Superposition of energy levels

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Discussion Overview

The discussion revolves around the preparation of quantum states in atoms, specifically the transition from a ground state to a superposition of states using laser pulses. Participants explore the implications of using a π/2 pulse and the distinction between pure states and mixtures in quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes preparing an atom in a superposition state |e> + |g> using a π/2 pulse, questioning how to achieve this without resulting in a 50/50 mixture.
  • Another participant challenges the clarity of the initial claim, emphasizing the need for context and questioning the meaning of a "π/2 pulse" in this scenario.
  • A later reply references a source that discusses the interaction of an atom in the ground state with a classical π/2 pulse, suggesting a rotation on the Bloch sphere.
  • There is a discussion about the nature of unitary processes, with one participant asserting that a pure state cannot transition to a mixture through a unitary process.
  • Concerns are raised about whether experimental apparatuses can be definitively known to use only unitary processes, with a participant noting the potential for non-unitarity due to ignored correlations.
  • Another participant introduces the concept of a cut in quantum mechanics between quantum systems and classical fields, discussing how this affects the evolution of the system and the representation on the Bloch sphere.
  • A suggestion is made to explore the Jaynes-Cummings model as a means to address the questions raised regarding the interaction of an atom with a coherent field of photons.

Areas of Agreement / Disagreement

Participants express differing views on the nature of quantum state preparation, the implications of unitary versus non-unitary processes, and the interpretation of interactions between quantum systems and classical fields. No consensus is reached on these topics.

Contextual Notes

Participants highlight the importance of definitions and context in discussing quantum states and processes, indicating that assumptions may vary and that the discussion is dependent on specific interpretations of quantum mechanics.

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