  The purpose of this paper is to propose quantum filters for a two-level atom
driven by two continuous-mode counter-propagating photons and under continuous
measurements. Two scenarios of multiple measurements, 1) homodyne detection
plus photodetection, and 2) two homodyne detections, are discussed. Filtering
equations for both cases are derived explicitly. As demonstration, the two
input photons with rising exponential and Gaussian pulse shapes are used to
excite a two-level atom under two homodyne detection measurements. Simulations
reveal scaling relations between atom-photon coupling and photonic pulse shape
for maximum atomic excitation.
