We call "proteons" -- from the ever-changing greek sea-god
Πρωτευς -- composite particles made of two fermions. Among them, are the semiconductor excitons, but also various atoms and molecules, like the giant molecules made of two
40K or
6Li atoms which have recently Bose condensed. In addition to their indistinguishability, these composite particles are ``ever-changing'' in the sense that there is no way to know with which fermions they are precisely made. As direct consequences, (i) the proteons are not true bosons, (ii) the basis made with proteon states is \emph{overcomplete}. In spite of these difficulties, these proteons do have a nice closure relation, unexpected at first, \emph{different from the boson one} and which makes the bosonization procedures used up to now to treat many-body effects between composite bosons, rather questionable, due to possibly incorrect sum rules resulting from it. This closure relation in particular explains, in a neat way, the surprising factor 1/2 between the inverse lifetime and the sum of scattering rates which exists for exact excitons but not for boson excitons, as we have recently shown.
We study the coherent single-photon scattering in a one-dimensional waveguide coupled to a giant artificial molecule consisting of two coupled giant atoms. Since each giant atom couples to the waveguide via two coupling points, the couplings of the molecule with the waveguide have three different coupling configurations: the separated-, braided-, and nested-coupling cases. We obtain the exact expressions of the single-photon transmission and reflection amplitudes with the real-space approach. It is found that the behavior of the scattering spectra depends on the phase shift between two neighboring coupling points, the coupling configuration, and the coupling between the two giant atoms. Concretely, we study the photon scattering in both the Markovian and non-Markovian regimes, in which the photon propagating time between two neighboring coupling points is neglected and considered, respectively. Under the Markovian limit, the asymmetric Fano line shapes in different coupling configurations of the giant-molecule waveguide-QED system can be obtained by choosing proper phase shift, and the transmission window can be adjusted by the coupling strength between the two giant atoms in these three coupling configurations. In particular, multiple reflection peaks and dips in these configurations are revived in the non-Markovian regime. This paper will pave the way for the study of controllable single-photon devices based on the giant-molecule waveguide-QED systems.