Composite bosons in transmon arrays: numerical approach

The dynamics of bosonic many-body systems are notoriously slow to simulate due to the exponential scaling of the Hilbert space size. Analogue quantum simulation of the Bose-Hubbard model can be realised with arrays of capacitively coupled transmons. In experimental realisations the transmon anharmonicity, that is, the on-site interaction, dominates the hopping of the bosons. This results in approximate conservation of the interaction energy.

To limit the complexity of modeling such systems, it is often assumed that the local number of bosons never exceeds one, that is, the transmons are considered as two-level systems. In the absence of this limitation, the dynamics are dominated by many-body effects. If multiple bosons are initially stacked onto a single site, being bound together by the on-site interactions, the bosons effectively act as a single composite particle. The composite bosons also experience effective off-site interactions with other composites, individual bosons, and the edges of the arrays.

Here we discuss the many-body effects as seen in numerical simulations of the Bose-Hubbard model within experimentally realistic parameter ranges of transmon arrays and timeframes limited by the onset of decoherence and dissipation.