Hi there, I am reading a text by Robert W. Boyd "Nonlinear optics", in page 228, he used pertubation theory on two-level system and let the steady-state solution of the dynamics equation of density matrix as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]w = w_0 + w_1 e^{-i\delta t} + w_{-1}e^{i\delta t}[/tex]

where [tex]w=\rho_{bb} - \rho_{aa}[/tex] is the inversion of population between level b (excited) and level a (ground), [tex]\Omega+\delta[/tex] is the frequency of the probe field, [tex]\Omega[/tex] is the frequency of the pump field. I have few questions

1) the author said the solution shown above is steady-state solution, but why it is time-dependent?

2) we know that, [tex]w[/tex] must be real, so [tex]w_1=w_{-1}^*[/tex], but if for [tex]w_1[/tex] only, is there any physical significance? Why we have to consider the first-order solution like that? What contribution of [tex]w_1[/tex] and [tex]w_{-1}[/tex] made?

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# Pertubation and density matrix

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