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Spatial linewidth and density matrix

  1. Aug 2, 2009 #1


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    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, [tex]\rho_{ee}[/tex] and it turns out that [tex]\rho_{ee}[/tex] is a function of a parameter G, which could be space dependent, i.e.

    [tex]\rho_{ee} = \rho_{ee}(G(x))[/tex]

    as we know, [tex]\rho_{ee}[/tex] 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 [tex]\rho_{ee}(G(x))[/tex] turns out to be somewhat localized around x=0, so what can I tell about the linewidth of the emitted light?
  2. jcsd
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