Transport measurements are fundamental for understanding condensed matter phenomena, from superconductivity to the fractional quantum Hall effect. Analogously, they can be powerfultools for probing synthetic quantum matter in quantum simulators. Here we demonstrate the measurement of in-situ particle current in a superconducting circuit lattice and apply it to study transport in both coherent and bath-coupled lattices. Our method utilizes controlled tunneling in a double-well potential to map current to on-site density, revealing site-resolved current and current statistics. We prepare a strongly interacting Bose-Hubbard lattice at different lattice fillings, and observe the change in current statistics as the many-body states transition from superfluid to Mott insulator. Furthermore, we explore non-equilibrium current dynamics by coupling the lattice to engineered driven-dissipative baths that serve as tunable particle source and drain. We observe steady-state current in discrete conduction channels and interaction-assisted transport. These results establish a versatile platform to investigate microscopic quantum transport in superconducting circuits.
Superconducting qubits utilize the strong non-linearity of the Josephson junctions. Control over the Josephson nonlinearity, either by a current bias or by the magnetic flux, can bea valuable resource that brings tunability in the hybrid system consisting of superconducting qubits. To enable such a control, here we incorporate a fast-flux line for a frequency tunable transmon qubit in 3D cavity architecture. We investigate the flux-dependent dynamic range, relaxation from unconfined states, and the bandwidth of the flux-line. Using time-domain measurements, we probe transmon’s relaxation from higher energy levels after populating the cavity with ≈2.1×104 photons. For the device used in the experiment, we find a resurgence time corresponding to the recovery of coherence to be 4.8~μs. We use a fast-flux line to tune the qubit frequency and demonstrate the swap of a single excitation between cavity and qubit mode. By measuring the deviation in the transferred population from the theoretical prediction, we estimate the bandwidth of the flux line to be ≈~100~MHz, limited by the parasitic effect in the design. These results suggest that the approach taken here to implement a fast-flux line in a 3D cavity could be helpful for the hybrid devices based on the superconducting qubit.