Composite bosons in transmon arrays: a perturbative approach

Capacitively coupled transmon arrays form a splendid platform to study the intricacies of few-body and many-body quantum physics in a precisely controllable environment. From a theoretical point of view, these arrays realise the disordered Bose–Hubbard model with attractive interactions.

Here, we study the model perturbatively in the limit of weak hopping, where it is possible to bind multiple bosons together simply by stacking them onto the same site. These composite bosons can be viewed as quasiparticles since they behave much like the bare bosons, although with some crucial differences. First, they are more massive, and the observed dynamics occurs at longer time scales. Second, even if the sites are all identical, boundary effects create an effective energy landscape for the quasiparticles, either keeping them trapped near a boundary or preventing them from getting close to a one. Finally, although the actual bosons can only interact when they are at the same site, the interactions between the quasiparticles can be of longer range, and either attractive or repulsive. For example, if two quasiparticles are placed near one another, they may form a bound state, but when approaching each other from a distance, they may scatter without actually colliding.