In this article, the interaction of an arbitrary number of quantum dots behaving as articial
molecules with dierent energy levels and a multi-mode electromagnetic eld is studied. We make the
assumption that each quantum dot can be represented as an atom with zero kinetic energy, and that all
excitonic eects except dipole-dipole interactions may be disregarded. We use the Jaynes-Cummings-Paul
model with applications to quantum systems based on a time-dependent Hamiltonian and entangled states.
We obtain a system of equations describing the interaction, and present a method to solve the equations
analytically for a single mode eld within the Rotating-Wave Approximation. As an example of the
applicability of this approach, we solve the system of two, two-level quantum dots in a lossless cavity with
two modes of electromagnetic eld. We, furthermore, study the evolution of entanglement by dening and
computing the concurrency.