Is My Calculation of the Photon State in a Mach-Zehnder Interferometer Correct?

[sirchick]

Hey

I been looking at the maths at a specific setup of a interferometer (see image).

This is my workings out and i seem to get the correct answer but have i missed out any thing or misunderstood the workings out and just happened to get lucky with my answer?

Legend:
s² = ½
Upper/Lower = Path of beam in image represented as lower and upper half of image.

Photon State:

|upper> = s*|upper> + s*|lower>

Super position:

s(s|upper> + s|lower>) + s(s|upper> - s|lower>)

Becomes:

(s² + s²)*|upper> + (s² - s²)*|lower>

Lower becomes canceled out.

So upper path is all that's left:

2*s²|upper>

Meaning its 100% guaranteed to be in upper path unless a measurement is made?

 

[StevieTNZ]

Yeah, I'm confused too. I just deleted my previous post. Watched the video where you must have got the information for your original post from.

My book is definitely saying if the source is where the one is in your image, then detector 1 (upper) won't register photons. Detector 2 (the one on the far right) will.

 

[sirchick]

The video is on my PC can't upload it to show you etc. But the video explains how the beam splitter reverses the lower wave and so it doesn't reach the lower photon detector due to interference. Which is now confusing...

 

[StevieTNZ]

Yup, I have the video you're speaking of, and watched the relevant area after posting, but before I saw your new post.

 

[sirchick]

Yeah, I'm confused too. I just deleted my previous post. Watched the video where you must have got the information for your original post from.

My book is definitely saying if the source is where the one is in your image, then detector 1 (upper) won't register photons. Detector 2 (the one on the far right) will.

there's a book with these videos or a different book ? So I am confused which is the right answer then if they say different things.

 

[StevieTNZ]

there's a book with these videos or a different book ? So I am confused which is the right answer then if they say different things.

Different book. I am also wondering which is telling the right answer.

 

[Edgardo]

This is a Mach-Zehnder interferometer.
The phase difference determines the probabilities for detection at detector 1 and 2.

1. How does a Mach–Zehnder interferometer work?

2. Photon quantum mechanics and beam splitters

3. Photons and Quantum Mechanics

The probabilities are:

$P_1 = \text{cos}^2(\delta/2) = \frac{1}{2} (1+ \text{cos} (\delta) )$

$P_2 = \text{sin}^2(\delta/2) = \frac{1}{2} (1- \text{cos} (\delta) )$

where $\delta$ is the phase difference.

 

[StevieTNZ]

1. How does a Mach–Zehnder interferometer work?

That article says detector A (lower - or one to the right, not top). Not sure where Ben Schumacher gets his answer.

 

[sirchick]

Ben Schumacher simplified it for us to understand the concept although edgardo has now over complicated it which has confused me more as the maths looks totally different to how the lecture shows it =/

The issue is which beam based on ben's design is correct =/ because we have seen two different answers from two different sources.

 

[Edgardo]

Here is another nice explanation by the Department of Physics, University of Toronto:
Mach-Zehnder Interferometer