1 Giant Atom

Model

Consider two waveguides. Between the two is a single giant atom coupled to each waveguide at two distinct points. To further simplify the problem, we consider only the case that the separation distance between coupling points within a waveguide is equal across both waveguides. Finally, we suppose there is a single incident photon from the left of the bottom waveguide traveling to the right towards the giant atom structure. We aim to determine the probability that the photon is routed to the top waveguide moving towards the right. We leave two parameters free to change: the distance between coupling points and the frequency of the incoming photon. 

Results

Proceeding with methods previously discussed, we find and plot the probability that the photon is in the top waveguide moving towards the right. The two parameters we change roughly correspond to the frequency of the photon (x-axis) and the distance between coupling points (y-axis). More specifically, we plot the detuning in units of the atom's decay rate on the x-axis. Detuning is the difference between the incoming photon frequency and the atomic transition frequency. The decay rate of the atom corresponds to the timescale that a photon is emitted by the atom back into the waveguide. Finally, the y-axis specifically plots the change in phase of a photon with the atomic transition frequency as it moves between between two consecutive coupling points. The phase corresponds to the particular point that a wave is in its cycle. 

For a single giant atom, we see that the probability of successful routing, i.e. the likelihood of the photon being found on the right side of the top waveguide, is always 25% or less. Although not explicitly shown, it turns out that the probabilities of the photon being found anywhere besides the bottom waveguide moving toward the right are all the same. Noting that the photon moving toward the right in the bottom waveguide corresponds exactly to what would happen if there were no giant atom present, we conclude that these plots essentially tell us how effective the coupling between waveguide and giant atom is for various parameters, but this configuration gives no preference to where the photon is then emitted back into the waveguides. Clearly, one giant atom is not going to produce the routing results we are looking for.