Transient Dynamics of Atoms Inside Submicron Rectangular Waveguides

The time evolution of the radiation pressure forces due to the action of a laser light on two-level atom moving inside a long hollow cylinder with a rectangular cross-section of sub-wavelength dimensions a × b is presented. This evolution is considered when the frequency of the light is comparable to a dipole allowed transition frequency. In this limit, the decay emission Γp is possible only via a very small number of modes. From the solutions of the Bloch equations in the dynamic regime, we find that the transient regime, applicable from the instant the laser is switched on. This is important for the gross motion, provided that the upper-state lifetime $\Gamma p^{-1}$ is relatively long while the steady-state regime, formally such that t ≫ $Γp^{-1}$, is appropriate for the evaluation of the forces and the dynamics for large Γp. Significant variations of the characteristics of the system are emphasized. These features are illustrated using typical parameters for the case of $Eu^{3+}$ that has a particularly small Γp.