# Spatial linewidth and density matrix

1. Aug 2, 2009

### KFC

Hi there,
I am thinking an interesting problem of spatial linewidth of two-level system. Suppose in some way I find out an element of the desinty matrix for the upper state of two-level system, $$\rho_{ee}$$ and it turns out that $$\rho_{ee}$$ is a function of a parameter G, which could be space dependent, i.e.

$$\rho_{ee} = \rho_{ee}(G(x))$$

as we know, $$\rho_{ee}$$ tells the inversed population of the system, when the atoms jump back to ground state from excited state, one line will be observed. Now, suppose I choose G(x) to be a specific function, e.g. Gaussian, such that $$\rho_{ee}(G(x))$$ turns out to be somewhat localized around x=0, so what can I tell about the linewidth of the emitted light?