Shedding new light on topological lattices

There are many differences between a donut and a cake, but a mathematician might point out one in particular: their differing topology. From a topological perspective, a donut — with its single hole — is fundamentally different from a cake, which is generally free from holes. Topology is the branch of mathematics that describes the essence of shapes, not by their angles and smoothness, but in terms of the number of holes, windings and connections they showcase.

These abstract properties can have surprising effects beyond pure mathematics. Since the 1980s, researchers have unveiled that topology can have many profound implications on material science and physics. For example, materials with topologically non-trivial crystal lattices can exhibit unusual properties, such as being electrically conductive on their surfaces while remaining insulating in their bulk.

IBM Research has been investigating alternative ways of processing information, including through varying topologies. The Exploratory Photonics research group at IBM Research Europe – Zurich has been actively pursuing computing paradigms that use light in place of traditional electronics.

In this context, the group is developing new ways to investigate the physics of topological lattices, using light to simulate and visualize their states. This approach constitutes a form of analog computing, one that relies on photons rather than electrons. The IBM team’s recent work led to a new paper published in the latest edition of the journal Science Advances, where it was also selected as the cover feature.

The results presented in this publication showcase a platform that enables room-temperature analog simulations. This allows for the study of several crystal lattice models, pushing the boundaries of material science knowledge. In particular, the investigation of topological effects — unique properties of a material that can exhibit different behavior at its boundaries — could inform the design of materials with enhanced electrical conductivity, as well as greater resilience to impurities or imperfections.  

Studying topological SSH lattices

In 1979, Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger (the latter two are Nobel laureates) developed a model to describe the conductivity of certain polymer chains, later known as the SSH model, after their initials. It is currently recognized as one of the simplest lattice systems that can exhibit topological effects in the form of protected states, which are located at its edges.

Exploring these phenomena, the IBM team worked with arrays of so-called microcavity exciton-polaritons — light-matter particles that arise when specific materials are placed between two mirrors. By engineering one of the mirror surfaces, synthetic crystal lattices for the polaritons can be induced, allowing for polariton confinement in a one-dimensional SSH lattice.  This system creates a platform where topological edge states can be clearly observed due to their energetic and spatial isolation from the bulk states.

The team used different configurations of the SSH lattice to investigate a variety of behaviors, and the morphology imprinted on the mirror surface was documented through the use of an atomic force microscope, a technology first invented by IBM. Direct measurements of the energetic band structure — a characteristic of all crystal lattices — were made using optical spectroscopy techniques, with the light emitted by the SSH chain allowing researchers to infer the state of the corresponding polaritons.

One-dimensional SSH chains are an ideal testbed for such phenomena, as they are fundamental systems whose topological properties can be theoretically calculated. A comparison of these measurements with mathematical simulations showed strong agreement, validating both the nanofabrication of the SSH chain and the accuracy of the platform as an analog simulator.  

A recipe for polariton condensation in topological lattice states

Using this adaptable setup, the researchers achieved selective polariton condensation — a process where light-matter particles gather into specific energy states within the lattice. By adjusting the cavity length and the position of the optical excitation, the team could induce condensation into different states, either at the edges or at the center of the chain. This tunability acts like a control knob for the simulation: Researchers can “dial in” the behavior they want to study by modifying these parameters, producing a recipe for tunable condensation in topological lattices. The obtained condensates, each possessing their distinct wave function, are beautifully illustrated on the journal’s cover image.

The setup developed by the Exploratory Photonics group allows for an easy exploration of the system’s properties, showcasing far greater flexibility and novel possibilities than through lattice investigation in real crystals. In addition, the level of accuracy achieved paves the way for the simulation of more complex, two-dimensional systems. Under such conditions, edge conductivity could be further understood, and its robustness against disorder could be leveraged for designing improved materials.

Though such analog computing methods are yet far from complementing traditional computational systems, this work offers a fresh perspective on how novel approaches could support the exploration of novel materials. It is through highly exploratory research efforts such as this one that critical advances are achieved — and the future of technology is continuously shaped.