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An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system’s entanglement, which is experimentally challenging to measure. We realize such a many-body–localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.

Entanglement, which describes non-local correlations between quantum objects, is very difficult to measure, especially in systems of itinerant particles; here spatial entanglement is measured for ultracold bosonic atoms in optical lattices. 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. Getting to grips with entanglement Although entanglement — in which physically separate particles can behave and can be completely specified as one — is arguably the most important measure of the quantumness of a system. However, it is difficult to measure entanglement directly. Most schemes suggested so far measure it in artificial quantum systems, like ultracold quantum gases, which require reconstruction of the quantum states via tomography and are restricted to localized systems. Here the authors find a way to directly access entanglement in a delocalized, itinerant system. After preparing two identical copies of a many-body quantum state composed of rubidium atoms, the authors let these copies interfere. With a special quantum gas microscope, properties directly connected to entanglement entropy, a characteristic measure of the entanglement of the system, can be observed. This new way of measuring entanglement entropy might allow for other properties connected to entanglement and entanglement entropy to become accessible.

Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis.

The combination of interparticle interactions and a synthetic gauge field leads to chirality in the propagation dynamics of particles in a ladder-like lattice. Gauging two-body interactions Simulating topological band structures, the corresponding edge states, and the quantum Hall effect with neutral atoms requires the introduction of artificial gauge fields. Although challenging, various groups have recently demonstrated artificial gauge fields in ultracold neutral-atom systems. However, up to now, these simulations have been limited to single-particle effects, meaning that many fascinating condensed-matter phenomena, such as the fractional quantum Hall effect, could not be studied. Here, the authors subject a two-dimensional Bose–Einstein condensate of rubidium-87 atoms to an artificial gauge field and use a quantum gas microscope to investigate how two-body interactions affect the chiral dynamics. If extended to many-body interactions, this strategy could enable the simulation of the interplay between many-body interactions and topology in condensed-matter physics. The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement 1 . Although these phases were discovered in a solid-state setting 2 , 3 , recent innovations in systems of ultracold neutral atoms—uncharged atoms that do not naturally experience a Lorentz force—allow the synthesis of artificial magnetic, or gauge, fields 4 , 5 , 6 , 7 , 8 , 9 , 10 . This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems 11 , 12 . However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states 4 , 13 , 14 , 15 , 16 , 17 . Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladder-like, real-space lattice governed by the interacting Harper–Hofstadter model, which describes lattice-confined, coherently mobile particles in the presence of a magnetic field 18 . We use a bottom-up strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a top-down approach that begins with a many-body system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.

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. We demonstrate such control over the quantum walk—the quantum mechanical analog of the classical random walk—in the regime where dynamics are dominated by interparticle interactions. Using interacting bosonic atoms in an optical lattice, we directly observed 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.

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we use a degenerate Bose gas of rubidium atoms 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 a magnetic 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, thereby improving our understanding of real magnetic materials. Giving quantum magnetism a spin Quantum simulation of condensed-matter systems using ultracold atoms provides a way to study problems that are computationally intractable on classical computers. Using an ultracold gas of rubidium atoms confined in an optical lattice, Simon et al . simulate quantum magnetism in a chain of spins and observe a quantum phase transition from a paramagnetic phase into an antiferromagnetic phase. This work provides a tunable platform for studies of magnetic quantum phase transitions, which have been realized in few real materials.

We propose a quantum-information-based scheme to reduce the temperature of quantum many-body systems and access regimes beyond the current capability of conventional cooling techniques. We show that collective measurements on multiple copies of a system at finite temperature can simulate measurements of the same system at a lower temperature. This idea is illustrated for the example of ultracold atoms in optical lattices, where controlled tunnel coupling and quantum gas microscopy can be naturally combined to realize the required collective measurements to access a lower, virtual temperature. Our protocol is experimentally implemented for a Bose-Hubbard model on up to 12 sites, and we successfully extract expectation values of observables at half the temperature of the physical system. Additionally, we present related techniques that enable the extraction of zero-temperature states directly.

A type of interaction blockade that occurs for ultracold atoms confined to an optical lattice may offer a means of reducing the temperature and, thus, entropy of quantum gases to the level necessary for quantum simulation. Atom blockade in a quantum gas This work demonstrates an atom-number-sensitive blockade mechanism with potential applications in condensed matter physics and quantum information processing. Blockade can occur when strong interactions in a confined few-body system prevent a particle from occupying an otherwise accessible quantum state. The authors observe a new form of interaction blockade for ultracold atoms in optical lattices, which they term orbital excitation blockade. In this system, a single atom on a lattice site can be excited to a higher orbital by resonantly modulating the lattice depth. But when two atoms occupy the same site, interactions between them lead to orbital-dependent energy shifts. Therefore, modulation at an appropriate frequency to excite one atom to the higher orbital is off-resonant for exciting the second, which is 'blocked'. The effect is used here to demonstrate algorithmic cooling with ultracold atoms, potentially important for reaching the ultralow entropies required for quantum simulation. In addition, orbital excitation blockade could enable the implementation of quantum gates in optical lattices. Interaction blockade occurs when strong interactions in a confined, few-body system prevent a particle from occupying an otherwise accessible quantum state. Blockade phenomena reveal the underlying granular nature of quantum systems and allow for the detection and manipulation of the constituent particles, be they electrons 1 , spins 2 , atoms 3 , 4 , 5 or photons 6 . Applications include single-electron transistors based on electronic Coulomb blockade 7 and quantum logic gates in Rydberg atoms 8 , 9 . Here we report a form of interaction blockade that occurs when transferring ultracold atoms between orbitals in an optical lattice. We call this orbital excitation blockade (OEB). In this system, atoms at the same lattice site undergo coherent collisions described by a contact interaction whose strength depends strongly on the orbital wavefunctions of the atoms. We induce coherent orbital excitations by modulating the lattice depth, and observe staircase-like excitation behaviour as we cross the interaction-split resonances by tuning the modulation frequency. As an application of OEB, we demonstrate algorithmic cooling 10 , 11 of quantum gases: a sequence of reversible OEB-based quantum operations isolates the entropy in one part of the system and then an irreversible step removes the entropy from the gas. This technique may make it possible to cool quantum gases to have the ultralow entropies required for quantum simulation 12 , 13 of strongly correlated electron systems. In addition, the close analogy between OEB and dipole blockade in Rydberg atoms provides a plan for the implementation of two-quantum-bit gates 14 in a quantum computing architecture with natural scalability.

Phase transitions are driven by collective fluctuations of a system’s constituents that emerge at a critical point 1 . This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behaviour is described by the general theory of phase transitions. Recently, however, fundamentally distinct phase transitions have been discovered for out-of-equilibrium quantum systems, which can exhibit critical behaviour that defies this description and is not well understood 1 . A paradigmatic example is the many-body localization (MBL) transition, which marks the breakdown of thermalization in an isolated quantum many-body system as its disorder increases beyond a critical value 2 – 11 . Characterizing quantum critical behaviour in an MBL system requires probing its entanglement over space and time 4 , 5 , 7 , which has proved experimentally challenging owing to stringent requirements on quantum state preparation and system isolation. Here we observe quantum critical behaviour at the MBL transition in a disordered Bose–Hubbard system and characterize its entanglement via its multi-point quantum correlations. We observe the emergence of strong correlations, accompanied by the onset of anomalous diffusive transport throughout the system, and verify their critical nature by measuring their dependence on the system size. The correlations extend to high orders in the quantum critical regime and appear to form via a sparse network of many-body resonances that spans the entire system 12 , 13 . Our results connect the macroscopic phenomenology of the transition to the system’s microscopic structure of quantum correlations, and they provide an essential step towards understanding criticality and universality in non-equilibrium systems 1 , 7 , 13 . Quantum critical behaviour at the many-body localization transition in a disordered Bose–Hubbard system of bosonic rubidium atoms in an optical lattice is observed, connecting the macroscopic phenomenology of the transition to the system’s microscopic quantum correlations.

AbstractObjectivePeople with cancer are increasingly more likely to visit an emergency department for acute care than the general population. They often have long wait times and more exposure to infection and receive treatment from staff less experienced with cancer‐related problems. Our objective was to examine emergency department (ED) visits among people with cancer to understand how often and why they seek care. MethodsWe conducted a retrospective study of ED visits using the National Syndromic Surveillance Program BioSense Platform. Cancer reported during an ED visit was identified using International Classification of Diseases, Tenth Revision codes for any cancer type, including bladder, breast, cervical, colorectal, kidney, liver, lung, ovary, pancreas, prostate, or uterine cancers. Symptoms prompting the visit were identified for people with cancer who visited EDs in the United States from June 2017 to May 2018 in ≈4500 facilities, including 3000 EDs in 46 states and the District of Columbia (66% of all ED visits during a 1‐year period). ResultsOf 97 million ED visits examined, 710,297 (0.8%) were among people with cancer. Percentages were higher among women (50.1%) than men (49.5%) and among adults aged ≥65 years (53.6%) than among those ≤64 years (45.7%). The most common presenting symptoms were pain (19.1%); gastrointestinal (13.8%), respiratory (11.5%), and neurologic (5.3%) complaints; fever (4.9%); injury (4.1%); and bleeding (2.4%). Symptom prevalence differed significantly by cancer type. ConclusionsThe Centers for Medicare & Medicaid Services encourages efforts to reduce acute care visits among people with cancer. We characterized almost 70% of ED visits among this population.