# Damped oscillator for 2-level atom

1. Nov 4, 2007

### Ffemtos

My question is why the books on laser always use a damped oscillator as a model for the transitions in a 2-level atom? I didn't find any more resemblance between the two except they both have a fixed upper and lower limit( but for the atom it is energy, for oscillator it is amplitude ) Thanks for your answers.

2. Nov 4, 2007

### f95toli

There is a mathematical equivalence. If you use e.g. a simple Rabi model for a 2-level atom coupled to an electromagnetic field you will find that the solution behaves exactly like a damped harmonic oscillator.
It doesn't mean that you should think of an atom as a mechanical "mass+spring" system or anything like that. It is just that the simplest model of an atom is that of an electron in a harmonic well. i.e. a potential of the type
$V(x)=\frac{1}{2} m \omega^2 x^2$
If you solve the Schrödinger equation using this potential you get a solution with discrete levels (eigenvalues) with energies

$E=(n+1/2) \hbar \omega$

In the case of a 2-level atom we only use the first two levels of the oscillator. Also, note that the amplitude does not enter into the equations. The coupling to the EM field will -in the simplest model- be equivalent to adding a damping term.
Books on laser physics tend to use a lot of semi-classical models, and it is not always clear how they relate to actual physical phenomena.
It is of course always possitive to use "real" QM models but they are much more complicated (even simple models like the Jaynes-Cummings Hamiltonian are quite messy) and semi-classical results are usually quite sufficient.

Last edited: Nov 4, 2007