magnetars, strongly magnetized neutron stars, have magnetic fields over the critical strength [@harding-lai06]. The quantum states of charged particles in such strong electromagnetic fields provide an essential ingredient to understand the vacuum structure and the pair production. The interaction of virtual pairs of the Dirac sea with a strong external electromagnetic field polarizes the vacuum and thus leads to a nonlinear effective action beyond the Maxwell theory. In particular, the complex effective action in an electric field implies the vacuum instability due to the pair production of charged particles. Hence, intense lasers have been proposed as a feasible tool to probe the vacuum structure via the pair production and the vacuum polarization (for review and references, see Refs. [@dunne09; @gies09]).

In this paper, we formulate the second quantized scalar field in homogeneous, time-dependent electromagnetic fields and employ the invariant operator method to find the quantum states of charged scalars. The Hamiltonian from the field action in a homogeneous, time-dependent electric field is a system of infinite number of decoupled, time-dependent oscillators, while it is equivalent to another system of infinite number of coupled oscillators in a time-dependent magnetic field with or without a parallel electric field. At the level of 