Quantum mechanical treatment of traveling light in an absorptive medium of two-level systems

•Traveling light in an absorptive medium is quantum mechanically described.•Time evolution of the field operator is derived from the Heisenberg equation with the Hamiltonian for light-atom interaction.•The paper provides a theoretical basis for a conventional phenomenological beam-splitter model.

Quantum mechanical treatment of a light wave that propagates through an absorptive medium is presented. Unlike a phenomenological beam-splitter model conventionally employed to describe a traveling light in a lossy medium, the time evolution of the field operator is derived using the Heisenberg equation with the Hamiltonian for a physical system, where the light wave interacts with an ensemble of two-level systems in a medium. Using the obtained time-evolved field operators, the mean values and variances of the light amplitude and the photon number are evaluated. The results are in agreement with those obtained in the beam-splitter model, giving a logical theoretical basis for the phenomenological beam-splitter model.