# Atomic natural line width

In laser cooling, with a model of a 2-level atomic system, spontaneous emission is stated to be dependent on the "natural line width" of the excited state of the atom. This width is defined as the inverse of the lifetime of the state. In a picture in the same article, however, this line width is represented as the width of the excited state itself (due uncertainty principle I believe). This is confusing to me, as I was persuaded that the line width was the width of the transition line from excited state to ground state.

Are these notions the same thing or in some way related?

What they are is resonances, which turn out to be fairly tricky to actually define. (For more on this, see 'Decay theory of unstable quantum systems', L. Fonda et al., Rep. Prog. Phys. 41 no. 4587 (1978).) This means is that they have a finite lifetime $\tau$, and equivalently they do not have a well-defined energy and have a finite natural linewidth $\Delta\omega$. These two are Fourier-dual versions of each other, so it is no surprise that they satisfy the relation $$\tau·\Delta\omega\approx1,$$ with the precise details depending on what exactly each symbol means.
If I understand your question correctly, you are confusing between two definitions of "width". One is the spread of the spectral line and the other is the lifetime of the atom in excited state. Well, these two are related(as you guessed) by uncertainty principle. $\Delta E\,\Delta t = h/4\pi$. So if the time the atom spends in excited state is less, the energy spread will be more and vice versa. So any one of them can be thought as the measure of linewidth.