Quasicrystals, unique states of matter with ordered but non-repeating structures, have fascinated physicists for decades due to their unusual symmetries and patterns. Among them, quantum quasicrystals—made of bosons, particles that can occupy the same quantum state—have recently drawn significant attention.
Researchers at the Max Planck Institute for the Physics of Complex Systems (MPIPKS) have developed a new theoretical framework to describe the low-energy excitations in bosonic quantum quasicrystals. Their work, published in Physical Review Letters, extends traditional elasticity theories while accounting for the special symmetries of quantum quasicrystals.
"This project started as part of a collaboration with Prof. Francesco Piazza and Dr. Mariano Bonifacio during my time as a guest scientist at MPIPKS in Dresden," explained Alejandro Mendoza-Coto, first author of the study. "We realized that studying the low-energy excitations of these systems would be crucial for experimental verification of our theoretical predictions."
Previous studies suggested, based on symmetry arguments, that five gapless excitation modes should exist in these systems, but a detailed first-principles theory had been lacking. Initially attempting to study the excitation spectrum numerically, Mendoza-Coto and his colleagues shifted toward a theoretical approach when faced with technical challenges.
Drawing inspiration from earlier research on supersolids, the team realized that an accurate first-principles theory needed to include not only phase fluctuations of the modulated patterns and condensate but also the corresponding density fluctuations, each linked to its phase fluctuation field.
"The key insight was recognizing that both phase and conjugate density fluctuations must be included to properly capture the degrees of freedom and symmetries of the system," Mendoza-Coto said. "Once that framework was established, the calculations became straightforward and didn’t rely on additional assumptions."
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After successfully constructing the low-energy action for a dodecagonal (12-fold symmetric) quasicrystal, Piazza suggested extending the analysis to other quasicrystalline structures. This broader investigation revealed that different quasicrystals exhibit distinct mode hybridizations and anisotropic properties, an important finding of the study.
"Our results are somewhat the analog of the Bogoliubov excitation spectrum known for homogeneous condensates, but adapted to non-homogeneous, quasicrystalline phases," Mendoza-Coto noted. "Achieving closed analytical expressions for excitation energies at low momentum in quantum quasicrystals is significant, especially since such calculations are typically done numerically."
This new theoretical framework could guide future research into bosonic quantum quasicrystals, helping scientists understand their phase transitions and even offering insights into related exotic phases such as supersolids—states of matter that combine crystalline order with superfluidity.
"We hope this work will assist in the search for novel phases, such as super-hexatic or super-nematic phases," Mendoza-Coto added. "Several projects are already underway, including extending this theory to one-dimensional quasicrystals under cavity QED conditions and applying it to the study of supersolids."