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.
Cavity quantum electrodynamics, which explores the granularity of light by coupling a resonator to a nonlinear emitter, has played a foundational role in the development of modern quantuminformation science and technology. In parallel, the field of condensed matter physics has been revolutionized by the discovery of underlying topological robustness in the face of disorder, often arising from the breaking of time-reversal symmetry, as in the case of the quantum Hall effect. In this work, we explore for the first time cavity quantum electrodynamics of a transmon qubit in the topological vacuum of a Harper-Hofstadter topological lattice. To achieve this, we assemble a square lattice of niobium superconducting resonators and break time-reversal symmetry by introducing ferrimagnets before coupling the system to a single transmon qubit. We spectroscopically resolve the individual bulk and edge modes of this lattice, detect vacuum-stimulated Rabi oscillations between the excited transmon and each mode, and thereby measure the synthetic-vacuum-induced Lamb shift of the transmon. Finally, we demonstrate the ability to employ the transmon to count individual photons within each mode of the topological band structure. This work opens the field of chiral quantum optics experiment, suggesting new routes to topological many-body physics and offering unique approaches to backscatter-resilient quantum communication.
One of the most popular approaches being pursued to achieve a quantum advantage with practical hardware are superconducting circuit devices. Although significant progress has been madeover the previous two decades, substantial engineering efforts are required to scale these devices so they can be used to solve many problems of interest. Unfortunately, much of this exciting field is described using technical jargon and concepts from physics that are unfamiliar to a classically trained electromagnetic engineer. As a result, this work is often difficult for engineers to become engaged in. We hope to lower the barrier to this field by providing an accessible review of one of the most prevalently used quantum bits (qubits) in superconducting circuit systems, the transmon qubit. Most of the physics of these systems can be understood intuitively with only some background in quantum mechanics. As a result, we avoid invoking quantum mechanical concepts except where it is necessary to ease the transition between details in this work and those that would be encountered in the literature. We believe this leads to a gentler introduction to this fascinating field, and hope that more researchers from the classical electromagnetic community become engaged in this area in the future.
. There is"]an active effort to develop synthetic materials where the microscopic dynamics and ordering arising from the interplay of topology and interaction may be directly explored. In this work we demonstrate a novel architecture for exploration of topological matter constructed from tunnel-coupled, time-reversalbroken microwave cavities that are both low loss and compatible with Josephson junction-mediated interactions [2]. Following our proposed protocol [3] we implement a square lattice Hofstadter model at a quarter flux per plaquette ({\alpha} = 1/4), with time-reversal symmetry broken through the chiral Wannier-orbital of resonators coupled to Yttrium-Iron-Garnet spheres. We demonstrate site-resolved spectroscopy of the lattice, time-resolved dynamics of its edge channels, and a direct measurement of the dispersion of the edge channels. Finally, we demonstrate the flexibility of the approach by erecting a tunnel barrier investigating dynamics across it. With the introduction of Josephson-junctions to mediate interactions between photons, this platform is poised to explore strongly correlated topological quantum science for the first time in a synthetic system.
In this letter we introduce a novel approach to Hamiltonian tomography of non-interacting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energyeffective Hamiltonian between sites i and j may be obtained directly from Sij(ω), the (suitably normalized) two-port measurement between sites i and j at frequency ω. This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is actually a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band-projectors in finite, disordered systems with good flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in-between.
We present a scalable architecture for the exploration of interacting topological phases of photons in arrays of microwave cavities, using established techniques from cavity and circuitquantum electrodynamics. A time-reversal symmetry breaking (non-reciprocal) flux is induced by coupling the microwave cavities to ferrites, allowing for the production of a variety of topological band structures including the α=1/4 Hofstadter model. Effective photon-photon interactions are included by coupling the cavities to superconducting qubits, and are sufficient to produce a ν=1/2 bosonic Laughlin puddle. We demonstrate by exact diagonalization that this architecture is robust to experimentally achievable levels of disorder. These advances provide an exciting opportunity to employ the quantum circuit toolkit for the exploration of strongly interacting topological materials.