as . As the atom cannot absorb a photon, it is unable to emit one and thus there is a restriction on the spectral density. This is illustrated by the second order correlation function . From the above equation it is clear that and thus resulting in the relation that describes photon antibunching . This shows that the power cannot be anything other than zero for . In the weak field approximation can only increase monotonically as increases, however in the strong field approximation oscillates as it increases. These oscillations die off as . The physical idea behind photon anti-bunching is that while the atom itself is ready to be excited as soon as it releases its previous photon, the electromagnetic field created by the laser takes time to excite the atom. Double Resonance Double Resonance is the phenomena when an additional magnetic field is applied to a two-level atom in addition to the typical electromagnetic field used to drive resonance fluorescence. This lifts the spin degeneracy of the Zeeman energy levels splitting them along the energies associated with the respective available spin levels, allowing for not only resonance to be achieved around the typical excited state, but if a second driving electromagnetic associated with the Larmor frequency is applied, a second resonance can be achieved around the energy state associated with and the states associated with . Thus resonance is achievable not only about the possible energy-levels of a two-level atom, but also about the sub-levels in the energy created by lifting the degeneracy of the level. If the applied magnetic field is tuned properly, the polarization of resonance fluorescence can be used to describe the composition of the excited state. Thus double resonance can be used to find the Landé factor, which is used to describe the magnetic moment of the electron within the two-level atom. Resonance fluorescence of a single artificial atom Any two state system can be modeled as a two-level atom. This leads to many systems being described as an "Artificial Atom". For instance a superconducting loop which can create a magnetic flux passing through it can act as an artificial atom as the current can induce a magnetic flux in either direction through the loop depending on whether the current is clockwise or counterclockwise. The hamiltonian for this system is described as where . This models the dipole interaction of the atom with a