Transport and entanglement for single photons in optical waveguide ladders

Transfer and scattering matrix theories are derived for studying single-photon (SP) transport in optical waveguide ladders (OWLs). The OWLs consist of two one-dimensional waveguides connected by Jaynes-Cummings emitters (JCEs) and have two input and two output channels. The von Neumann entropy is introduced to describe the entanglement between the transmitted states from the two output channels. Two types of the OWLs are studied, i.e., the OWLs with two identical waveguides (i-OWLs) and those with two different waveguides (d-OWLs). When the OWLs contain only one JCE, the SP transport behavior in the i-OWLs is the same as that in the d-OWLs. When two JCEs are introduced, the quantum interference among the JCE-scattered waves can lead to the SP jumping with a 100% chance between the waveguides for the i-OWLs, while this is hard for the d-OWLs. As a result, the i-OWLs can serve as a SP router with respect to the d-OWLs. When the number of JCEs increases to a large value (e.g., 16), the transmission probabilities of the two output channels both tend to be 0.25 for the i-OWLs, but zero for d-OWLs. Correspondingly, the entanglements approximate a constant of 1 for the i-OWLs, but of zero for the d-OWLs. It shows that a large number of JCEs can suppress the influence of other system parameters including the SP frequency and JCE loss. Therefore, the i-OWLs with a large number of the JCEs show potential for a SP splitter and entanglement generator.