We grew (GaAs)m(GaP)n strained-layer superlattices using pulsed jet epitaxy, a new type of atomic layer epitaxy. We investigated growth procedures for the heteroepitaxy and proposed a growth mechanism which includes adsorption, desorption, and decomposition of TMGa molecules on the surface. Structural analyses were carried out using x-ray rocking curves and Raman scattering measurements, and showed that growth of superlattices was completely controlled to within one atomic layer even for a monolayer (GaAs)1(GaP)1 superlattice. The photoluminescence and reflectance measurements suggest that (GaAs)1(GaP)1 has a direct energy band structure differing from the other superlattices (GaAs)m(GaP)n (m,n=2,3,4,5) and from alloy crystal GaAs0.5P0.5.