Reviews of Modern Physics

Coulomb crystals form when the Coulomb interaction between charged particles dominates over kinetic energy; the prototype is the Wigner crystal formed by conduction electrons in metals at low densities. In recent years, it has become possible to realize Coulomb crystals using laser-cooled trapped ions, and these systems allow for unprecedented control of experimental parameters. This review describes the state of the art of ion Coulomb crystals in one, two, and three dimensions, their properties in and out of equilibrium, and their importance across fields ranging from condensed matter to astrophysics.

Social systems, when considered on an appropriately coarse-grained scale, display phenomena reminiscent of the behavior of physical many-body systems and can be studied using the methods of statistical mechanics. A particularly interesting subfield is opinion dynamics, which aims to understand the emergence of collective social phenomena, such as consensus, polarization, and fragmentation. This review systematizes the terminology and methods of opinion dynamics, surveys empirical findings alongside theoretical models, and summarizes the current state and future directions of this field.

It is sometimes said that if one uses quantum cryptography methods to distribute keys, their secrecy is guaranteed by the laws of physics. This is only partly true: while quantum physics provides a strong boost to security, the proper mathematical analysis of the full detailed protocol is still nontrivial. This review provides details of this analysis for one of the most important quantum protocols for key distribution and its variants, in which weak (few photon) coherent pulses are transmitted and threshold detectors are used for measurements.

The polaron, a single impurity embedded in a quantum many-body environment, conceptually bridges few- and many-body physics. Its properties provide both a test bed for many-body theories and physical insight into the phase structure of more complicated many-body systems. This review discusses two pristine experimental platforms in which polarons have recently been realized: ultracold atomic gases and atomically thin transition-metal dichalcogenides. The authors discuss the theory of Bose and Fermi polarons, compare theory to experiment, and provide a perspective on how polarons may serve as precise sensors in complex environments.

Recent advances in molecular cooling have enabled the realization of strongly dipolar molecular Bose-Einstein condensates. Such systems provide a unique platform for investigating new states of matter, from quantum droplets to supersolids. This Colloquium surveys the collisional shielding techniques that make stable molecular condensates possible, the theoretical challenges that arise in the strongly dipolar regime, and the exotic quantum phases now within experimental reach.

Scanning probe techniques have transformed our ability to study materials at the atomic scale, providing atom-by-atom views of surfaces. Tip-enhanced molecular fluorescence microscopy combines scanning probes with optical fluorescence. Such optical techniques normally have spatial resolution limited by the wavelength of the light used. However, using the scanning tip itself as a nanoscale optical antenna confines the electromagnetic field to the tip apex, achieving superresolution down to the atomic scale. Fluorescence is a fundamental probe of materials that reveals electronic structure and vibronic properties by exciting electrons to higher levels and observing the photons emitted when they relax. These capabilities are of particular interest for studying and identifying molecules, submolecular structures, and their reactions. This review discusses the techniques of tip-enhanced molecular fluorescence microscopy and the new insights they have revealed.

In this review, the authors provide a comprehensive multiwavelength view of high-energy emission from the center of our Galaxy. This region contains the closest supermassive black hole to us, which offers the best studied galactic nucleus in the Universe, with its quiescent emission and accretion contrasted by flaring activity. The Galactic Center also hosts diverse compact sources, plasma bubbles, and x-ray chimneys, altogether forming a dense interacting molecular zone—a gigantic powerhouse in the Milky Way.

Given vector b and matrix $A$, solve for vector x such that $A$x=b: this problem of solving linear-algebraic equations is arguably the central task of machine computation. The quantum linear system problem (QLSP) asks whether, given efficient quantum access to $A$ and a state encoding b, a quantum computer can prepare a state encoding the solution.The QLSP has driven extensive algorithmic development since Harrow, Hassidim, and Lloyd (HHL)’s pioneering 2009 algorithm. This review explores quantum algorithmic techniques that have been devised for efficiently tackling the QLSP, with a thorough explanation of HHL and subsequent post-HHL developments.

Vacuum breakdown or arcing happens when a very strong electric field causes a metal surface in a vacuum to suddenly form plasma, allowing large electrical currents to flow. Breakdown can damage particle accelerators, fusion reactors, satellites, and x-ray devices, though it is useful in technologies like plasma thrusters. Scientists have studied this unpredictable and fast phenomenon for over a century. Recent advances in experiments and computer simulations now provide a coherent mechanistic picture: tiny surface defects, electrical stress, heat, and emitted particles interact in complex ways to trigger breakdowns. These insights could improve high-power technologies and make advanced accelerators more reliable and efficient.