  Studying the spontaneous emission of a V-type three-level atom embedded in a
photonic crystal (PC) by fractional calculus, we found that the atomic excited
states in the anisotropic PC can be expressed as a superposition of four
dressed states analytically. Through detuning two allowed atomic transition
energies with respect to the photonic band edge, the coupling between these two
transitions leads to three dynamic regimes, namely non-Markovian decay, damped
quantum interference and quantum interference, classified by the numbers of
contributed bounded dressed states. From the degree of quantum interference of
two atomic transitions, we found the energy exchange between the atom and PC
reservoir is the lowest as the excited states become degenerate but with
maximum quantum interference when the atom is prepared at one of the excited
states. The results also show that excited states prefer to stay out of phase
at all detuning energy except for near degenerate. Therefore, we can control
the spontaneous emission rate not only by the amount of detuning frequencies
but also the relative phase of initial states.
