The carrier-envelope phase (CEP) dependent ultrafast multiphoton processes in polar molecule media is investigated. The conversion efficiency of four-wave mixing can be controlled by the CEP of ultrashort pulses is found. Moreover, the initial CEP of the incident ultrashort pulse propagating in a polar molecule medium can be "remembered" by the subsequent generated soliton pulse, which provides a new method to measure the CEP of non-amplified few-cycle ultrashort pulse. Furthermore, the physics mechanism of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well (QW) is studied.