Collapsing energy bands to discover their geometric shape

The geometry and topology of digital states in solids plays a central role in a huge variety of contemporary condensed-count systems along with graphene or topological insulators. however, experimentally getting access to this information has established to be hard, specifically when the bands aren't nicely-remoted from one another. As reported in last week's problem of technological know-how, an global group of researchers working with T. Li, Prof. I. Bloch and Dr. U. Schneider from the Ludwig-Maximilians-Universität Munich and the Max Planck Institute of Quantum Optics have devised a honest technique to probe the band geometry using ultracold atoms in an optical lattice. Their approach, which mixes the controlled guidance of atoms thru the strength bands with atom interferometry, is an crucial step within the endeavor to analyze geometric and topological phenomena in artificial band systems.

A big selection of essential phenomena in condensed matter physics, inclusive of why a few materials are insulators whilst others are metals, can be understood definitely through inspecting the energies of the material's constituent electrons. certainly, band principle, which describes these electron energies, was one of the earliest triumphs of quantum mechanics and has pushed a great deal of the technological advances of our time, from the computer chips in our laptops to the liquid-crystal shows on our smartphones. We now know, but, that conventional band theory is incomplete.

most of the most sudden and fruitful developments in current condensed rely physics became the realization that there may be greater than the energies -- instead, the geometric shape of the bands additionally performs an crucial role. This geometric facts is responsible for lots of the uncommon physics in newly determined substances inclusive of graphene or topological insulators and underlies an array of thrilling technological possibilities from spintronics to topological quantum computing. it's far, however, notoriously difficult to experimentally access.

Now, an worldwide group of researchers, with experiments accomplished on the Ludwig-Maximilians-Universität Munich and the Max Planck Institute of Quantum Optics, has devised a straightforward technique to probe the band geometry using ultracold atoms in an optical lattice, a synthetic crystal formed from standing waves of mild. Their approach relies on growing a machine that can be defined via a amount referred to as the Wilson line.

although at first formulated in the context of quantum chromodynamics, Wilson strains relatively additionally describe the evolution of degenerate quantum states, i.e., quantum states with the same strength. applied to condensed matter structures, the factors of the Wilson line without delay encode the geometric structure of the bands. therefore, to get entry to the band geometry, the researchers need handiest to access the Wilson line elements.

The hassle, but, is that the bands of a strong are typically now not degenerate. The researchers found out that there was a work-round: when moved speedy sufficient in momentum space, the atoms no longer experience the effect of the energy bands and probe most effective the vital geometric data. on this regime, two bands with  specific energies behave like  bands with the same strength.

in their work, the researchers first cooled atoms to quantum degeneracy. The atoms were then placed into an optical lattice fashioned via laser beams to recognise a device that mimics the behavior of electrons in a stable, however without the added complexities of actual substances. in addition to being particularly clean, optical lattices are highly tunable -- specific styles of lattice systems can be created via changing the intensity or the polarization of the light. of their test, the researchers interfered 3 laser beams to shape a graphene-like honeycomb lattice.

although spread out over all lattice sites, the quantum degenerate atoms carry a well-described momentum within the light crystal. The researchers then unexpectedly improved the atoms to a different momentum and measured the quantity of excitations they created. while the acceleration is rapid enough, such that the device is defined with the aid of the Wilson line, this trustworthy size reveals how the digital wavefunction at the second momentum differs from the wavefunction at the first momentum. Repeating the identical test at many distinctive crystal momenta might yield a complete map of how the wavefunctions trade over the complete momentum area of the artificial strong.

The researchers now not best confirmed that it was feasible to transport the atoms such that the dynamics had been defined by way of two-band Wilson traces; additionally they found out each the neighborhood, geometric houses and the global, topological shape of the bands. at the same time as the bottom  bands of the honeycomb lattice are known no longer to be topological, the outcomes exhibit that Wilson traces can certainly be experimentally used to probe and display the band geometry and topology in these novel artificial settings.