# Dipole term in light-matter interaction

I have a question regarding the description of the term “dipole” in light-matter interactions.

If I understand it correctly, there are 3 different things that one can declare as a dipole during light-matter interaction:

1. Classical dipole: created by the 2 different charges of the nucleus and the electron
2. Transition dipole: Since you have a ground and an excited state of the atom, there is a transition dipole from these two states.
3. Electrical dipole: If these two states are in a superposition, the location of the electron will oscillate between 2 positions and hence create a dipole.

Do I understand these occurring dipoles correctly and which of them couples to the light field?

The picture of the superposition state maybe helps to understand what I mean.

These are not distinct things, but rather different side of the same notion.

More systematically dipole, quadrupole and other moments arise when performing Multipole expansion of a charge distribution. The dipole moment is the lowest term in this expansion, provided that the overall distribution is charge neutral.

Retaking the terminology introduced in the Q., classical dipole is but the simplest realization of a distribution that has a dipole moment and no other moments. In classical electromagnetism one often speaks of dipole radiation or dipole antenna, which is but a small piece of wire with a current oscillating with it, whose size is negligible compared to the distances to which the EM wave propagates - the only important feature here is the cylindrical symmetry due to the direction of the wire (dipole axis.)

In atom the electron wave function affected by electromagnetic radiation (and described by time-dependent Schrödinger equation) can be seen as a time-dependent charge density $$|\psi(x,t)|$$, and performing multipole expansion naturally leads to describing its interaction with EM field as that of a dipole.

If we limit the discussion to only two atomic levels - often referred to as the 'ground state' and the 'excited state' - we can expand this wave function in terms of the eigenstates (i.e., in the basis provided by the solutions of the time-independent Schrödinger equation): $$\psi(x,t) = c_g(t) \phi_g(x) + c_e(t) \phi_e(x)$$

See also this post for the discussion of the dipole approximation for light-atom interaction (I do not reproduce it here, but it makes the logical continuation of this answer.)

The coupling to the light field is related to your second dipole: an eletromagnetic field of a given frequency $$\omega$$ will couple two states of the electron that roughly of the order of $$\omega$$ as well. Your third dipole is a consequence of the interaction given by the second one. In a normal setting, you will hardly find an atom in a superposition of energy states as a consequence of its interaction with its environment. For the clarity of the response, I'm skipping the details. But you can find a more detailed description of the phenomenon in Atom-Photon Interactions: Basic Processes and Applications, from Cohen-Tannoudji.