Transient linear response of a two-level system interacting with an environment to a phase modulating field

A transient linear response to a phase modulating field is studied for a two-level system which is placed under the influence of a surrounding environment. Both initial correlation and detuning between a two-level system and environment are taken into account. An exact expression of the transient linear response function is derived when the whole system contains no more than single excitation. If the reduced time evolution is non-Markovian, the transient response strongly depends on initial correlation, detuning and initial coherence. The detuning and initial coherence are more important than the initial correlation in the transversal response while the detuning and the initial correlation become significant in the longitudinal response. In particular, it is found that the longitudinal response is greatly enhanced and its decay becomes sufficiently slow under certain conditions.