Retardation of quantum uncertainty of two radiative dipoles

In this paper we consider the excitation of one quantum dipole by another in the deep quantum limit. We use a full quantum mechanical theory to describe the interaction of the dipoles through the electromagnetic field. Our nonperturbative analytical calculations result in the exact solution. We show that minimal quantum uncertainty of the dipole oscillation amplitudes, taken at different times, have a retarded character. It is demonstrated that the commutator of the dipole oscillation amplitudes becomes nonzero inside the light cone only. Moreover, due to radiation in free space the value of the commutator has a global maximum.