# What happens to atoms in far detuned states?

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• Malamala
In summary, the conversation discusses the interaction between a 2 level system and an EM field in the rotating wave approximation and dipole approximation. By diagonalizing the Hamiltonian, dressed states are obtained which are shifted relative to the unperturbed levels. The atom feels the EM field through the electric dipole interaction, regardless of the detuning. However, there are two types of far detuning and the validity of the dressed state picture depends on the magnitude of the detuning.
Malamala
Hello! Assuming we have a 2 level system interacting with an EM field in the RWA and dipole approximation, we would have in the basis of the 2 unperturbed atomic states a 2x2 Hamiltonian matrix with off-diagonal terms. By diagonalizing this Hamiltonian we obtain dressed states which are the eigenstates of the atom-EM field interacting system and are shifted by a given amount relative to the unperturbed levels. Mathematically it makes sense and it is straightforward, but I am not sure what is happening physically, especially in the case of far detuning. On resonance for example, the atom undergoes Rabi oscillations and there is a clear interaction with the EM field, but in the far detuned region, how does the atom knows about the existence of the EM? Is it simply because there is a very small probability (small Rabi frequency) of Rabi oscillations due to the fact that the transition between the 2 levels has a line width and even if the laser frequency is far detuned it will still excite the transition once in a while? Or is there some other mechanism by which the atom feels the EM field?

The atom feels the EM field through the electric dipole interaction (the coupling of the electric dipole moment of the atom to the electric field), whether it's near detuned or far detuned. Now there are two kinds of "far detuned", there's ##\omega - \omega_0 \gg \Gamma## and there's ##\omega - \omega_0## being on the same order as ##\omega_0##. In the former case, the dressed state picture is still valid, and in the latter case the whole RWA fails and there be monsters. Which do you mean when you say "far detuned"?

## 1. What is a far detuned state?

A far detuned state refers to a state in which an atom is excited to a higher energy level by absorbing a photon with a significantly higher energy than the energy difference between the atom's ground state and the excited state.

## 2. How do atoms behave in far detuned states?

In far detuned states, atoms behave differently depending on the specific conditions. In general, they can exhibit behaviors such as increased scattering of light, reduced absorption of photons, and altered atomic energy levels.

## 3. What are the applications of far detuned states in research?

Far detuned states have various applications in research, including the study of atomic interactions and the development of quantum technologies such as atomic clocks and quantum computers.

## 4. Can atoms be trapped in far detuned states?

Yes, atoms can be trapped in far detuned states using techniques such as optical trapping. This allows for precise control and manipulation of the atoms for research purposes.

## 5. How do far detuned states affect the behavior of atoms in a material?

Far detuned states can affect the behavior of atoms in a material by altering their electronic and magnetic properties. This can lead to changes in the material's conductivity, magnetism, and other physical properties.

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