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Displacement in phase space

  1. Nov 23, 2014 #1

    naima

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    Hi PF

    I read the definition of the displacement operator:
    ##D(\lambda) = e^{\lambda a^\dagger - \lambda ^* a}##
    but i did not find how this operator can be implemented say in a cavity with a photonic state inside.
    Could you give me links?
    thanks.
     
  2. jcsd
  3. Nov 23, 2014 #2

    vanhees71

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    Have a look at this:

    http://en.wikipedia.org/wiki/Coherent_states

    Note that the application of this "displacement operator" to the vacuum does not create a photon Fock state (i.e., a state with definite photon number) but a coherent state!
     
  4. Nov 23, 2014 #3

    naima

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    Danke Vanhees71
    I read in this wiki
    ""...letting the unitary displacement operator D(α) operate..."
    The problem is not to let it operate. The problem is to prepare a device which will enable an experimentalist to displace a sate by ##\alpha##
    I read the external links at the end of the article but i did not find any device's
    description. I think that it needs pulses but with which interaction?
     
    Last edited: Nov 23, 2014
  5. Nov 24, 2014 #4

    vanhees71

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    I only know that lasers produce coherent states. How you prepare a given coherent state in detail, I cannot say :-(.
     
  6. Nov 24, 2014 #5

    strangerep

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    Mandel & Wolf (sect. 11.13, p568) give a derivation of the field produced by a time-dependent classical current, and show (iiuc) that it's a coherent state. As the current changes, the state changes continuously, but it's always a coherent state. I.e., changing the current is equivalent (in that case) to acting with a ##D(\alpha)##--like operator.
     
    Last edited: Nov 24, 2014
  7. Nov 25, 2014 #6

    naima

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  8. Nov 25, 2014 #7

    naima

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    Suppose that, using a pulse during t, i displace the vacuum to a gaussian centered around a point P in the phase space. This point will rotate in this plane. At a given moment the gaussian will be centerd around -P. If i apply the same pulse will the atom return to its vacuum?
    If yes how can we know when we have to light the atom ?


    Edit
    As i have many copies of the ground state |g> i can vary the ##\Delta t## between two pulses and for which it returms to |g> and know the rotation period.
     
    Last edited: Nov 25, 2014
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