Superposition of energy levels

In summary, the conversation discusses the preparation of a state with atoms in the ground level being excited to the first energy level using a laser. The use of a ##\pi/2## pulse with the same laser is mentioned as a way to prepare a state of |e> + |g> instead of a 50/50 mixture. The concept of unitary processes and the interaction between a quantum system and a classical world is also discussed, along with the Jaynes-Cummings model as a way to understand the formalism of the interaction between an atom and a field of photons.
  • #1
naima
Gold Member
938
54
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)?
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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:
  • #4
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.
 
  • #5
When i prepare a state with a device can i know if the apparatus uses only unitary process?
 
  • #6
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.
 
  • #7
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
 
  • #8
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.
 

What is the concept of superposition of energy levels?

The concept of superposition of energy levels refers to the ability of a particle or system to exist in multiple energy states simultaneously. This concept is a fundamental principle in quantum mechanics and is often used to describe the behavior of subatomic particles.

How does superposition of energy levels explain the behavior of particles?

Superposition of energy levels allows particles to exist in multiple energy states at the same time, which can explain their seemingly unpredictable behavior. This concept helps to explain phenomena such as wave-particle duality and quantum tunneling.

What is the relationship between superposition of energy levels and the uncertainty principle?

The uncertainty principle states that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa. Superposition of energy levels is closely related to this principle, as it allows particles to exist in multiple states at once, making it impossible to know their exact position and momentum simultaneously.

How is superposition of energy levels observed in real-world experiments?

Superposition of energy levels has been observed in various experiments, such as the famous double-slit experiment. In this experiment, a particle is sent through two parallel slits, and it is found to exhibit interference patterns, indicating that it exists in multiple energy states at the same time.

What are the potential applications of superposition of energy levels?

Superposition of energy levels has potential applications in quantum computing, where the ability of particles to exist in multiple states simultaneously can be harnessed to perform complex calculations much faster than classical computers. It also has implications in fields such as cryptography and communication.

Similar threads

  • Atomic and Condensed Matter
Replies
6
Views
1K
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
3
Views
999
  • Atomic and Condensed Matter
Replies
3
Views
1K
  • Atomic and Condensed Matter
Replies
6
Views
1K
  • Atomic and Condensed Matter
Replies
23
Views
2K
Replies
1
Views
919
  • Atomic and Condensed Matter
Replies
9
Views
2K
  • Atomic and Condensed Matter
Replies
10
Views
1K
Replies
4
Views
2K
Back
Top