Submitted by Dr Ulrich Schneider on Sat, 28/06/2025 - 11:09
Topology in condensed matter physics refers to global properties of a system’s quantum states that remain stable under continuous deformations, like stretching or bending — but not tearing. Unlike conventional phases of matter, topological phases are protected by more abstract, global properties, such as Chern numbers. These properties are immune to many forms of noise and disorder, making them especially appealing for robust quantum technologies such as error-protected quantum bits - the key building block for building scalable quantum computers.
In a topological charge pump, each slow cycle of an external field moves the same exact number of particles across the system — the number is perfectly constant over a wide range of different microscopic landscapes. Conventional wisdom attributes such precision to an energy gap separating occupied quantum states from empty states or to a mobility gap only protecting the occupation of delocalized states. Our work, however, shows that such gaps are not essential.
We focus on the one-dimensional Aubry-André–Harper lattice, whose incommensurate (quasiperiodic) modulation localizes single-particle states and sculpts the spectrum into a rigid, self-similar Hofstadter hierarchy. For this system, we find that quantization endures even after strong on-site disorder closes the mobility gap. Three ingredients enforce this robustness: (i) Anderson localization confines particles locally, (ii) the fractal set of mini-gaps constrains level crossings, and (iii) the drive rate can be chosen slow enough to suppress the few remaining long-range hops. Quantization is therefore protected by locality and quasiperiodicity rather than energetic isolation.
This dynamically protected channel can shuttle states of large Chern number without fine-tuning and relies only on on-site potentials and lattice phase modulation—ingredients already available in ultracold-atom lattices, photonic waveguides, and superconducting-qubit arrays—opening a new route (outlined in the paper) to robust state preparation and noise-resilient transport for quantum-information architectures.
Original article:
Quasiperiodicity protects quantized transport in disordered systems without gaps
Emmanuel Gottlob, Dan S. Borgnia, Robert-Jan Slager, Ulrich Schneider
PRX Quantum 6, 020359 (2025)