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Joint Number state switching operator?

  1. Feb 23, 2014 #1

    I was just wondering if anyone know of an operator, which has some realistic analogue, that would perform the following action:

    A|N,0> = A|0,N>

    Where the ket's represent two joint fock states (i.e. two joint cavities) and A is the opeator I desire.

    I thought that the beam splitter operator might perform this task with a proper selection of parameters, but I don't think it can.

    Any ideas?

  2. jcsd
  3. Feb 24, 2014 #2


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    just destroy the 1st N, and then create the 2nd N.... that's the operator...
  4. Feb 24, 2014 #3
    That would be 2 different operators....


    A1|0,N> = |N,0>

    A2 |N,0> = |0,N>

    with A1 ≠ A2.

    (Not what I looking for - see first post)

    It seems the beam splitter operator does do the trick with the right phase selected (pi/2), I was hoping I could set it to zero though so I missed that. Still, any alternatives would be nice to try.
    Last edited: Feb 24, 2014
  5. Feb 24, 2014 #4


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    Ah yes, sorry now I understand the question...
    well due to the orthonormality of the states, you can have that only if A makes both states identical...
    so I think there is not such operator.
  6. Feb 24, 2014 #5
    The beam splitter operator does do the trick,

    It basically expands the state out into a superposition of each possible combinations of the joint fock states, the problem I was having is that the weightings were different for each of the two input states. My expression was a bit complicated so I didn't immediately see that a phase of pi/2 produced the results I require, and I was kind of hoping for the phase to be zero.

    I have had a number of alternative ideas, however, most are not so physical.
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