One-Dimensional Chain of n-Level Atoms and Discrete Nonlinear Schrödinger Equation

The Hamiltonian of one-dimensional chain of n-level atoms is represented in terms of Boson operators by using the Dyson-Maleev transformation and it is shown that the finite-ladder effect disappears when n tends toward infinity. In this way, it is found that the Heisenberg equation of motion of this system is exactly described in the coherent state representation by the dark discrete nonlinear Schrödinger (DNLS) equation. It is also briefly shown that the DNLS equation has some general soliton solutions. This indicates that this simple system has richness of nonlinear waves.