Superposition of energy levels

naima

Gold Member
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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Simon Bridge

Homework Helper
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.

naima

Gold Member
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?

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kith

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)?
You cannot go from a pure state to a mixture with a unitary process.

naima

Gold Member
When i prepare a state with a device can i know if the apparatus uses only unitary process?

kith

When i prepare a state with a device can i know if the apparatus uses only unitary process?
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.

naima

Gold Member
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

kith

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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