There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

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, Renyi 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.

Measuring entanglement entropy in a quantum many-body system

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 Schrodinger 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.

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Quantum thermalization through entanglement in an isolated many-body system

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 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

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Quantum simulation of antiferromagnetic spin chains in an optical lattice

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.

Quantum Simulation of an Antiferromagnetic Spin Chain in an Optical Lattice

From Superfluid to Mott Insulator One of the most attractive characteristics of cold atomic gases in optical lattices is their ability to simulate condensed-matter systems. The results of these quantum simulations are usually averaged over the atomic ensemble, or course-grained over several lattice sites. Now, Bakr et al. (p. 547, published online 17 June; see the Perspective by DeMarco) provide a single lattice site view onto the transition of a Bose gas of Rb-87 from the superfluid to the Mott-insulating state. Characteristic concentric shells of uniform number density were observed deep in the Mott insulator regime, and probing the local quantum dynamics revealed unexpectedly short time scales. The low-defect Mott structures identified may provide a starting point for quantum magnetism experiments. Imaging of atoms that were optically trapped in lattice sites reveals local dynamics of a quantum phase transition. Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We used single atom–single lattice site imaging to investigate the Bose-Hubbard model on a microscopic level. Our technique enables space- and time-resolved characterization of the number statistics across the superfluid–Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low-entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition time scales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low-entropy phases in a lattice.

Philipp M. Preiss

Papers

Measuring entanglement entropy in a quantum many-body system

Quantum thermalization through entanglement in an isolated many-body system

Quantum simulation of antiferromagnetic spin chains in an optical lattice

Quantum Simulation of an Antiferromagnetic Spin Chain in an Optical Lattice

Probing the Superfluid to Mott Insulator Transition at the Single Atom Level