Superconducting circuits have emerged as a competitive platform for quantum computation, satisfying the challenges of controllability, long coherence and strong interactions between individual systems. Here we apply this toolbox to the exploration of strongly correlated quantum matter, building a Bose-Hubbard lattice for photons in the strongly interacting regime. We develop a versatile recipe for dissipative preparation of incompressible many-body phases through reservoir engineering and apply it in our system to realize the first Mott insulator of photons. Site-and time-resolved readout of the lattice allows us to investigate the microscopic details of the thermalization process through the dynamics of defect propagation and removal in the Mott phase. These experiments demonstrate the power of superconducting circuits for studying strongly correlated matter in both coherent and engineered dissipative settings. In conjunction with recently demonstrated superconducting microwave Chern insulators, the approach demonstrated in this work will enable exploration of elusive topologically ordered phases of matter. arXiv:1807.11342v1 [cond-mat.quant-gas] 30 Jul 2018

Topological and strongly correlated materials are exciting frontiers in condensed matter physics, married prominently in studies of the fractional quantum hall effect [1]. 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 (α = 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 and 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.

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Cavity quantum electrodynamics, which explores the granularity of light by coupling a resonator to a nonlinear emitter [1], has played a foundational role in the development of modern quantum information 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 [2-4], 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 [5]. To achieve this, we assemble a square lattice of niobium superconducting resonators [6] and break time-reversal symmetry by introducing ferrimagnets [7] before coupling the system to a single transmon qubit. We spectroscopically resolve the individual bulk and edge modes of this lattice, detect vacuumstimulated 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 [8] within each mode of the topological band structure. This work opens the field of chiral quantum optics experiment [9], suggesting new routes to topological many-body physics [10,11] and offering unique approaches to backscatter-resilient quantum communication.

We report on a device to electronically stabilize the optical injection lock of a semiconductor diode laser. Our technique uses as discriminator the peak height of the laser's transmission signal on a scanning Fabry-Perot cavity and feeds back to the diode current, thereby maintaining maximum optical power in the injected mode. A two-component feedback algorithm provides constant optimization of the injection lock, keeping it robust to slow thermal drifts and allowing fast recovery from sudden failures such as temporary occlusion of the injection beam. We demonstrate the successful performance of our stabilization method in a diode laser setup at 399 nm used for laser cooling of Yb atoms. The device eases the requirements on passive stabilization and can benefit any diode laser injection lock application, particularly those where several such locks are employed.