Constraint-satisfaction problems are among the computationally hardest tasks: solutions are efficiently checkable, but no efficient algorithms are known to compute those solutions. Fresh insight might come from physics. A study mapping optimization hardness onto the phenomena of turbulence and chaos suggests that constraint-satisfaction problems can be tackled using analog devices. Letter p966 IMAGE: MáRIA ERCSEY-RAVASZ COVER DESIGN: KAREN MOORE

The cover image of the December 2011 issue of Nature Physics should have been credited to Mária Ercsey-Ravasz. Corrected in the HTML and PDF versions after print, 13 December 2011.

Time-reversal symmetry makes massless Dirac fermions in topological insulators 'gapless'. When a gap opens, it breaks this symmetry and confers mass to the fermions. But now a quantum phase transition has been observed in a three-dimensional topological insulator that allows these particles to acquire mass without symmetry breaking. Letter p840 IMAGE: T. SATO COVER DESIGN: KAREN MOORE

The Tomonaga–Luttinger liquid model is the leading candidate for describing 1D metallic conductors at low temperature. Yet, experimental evidence that it is valid is sketchy. Scanning tunnelling and photoemission spectra suggest it does, in fact, describe the behaviour of chains of gold atoms self-assembled on the surface of germanium. Letter p776; News & Views p744 IMAGE: C. BLUMENSTEIN COVER DESIGN: KAREN MOORE

Bell's theorem experiments, which test the completeness of quantum mechanics, have a number of loopholes. However, one type [|ndash|] detection loopholes [|ndash|] becomes smaller when the measurement has more possible outcomes. Bell's inequality is now violated in tests with as many as eleven different results. Letter p677 IMAGE: ADETUNMISE DADA COVER DESIGN: DENIS MALLET

Exciton-polariton fluids — which are composed of composite light–matter bosons — provide an experimental means for studying quantum fluids that are intrinsically out of equilibrium. These authors demonstrate the nucleation and dynamics of vortex–anti-vortex pairs in the flow of exciton-polaritons passing around an obstacle, and establish these systems as a platform for studying quantum turbulence. Article p635 IMAGE: GREGORY PACHE COVER DESIGN: DENIS MALLET

Antihydrogen has been created, trapped and stored for 1,000 seconds. The improved holding time means that we now have access to the ground state of antimatter – long enough to test whether matter and antimatter obey the same physical laws. Article p558; News & Views p520 Image courtesy of Chukman So/ALPHA

The ability to switch a semiconductor into a topological insulator would produce topological states on demand. Applying a time-dependent field to well-studied semiconductor quantum wells may lead to this kind of control. Article p490 Image courtesy of Netanel Lindner, Gil Refael and Victor Galitski.

Topological quantum computation schemes — in which quantum information is stored non-locally — provide, in theory, an elegant way of avoiding the deleterious effects of decoherence, but they have proved difficult to realize experimentally. A proposal to engineer topological phases into networks of onedimensional semiconducting wires should bring topological quantum computers a step closer. Article p412 Image courtesy of Erik Lucero, Dario Mariantoni and Matteo Mariantoni.

The ability to coherently switch a state between two systems is a key requirement for quantum information processing. Such control is now demonstrated by shifting the quantum state of a microwave photon between any one of three superconducting-circuit resonators: in analogy to the classic three cups and a ball game. Letter p287 Image courtesy of Erik Lucero, Dario Mariantoni and Matteo Mariantoni.

Quantum dots are usually assumed to interact with light as atom-like point sources. A study of the behaviour of quantum dots placed close to a metal mirror suggests this isn't the case. Rather, a quantum dot's finite size causes the strength of its interaction with light to oscillate with its distance from a nearby mirror. Letter p215 Cover design by David Shand

High-order harmonic generation is a nonlinear optical process that enables the creation of light pulses at frequencies much higher than that from a seed laser. The host medium for this interaction is typically a gas. Now, the process has been observed in a bulk crystalline solid, with important implications for attosecond science. Letter p138; News & Views p97 Cover design by Greg Stewart

An array of nanomagnets in a kagome lattice structure should support the creation and separation of oppositely charged monopoles, which are connected by Dirac strings of flipped dipoles. And indeed, such monopoles and their Dirac strings have now been observed at room temperature. (This image shows a related sevenring kagome spin-ice structure, with colours representing magneticmoment orientations.) Article p68 Cover design by David Shand