  Coherent control of a spin is limited by both the decoherence due to coupling
with the environment and noise coming from the quantized control. The quantum
noise study of this system is particularly important in fault tolerant quantum
computation where a very high fidelity is demanded. Here, we present a time
evolution study of a two level system (TLS) interacting with a laser pulse and
the electromagnetic vacuum based on the multimode Jaynes-Cummings model. We
develop a diagrammatic formalism in which one can easily identify the coherent
Rabi oscillation of the TLS and its relaxation from corresponding diagrams. In
the small time limit ($t\ll T_1$), where the noise level is small but still an
issue to fault tolerant quantum computing, this method gives a quantitative
evaluation of the quantum noise of the TLS under an optical control with an
arbitrary pulse shape. Furthermore, this approach can be naturally extended
from the Markovian to the non-Markovian regime, resulting in dynamics different
from that obtained in the optical Bloch analysis. All these calculations are
done without any stochastic assumption.
