Review Articles

Although the complexity of quantum systems scales exponentially with their size, classical algorithms and optimization strategies can still play an important role in the characterization of quantum states, their dynamics and the detection process.

Quantum sensors enable new possibilities in biomedical applications due to their high sensitivity. In this Review, the status of quantum sensing is presented, and the path towards real-world applications on the molecular, cellular and organism scale is evaluated.

Computer simulations may unlock crucial aspects of how a liquid transforms into a glass, but are hampered by rapidly growing relaxation times near the transition. This Review summarizes progress towards overcoming this problem and creating realistic in silico glasses, and discusses what understanding has been enabled.

Thouless pumping is a dynamical quantum effect that results in a quantized response of a many-body system. It stems from the topological properties of the band structure that emerge under a periodic drive in the adiabatic limit. This Review addresses the robustness of topology in adiabatically driven systems exploring fundamental issues regarding the roles of interactions, disorder and higher dimensions in quantum transport.

Randomized measurements provide a feasible procedure for probing properties of many-body quantum states realized in today’s quantum simulators and quantum computers. This Review covers implementation, classical post-processing and theoretical performance guarantees of randomized measurement protocols, surveying their many applications and discussing current challenges.

Magnetic resonance elastography captures multiscale mechanical information conveyed by shear waves, enabling noninvasive measurement of the physical behaviour of biological tissues—a behaviour that can change markedly with disease. This Review summarizes the basic technical concepts of magnetic resonance elastography and outlines preclinical and clinical applications.

Non-Hermitian theory consists of mathematical structures that are used to describe open systems, which can give rise to non-Hermitian topology not found in Hermitian systems. This Review provides an overview of non-Hermitian band topology and discusses recent developments, such as the non-Hermitian skin effect and non-Hermitian topological classifications.

The discovery of high-energy astrophysical neutrinos and the first hints of coincident electromagnetic and neutrino emissions opened new opportunities in multi-messenger astronomy. We review theoretical expectations of neutrino emission from transient astrophysical sources and the current and upcoming experimental landscape.

Spin–orbit coupling in non-centrosymmetric heterostructures is called the Rashba effect. This Review highlights the latest progress covering new classes of materials with a variety of ‘Rashba-like’ spin–momentum locking schemes and new trends in non-equilibrium transport leading to enhanced functionalities in spin- and optoelectronics.

Controlled dissipation can be used to protect quantum information, control dynamics and enforce constraints. This Review explains the basic principles and overviews the applications of dissipation engineering to quantum error correction, quantum sensing and quantum simulation.

Understanding the fundamental limits to photonic design is both theoretically important and critical to the development of future high-performance photonic devices. This Review surveys progress made in this area and discusses an emerging general framework for evaluating photonic design limits based on conservation principles and optimization theory.

The study of Bose–Einstein condensation in photonic systems has attracted strong interest in a variety of physical platforms, including conventional lasers and optical parametric oscillators, exciton and exciton–polariton gases, and photons in dye-filled cavities and propagating geometries. The focus of this Review is to highlight those universal phenomena that stem from the driven-dissipative, non-equilibrium nature of these systems and affect the static, dynamic, superfluid and coherence properties of the condensate.

Flat bands enhance the effect of electronic interactions and have emerged as a promising platform for superconductivity. This Review explains the quantum geometric origin of flat-band superconductivity and superfluidity, and discusses its relevance in graphene and ultracold gas moiré systems.

Owing to the growing volumes of data from high-energy physics experiments, modern deep learning methods are playing an increasingly important role in all aspects of data taking and analysis. This Review provides an overview of key developments, with a focus on the search for physics beyond the standard model.

The polarization of the cosmic microwave background (CMB) may shed light on the nature of dark matter and dark energy, and on the origin of all structures in the Universe. Discovering a signature of such new physics in the CMB will require new observational and calibration strategies for future CMB experiments.

Living cells use geometric, biochemical and mechanical guiding cues to control intracellular protein patterns that regulate many vital functions. This Review discusses mechanisms of pattern guidance unveiled in living cells and how to study them from a physics perspective.

Active matter encompasses various non-equilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This Review provides an elementary introduction to the role of topology in active matter through experimentally relevant examples.

Minimizing the energy of the Ising model is a prototypical combinatorial optimization problem, ubiquitous in our increasingly automated world. This Review surveys Ising machines — special-purpose hardware solvers for this problem — and examines the various operating principles and compares their performance.

Polaritonics is the physics of strongly coupled light–matter states that studies condensates and superfluids of bosonic quasiparticles in solid-state systems. Coherent flows of exciton–polaritons can be used for classical and quantum information processing, offering advantages of full optical control and read-out.

Multi-messenger observations of gravitational waves and electromagnetic radiation directly probe the synthesis of heavy elements in the Universe. This Review summarizes recent results and charts future challenges and opportunities for identifying the astrophysical origin of roughly half of the elements heavier than iron.