Phonon as environmental disturbance in three level system

This work investigates the effect of phonon coupling on the transfer of population and creation of coherence using variant of stimulated Raman adiabatic passage (STIRAP) known as \emph{fractional} stimulated Raman adiabatic passage (FSTIRAP). The study is based on the Liouville equation, which is solved numerically in the adiabatic limit. Although the phonon is assumed to be coupled only to the intermediate state, it is coupled to the other two states by dipolar system-environment interaction, inducing phonon coupling to the other states which are not directly in contact with the phonon. At zero temperature the STIRAP pulse protocol's efficiency of the transfer decreases exponentially with the electron-phonon coupling, until the coupling strength is strong enough to make the process fully incoherent, in which case the population transfer is $\frac{1}{3}$ in each level. For the FSTIRAP protocol we find that the transferred population to target state decreases, leaving some population on the intermediate state. Consequently, there is an increase in the magnitude of the coherences $\rho_{01}, \rho_{12}$, albeit small. Furthermore population transfer for non-zero temperature and effect of coupling strength is investigated, it is observed that while both parameters negatively influence the efficiency of transfer the former decrease the transfer exponentially, thereby equilibrating the system fast, while the latter seen to decrease the transfer monotonically, and hence equilibrates slowly.