Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.

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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]...

Full control over the dynamics of interacting, indistinguishable quantum particles is an important prerequisite for the experimental study of strongly correlated quantum matter and the implementation of high-fidelity quantum information processing. Here we demonstrate such control over the quantum walk -the quantum mechanical analogue of the classical random walk -in the strong interaction regime. Using interacting bosonic atoms in an optical lattice, we directly observe fundamental effects such as the emergence of correlations in two-particle quantum walks, as well as strongly correlated Bloch oscillations in tilted optical lattices. Our approach can be scaled to larger systems, greatly extending the class of problems accessible via quantum walks.Quantum walks are the quantum-mechanical analogues of the classical random walk process, describing the propagation of quantum particles on periodic potentials [1,2]. Unlike classical objects, particles performing a quantum walk can be in a superposition state and take all possible paths through their environment simultaneously, leading to faster propagation and enhanced sensitivity to initial conditions. These properties have generated considerable interest in using quantum walks for the study of position-space quantum dynamics and for quantum information processing [3]. Two distinct models of quantum walk with similar physical behavior were devised: The discrete time quantum walk [1], in which the particle propagates in discrete steps determined by a dynamic internal degree of freedom, and the continuous time quantum walk [2], in which the dynamics is described by a time-independent lattice Hamiltonian.Experimentally, quantum walks have been implemented for photons [4], trapped ions [5,6], and neutral atoms [7][8][9], among other platforms [4]. Until recently, most experiments were aimed at observing the quantum walks of a single quantum particle, which are described by classical wave equations.An enhancement of quantum effects emerges when more than one indistinguishable particle participates in the quantum walk simultaneously. In such cases, quantum correlations can develop as a consequence of Hanbury Brown-Twiss (HBT) interference and quantum statistics, as was investigated theoretically [10,11] and experimentally [12][13][14][15][16][17]. In the absence of interactions or auxiliary feed-forward measurements of the KnillLaflamme-Milburn type [18] this problem is believed to lack full quantum complexity, although it can still become intractable by classical computing [11].The inclusion of interaction between indistinguishable quantum walkers [19,20] may grant access to a much wider class of computationally hard problems, such as many-body localization and the dynamics of interacting quantum disordered systems [21]. Similarly, in the presence of interactions the quantum walk can yield universal Starting from a localized initial state (I), individual atoms perform independent quantum walks in an optical lattice (II). Right: The single-particle density distribution ex...

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