  Solving the challenging problem of the amplification and generation of an
electromagnetic field in nanostructures enables to implement many properties of
the electromagnetic field at the nanoscale in novel practical applications. A
first-principles quantum mechanical consideration of such a problem is
sufficiently restricted by the exponentially large number of degrees of
freedom, and does not allow the electromagnetic field dynamics to be described
if it involves a high number of interacting atoms and modes of the
electromagnetic field. Conversely, the classical description of electromagnetic
fields is incorrect at the nanoscale due to the high level of quantum
fluctuations connected to high dissipation and noise levels. In this paper, we
develop the framework with a significantly reduced number of degrees of
freedom, which describes the quantum spatial dynamics of electromagnetic fields
interacting with atoms. As an example, we consider the interaction between
atoms placed in a metallic subwavelength groove, and demonstrate that a
spontaneously excited electromagnetic pulse propagates with the group velocity.
The developed approach may be exploited to describe non-uniform amplification
and propagation of electromagnetic fields in arbitrary dispersive dissipative
systems.
