The ground state phases of the disordered Bose-Hubbard model with attractive interactions

In this work we describe the ground state phases of the disordered Bose-Hubbard model with attractive interactions. The model can be experimentally realised with a chain of capacitively coupled superconducting transmon devices. For a fixed number of photons, the model exhibits three distinct ground state phases. With strong enough disorder, all the photons are localised onto the site with the lowest on-site energy. With weaker disorder and with low hopping frequency J relative to the strength of the interactions U, the ground state is a symmetric superposition of localised states, or a W-state. At the other end of the J / U axis, the ground state is superfluid.

In addition to the analytical description of the ground states at the limits of the parameter space, we have performed numerical calculations to study the regions where transitions between ground state phases occur, and mapped the ground state phase diagram as one of the main results of this work.

We have determined that each phase is realisable in transmon chains with experimentally reasonable parameters, chain lengths, and numbers of photons, and is distinguishable via measurable quantities. It is also possible to effectively traverse the phase boundaries simply by changing the number of photons.