image might give some clarity.
 

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  • #2
Why did you put the i in the middle of the ket for the third term?

If you include it and normalize, you will find that the third and fourth term have equal magnitude, but different sign. So they cancel out. As a consequence exactly identical and indistinguishable single photons entering different ports of a beam splitter will always leave as a pair of two photons via the same exit port. This is the Hong-Ou-Mandel effect.
 
  • #3
Cthugha said:
Why did you put the i in the middle of the ket for the third term?

Because both reflected.
 
  • #4
Oh, sorry. Maybe my post was not clear. I was rather puzzled why you wrote |i45> instead of i|45>.
 
  • #5
Cthugha said:
Oh, sorry. Maybe my post was not clear. I was rather puzzled why you wrote |i45> instead of i|45>.

My bad! Thanks for spotting that out for me. Should be i|45>.
 

Related to Beam Splitter Physics: |45>,-|45> State Output

1. What is a beam splitter in physics?

A beam splitter is a device that splits a beam of light into two or more separate beams. It is typically made of a partially reflective material, such as a glass plate or prism, that allows some of the light to pass through while reflecting the rest.

2. How does a beam splitter work?

A beam splitter works by using interference to separate the light beam into two or more beams. When a beam of light hits the partially reflective surface, some of the light is transmitted through while the rest is reflected. This creates two separate beams that are split based on the reflective properties of the material.

3. What is the |45>,-|45> state output in beam splitter physics?

The |45>,-|45> state output refers to a quantum state produced by a beam splitter where the input state is a superposition of two orthogonal states, one at an angle of 45 degrees and the other at an angle of -45 degrees. This means that the output state will be a combination of the two original states, with some probability of being in each state.

4. What is the significance of the |45>,-|45> state output in quantum physics?

The |45>,-|45> state output is significant in quantum physics because it demonstrates the principle of superposition, where a quantum system can exist in multiple states at the same time. This has important implications for quantum computing and quantum information processing.

5. How is the |45>,-|45> state output used in practical applications?

The |45>,-|45> state output is used in various applications, such as quantum cryptography and quantum teleportation, where the ability to manipulate and control quantum states is crucial. It is also used in research to study the behavior of quantum systems and to develop new quantum technologies.

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