- #1
BillKet
- 313
- 29
Hello! I have the following situation: I have a 3 level system, with 2 ground states, call them ##g_1## and ##g_2## and an excited state, ##e##, with energies ##E_{g1}<E_{g2}## and ##E_e##. I have a driving field with frequency ##\omega## such that ##\Gamma \ll \Delta \ll E_{g2}-E_{g1} \ll E_e - E_{g1}##, where ##\Gamma## is the linewidth of the excited state and ##\Delta## is the detuning of the excited state from the ##g_1\to e## transition. So basically the laser is very detuned from any transition in the system and we can assume that the laser power is small enough such that the saturation parameter, ##s## is much smaller than 1, so the probability of the atom getting excited to ##e## is virtually zero. I found in AMO books that in this case Rayleigh scattering dominates i.e. coherent scattering, compared to incoherent scattering i.e. decays from ##e## and the ratio of the 2 rates is ##\sim s##. However, as far as I can tell, these derivations don't take into account Raman transitions to ##g_2## (assuming we start in ##g_1##) in which ##e## doesn't get excited. These kinds of transitions are not Rayleigh (as the light frequency changes), but they are also not incoherent, as there is still a clear phase between the driving field and the emitted photon (but they have different frequencies). So, given my situation, how can I calculate the Rayleigh scattering rate vs Raman scattering rate (i.e. with both of them coherent processes and assuming that the dipole moment coupling between ##e## and ##g_1## is the same as the one between ##e## and ##g_2##)? Thank you!