Simulating the Bose Hubbard Model in Superconducting Circuits – BOCA

Simulating the Bose Hubbard Model in Superconducting Circuits

Quantum simulators are ideally controlled systems for simulating complex quantum matter. Experimental efforts to implement this idea are being pursued in particular in the field of ultra-cold atoms, trapped ions, superconducting circuits, photonic and NMR systems. This project focuses on a new implementation using micro-fabricated mesoscopic superconducting circuits to simulate the Bose-Hubbard model.

The Bose-Hubbard model

The main goal of this project is to demonstrate the potential of circuit QED to simulate the Bose-Hubbard (BH) model, which is the canonical model for interacting bosons on a lattice.The BH model has found applications in various fields of condensed matter physics including superconducting thin-films and Josephson junction arrays, optical cavity arrays, and cold atoms in optical lattices. It describes bosons hopping on a lattice and on-site interaction. The non-trivial properties of the model stem from the competition between the hopping that delocalizes the particles and the interaction term that has the opposite effect. As a result of these two competing effect, the BH model generally predicts a quantum phase transition from a superfluid to a Mott insulator phase when the interaction increases. But, the BH can also lead to more exotic phases that are less understood. In the presence of disorder affecting the on-site energy, a Bose glass phase appears as an intermediate phase between the superfluid and the Mott insulator phases. New physics is also expected in lattices with exotic band structures, such as flat bands or topological bands. In the case of flat bands, charge density waves have been predicted at certain fillings but questions remain on the nature of the phase at intermediate fillings. Lattices with topological bands, which can be obtained using complex valued hopping have been predicted to host states that are similar to the ones of the fractional quantum Hall effect for electrons. Finally, the addition of loss terms and pump has given rise to many recent theoretical development. The resulting driven dissipative Bose-Hubbard model is actively studied and still poorly understood. No clear view has emerged regarding the nature and shape of the phase diagram and its relation to the equilibrium BH model if any.