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

  • Context: Graduate 
  • Thread starter Thread starter StevieTNZ
  • Start date Start date
  • Tags Tags
    Beam Beam splitter
Click For Summary

Discussion Overview

The discussion revolves around the behavior of photons interacting with a beam splitter, specifically analyzing the output states when two photons, one in the state |45> and the other in the state -|45>, are incident on the splitter simultaneously. The focus is on the mathematical representation of the output states and the implications of the Hong-Ou-Mandel effect.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes a specific output state for the photons after interacting with the beam splitter, including terms for both reflected and transmitted states.
  • Another participant questions the notation used in the proposed output, specifically the inclusion of 'i' in the ket notation for one of the terms, suggesting it may lead to cancellation of terms.
  • A subsequent reply clarifies that the 'i' was intended to indicate a phase factor and not a notation error, but acknowledges the confusion caused by the representation.
  • There is a mention of the Hong-Ou-Mandel effect, which states that indistinguishable photons entering a beam splitter will exit together from the same port, implying a deeper connection to the proposed output states.

Areas of Agreement / Disagreement

Participants express differing views on the notation and representation of the output states, indicating a lack of consensus on the correct mathematical formulation. The discussion remains unresolved regarding the implications of the notation on the output states.

Contextual Notes

There is uncertainty regarding the normalization of the output states and the implications of the phase factors included in the mathematical representation. The discussion does not resolve these aspects.

StevieTNZ
Messages
1,944
Reaction score
837
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.
 

Attachments

  • CCI18082013.jpg
    CCI18082013.jpg
    10.9 KB · Views: 469
Physics news on Phys.org
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.
 
Cthugha said:
Why did you put the i in the middle of the ket for the third term?

Because both reflected.
 
Oh, sorry. Maybe my post was not clear. I was rather puzzled why you wrote |i45> instead of i|45>.
 
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>.
 

Similar threads

High School Calculating Photon Polarization States with PBS & Wave Plates
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Two Different Fock State Inputs into a Beam Splitter
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Use of the Beam Splitter Operator
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad How does the thickness of a beam splitter affect the phase shift produced?
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Hong-Ou-Mandel with two beam splitters
  • · Replies 5 ·
Replies
5
Views
2K
Graduate What Happens to Entangled Photons at a Beam Splitter?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What happens when entangled photons are split into different paths?
  • · Replies 41 ·
2
Replies
41
Views
6K
Undergrad Polarization entanglement - multiple tests
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Quantum entanglement by the means of beam splitters
  • · Replies 34 ·
2
Replies
34
Views
9K
High School Beam splitter, one photon, one detector?
  • · Replies 11 ·
Replies
11
Views
3K