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Superposition of energy levels

  1. Mar 28, 2015 #1

    naima

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    Hi PFs

    whith atoms in the ground level |g> we can prepare them in the first excited energy level |e> by giving them the transition energy with a laser. if one photon is absorbed it will be in |e>.
    I read that to prepare a |e> + |g> state i can use a ##\pi/2## pulse with this same laser.
    What is the trick to get a such a state and not a 50/50 mixture of the two states (or to get this mixture)?
     
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  3. Mar 28, 2015 #2

    Simon Bridge

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    Lets see:
    you superpose states not energy levels.
    "I read"... what? Where? Citations please. Without the context it is very difficult to figure out what the author was trying to say.
    "p/2 pulse with this same laser" does not make sense by itself. Perhaps you are thinking of push-pull pumping or perhaps VSCPT in atom trapping experiments?

    Note: the |e>+|g> state is not normalized, and would represent a 50:50 probability of finding the atom in either e or g.
     
  4. Mar 28, 2015 #3

    naima

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    you can find the context in
    http://www.cqed.org/spip.php?article122
    Here the atom in the grount state interact during T with a "classical" ##\pi/2## pulse and becomes |g> + |e>. there is a rotation on the Bloch sphere. if the duration was 2T we would get a pure excited state with certainty.

    What if the state is not classical?
     
    Last edited: Mar 28, 2015
  5. Mar 30, 2015 #4

    kith

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    You cannot go from a pure state to a mixture with a unitary process.
     
  6. Mar 30, 2015 #5

    naima

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    When i prepare a state with a device can i know if the apparatus uses only unitary process?
     
  7. Mar 30, 2015 #6

    kith

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    The distinction is not so clear. Even if the interaction between a small and a big system can be described as unitary, the experimenter may introduce non-unitarity by ignoring correlations.

    Regarding your case, I would say that you are fine at least as long as you can treat the influence of the field as a perturbation acting on the atom.
     
  8. Mar 30, 2015 #7

    naima

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    There is a cut in QM between a quantum system and a classical word. So when a two level atom and a classical field interact the quantic system evolves unitarily. We can describe this with a point moving on the Bloch spere.
    We may move the cut so that the quantic side includes the atom and other particles. Then the new system "atom + particles" will be in a tensor product Hilbert space (they may be entangled) have to evolve unitarily The state of the atom is given by tracing out the particles and can be a mixture. so the corresponding point is no more on the Bloch sphere but inside it.
    I am trying to understand the formalism describing what happens when i have an atom and a field of photons. I am not sure but i think that if the field is coherent the atom alone will stay on the Bloch sphere. Could you help me ?
    Thanks
     
  9. Mar 31, 2015 #8

    kith

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    You should read about the Jaynes-Cummings model. Conceptually, it is very simple, because it couples a two-level system (the atom) to a single field mode, but I think it is powerful enough to answer all your questions.
     
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