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Interferometer questions, pure states?

  1. Jan 25, 2005 #1
    Hello, I have a few questions about this interferometer setup, see attached picture.

    The beamsplitters are 50/50 and the setup is symmetric.

    first beamsplitter, where U is unitary and represents the beamsplitter.
    U|i> = 1/sqrt(2)( |u> + exp(ix)*|d> )
    second beamsplitter, A and B are detectors (upper and lower)
    U|d> = 1/sqrt(2)( |A> + exp(ix)*|B> )

    U|u> = 1/sqrt(2)( |A> + exp(iy)*|B> )

    now what is x and y? I let x = 0 and then assume that <d|u> = 0 and use this to determine y under the assumption that U is unitary this gives y = pi.

    U|d> = 1/sqrt(2)( |A> + |B> )
    U|u> = 1/sqrt(2)( |A> - |B> )

    this gives the state after the second beamsplitter to be
    1/sqrt(2)( 1/sqrt(2)( |A> + |B> ) + 1/sqrt(2)( |A> - |B> )) = |A>
    and this gives probability of detection in A to be
    |<A|A>|^2 = 1
    and B
    |<B|B>|^2 = 0

    I have questions about this experiment.
    1. How come its valid to assume that |u> and |d> are pure states?

    2. Will the experimental outcome be different if we put up a wall on the horizontal symmetry line? Or wont that affect the experiment cause all the interference takes place at the second beamsplitter?

    3. is possible to view the |u> (and |d>) as being pure states because they are sort of statistically pure as long as the paths are separated well enough? Has this anything to do with the statistical interpretation of QM ?

    Attached Files:

    Last edited: Jan 25, 2005
  2. jcsd
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