eventually reach a quasi-stationary state as It is also clear that there are terms in the equation that go to zero as . These are the result of the Markovian processes of the quantum fluctuations of the system. We see that in the weak field approximation as well as , the coupled system will reach a quasi-steady state where the quantum fluctuations become negligible. Resonance fluorescence in the Strong Field The Strong Field Limit is the exact opposite limit to the weak field where the square modulus of the Rabi frequency of the electromagnetic field is much larger than the rate of spontaneous emission of the two-level atom. When a strong field is applied to the atom, a single peak is no longer observed in fluorescent light's radiation spectrum. Instead, other peaks begin appearing on either side of the original peak. These are known as side bands. The sidebands are a result of the Rabi oscillations of the field causing a modulation in the dipole moment of the atom. This causes a splitting in the degeneracy of certain eigenstates of the hamiltonian, specifically and are split into doublets. This is known as dynamic Stark splitting and is the cause for the Mollow triplet, which is a characteristic energy spectrum found in Resonance fluorescence. An interesting phenomena arises in the Mollow triplet where both of the sideband peaks have a width different than that of the central peak. If the Rabi frequency is allowed to become much larger than the rate of spontaneous decay of the atom, we can see that in the strong field limit will become . From this equation it is clear where the differences in width of the peaks in the Mollow triplet arise from as the central peak has a width of and the sideband peaks have a width of where is the rate of spontaneous emission for the atom. Unfortunately this cannot be used to calculate a steady state solution as and in a steady state solution. Thus the spectrum would vanish in a steady state solution, which is not the actual case. The solution that does allow for a steady state solution must take the form of a two-time correlation function as opposed to the above one-time correlation function. This solution appears as . Since this correlation function includes the steady state limits of the density matrix, where and , and the spectrum is