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We develop a dynamical theory for the optical injection of charge and spin current originating from the interferences between two coherent laser pulses of frequencies omega and 2omega. Multiband Bloch equations which include one- and two-photon interband transitions are derived. They also account for ac Stark shifts and intersubband two-photon transitions. The model is used to describe the case of time-dependent charge and spin current injection in a symmetric GaAs/AlGaAs quantum well. A comparison to the bulk case is also made. The separate contributions of the populations and intersubband coherences to the charge current and THz emission are identified. The influence of the Stark shifts and the inter-valence-band two-photon transitions are calculated and discussed.