Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media

摘要

Solving the challenging problem of the amplification and generation of anelectromagnetic field in nanostructures enables to implement many properties ofthe electromagnetic field at the nanoscale in novel practical applications. Afirst-principles quantum mechanical consideration of such a problem issufficiently restricted by the exponentially large number of degrees offreedom, and does not allow the electromagnetic field dynamics to be describedif it involves a high number of interacting atoms and modes of theelectromagnetic field. Conversely, the classical description of electromagneticfields is incorrect at the nanoscale due to the high level of quantumfluctuations connected to high dissipation and noise levels. In this paper, wedevelop the framework with a significantly reduced number of degrees offreedom, which describes the quantum spatial dynamics of electromagnetic fieldsinteracting with atoms. As an example, we consider the interaction betweenatoms placed in a metallic subwavelength groove, and demonstrate that aspontaneously excited electromagnetic pulse propagates with the group velocity.The developed approach may be exploited to describe non-uniform amplificationand propagation of electromagnetic fields in arbitrary dispersive dissipativesystems.