Many-body Ramsey as a Probe of Superfluid Compressibility in the Bose-Hubbard Circuit

Superconducting circuits are an ideal platform for applying the tools of quantum computing to experiments probing many-body physics. We engineer a 1D Bose Hubbard chain using capacitively coupled transmon qubits, with individual qubit frequency tuning and single-site resolved readout. We deterministically prepare low-entropy fluid eigenstates of our system using particle-by-particle assembly and adiabatic tuning of disorder. This state preparation technique is reversible; combining it with a many-body Ramsey experiment, we prepare cat states of quantum fluids, and then localize the information about energy differences of these highly entangled and delocalized states into one qubit for measurement. We then use this manybody Ramsey as a probe of adiabaticity and compressibility of the fluids at different system sizes and particle numbers.