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Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications from high temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers due to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we employ a degenerate Bose gas confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary an applied field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase the interaction between the spins is overwhelmed by the applied field which aligns the spins. In the antiferromagnetic phase the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in-situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, improving our understanding of real magnetic materials.Ensembles of quantum spins arranged on a lattice and coupled to one another through magnetic interactions constitute a paradigmatic model-system in condensed matter physics. Such systems produce a rich array of magnetically-ordered ground states such as paramagnets, ferromagnets and antiferromagnets. Certain geometries and interactions induce competition between these orderings in the form of frustration, resulting in spin liquids [1] and spin glasses [2], as well as phases with topological order [3]. Varying system parameters can induce quantum phase transitions between the various phases [4]. A deeper understanding of the competition and resulting transitions between magnetic phases would provide valuable insights into the properties of complex materials such as high-temperature superconductors [5], and more generally into the intricate behaviours that can emerge when many simple quantum mechanical objects interact with one another.Studying quantum phase transitions of magnetic condensed matter systems is hindered by the complex structure and interactions present in such systems, as well as the difficulty of controllably varying system parameters. With a few notable exceptions [6,7], these issues make it difficult to capture the physics of such systems with simple models. Accordingly, there is a growing effort underway to realize condensed matter simulators using cold atom systems [8,9] which are understood from first principles. The exquisite control afforded by cold atom experiments permits adiabatic tuning of such systems through quantum phase transitions [9,10], enabling investigations of criticality [11,12] and scaling [13]. Time-resolved local readout [14][15]...

From studies of exotic quantum many-body phenomena to applications in spintronics and quantum information processing, topological materials are poised to revolutionize the condensed-matter frontier and the landscape of modern materials science. Accordingly, there is a broad effort to realize topologically nontrivial electronic and photonic materials for fundamental science as well as practical applications. In this work, we demonstrate the first simultaneous site-and time-resolved measurements of a time-reversalinvariant topological band structure, which we realize in a radio-frequency photonic circuit. We control band-structure topology via local permutation of a traveling-wave capacitor-inductor network, increasing robustness by going beyond the tight-binding limit. We observe a gapped density of states consistent with a modified Hofstadter spectrum at a flux per plaquette of ϕ ¼ π=2. In situ probes of the band gaps reveal spatially localized bulk states and delocalized edge states. Time-resolved measurements reveal dynamical separation of localized edge excitations into spin-polarized currents. The radio-frequency circuit paradigm is naturally compatible with nonlocal coupling schemes, allowing us to implement a Möbius strip topology inaccessible in conventional systems. This room-temperature experiment illuminates the origins of topology in band structure, and when combined with circuit quantum electrodynamics techniques, it provides a direct path to topologically ordered quantum matter. [7], and 2DEGs [8,9]. In a condensed-matter context, such "topologically protected" properties include single-particle features of the band structure and many-particle ground-state degeneracies, with the latter typically emerging from the former in conjunction with strong interactions. To explore the nature of topologically derived material properties, it is desirable to develop materials that not only support conserved topological quantities but that may be precisely produced, manipulated, and probed. The aim, then, is to realize material test beds that marry favorable coherence properties, strong interactions, and topologically nontrivial single-particle dynamics.Metamaterials, where interaction strengths and length scales can be engineered, are a promising avenue for studying topological physics. Efforts are ongoing to produce the requisite topological single-particle dynamics in ultracold atomic gases [10][11][12][13][14][15][16], gyrotropic metamaterials [17,18], and photonic systems [17,[19][20][21][22][23][24][25][26].In cold atomic gases, gauge fields are generated either through spatially dependent Raman coupling of internal atomic states [10,14], or time-and space-periodic modulation of lattice tunneling rates [15,27,28]. In the optical domain, synthetic magnetic fields were realized via strain of a honeycomb lattice [29]. A Floquet topological insulator [30,31] was realized under a space-to-time mapping of an array of tunnel-coupled waveguides modulated along their propagation direction [21]. A photonic topologic...

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