We investigate the quasiparticle and condensate dynamics in response to the terahertz optical pulses in the weak spin-orbit-coupled s-wave superconducting semiconductor quantum wells by using the gauge-invariant optical Bloch equations in the quasiparticle approximation. Specifically, in the Bloch equations, not only can the microscopic description for the quasiparticle dynamics be realized, but also the dynamics of the condensate is included, with the superfluid velocity and the effective chemical potential naturally incorporated. We reveal that the superfluid velocity itself can contribute to the pump of quasiparticles (pump effect), with its rate of change acting as the drive field to drive the quasiparticles (drive effect). We find that the oscillations of the Higgs mode with twice the frequency of the optical field are contributed dominantly by the drive effect but not the pump effect as long as the driven superconducting momentum is less than the Fermi momentum. This is in contrast to the conclusion from the Liouville or Bloch equations in the literature, in which the drive effect on the anomalous correlation is overlooked with only the pump effect considered. Furthermore, in the gauge-invariant optical Bloch equations, the charge neutrality condition is consistently considered based on the two-component model for the charge, in which the charge imbalance of quasiparticles can cause the fluctuation of the effective chemical potential for the condensate. It is predicted that during the optical process, the quasiparticle charge imbalance can be induced by both the pump and drive effects, leading to the fluctuation of the chemical potential. This fluctuation of the chemical potential is further demonstrated to directly lead to a relaxation channel for the charge imbalance even with the elastic scattering due to impurities. This is very different from the previous understanding that in the isotropic s-wave superconductivity, the impurity scattering cannot cause any charge-imbalance relaxation.
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