Optical response of two-level atoms with reflection geometry as a model of a quantum phase gate

The nonlinear optical response obtained from a model system of a quantum phase gate is investigated. The model system consists of a thin infinite atomic layer of two-level atoms placed in front of a perfect reflecting mirror. The optical response obtained from the model system is semiclassically analyzed using the finite difference time domain method with the optical Bloch equations. It is shown that a nonlinear phase shift of π is achieved when the atomic layer is placed at an antinode of the input field. This result is consistent with the theoretical result obtained from a one-dimensional atom model [H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B: Quantum Semiclassical Opt. 5, 218 (2003)]. The dependence of the nonlinear phase shift on the position of the atomic layer is also studied in detail