# Emergent Quasicrystalline Symmetry in Light-Induced Quantum Phase Transitions

## TL;DR

This paper theoretically demonstrates how a nonequilibrium cavity-QED system can dynamically generate an emergent eight-fold symmetric quasicrystalline order in a quantum phase transition, without this symmetry being explicit in the system's Hamiltonian.

## Contribution

It reveals the emergence of quasicrystalline symmetry in a quantum phase transition driven by light scattering, a novel dynamical formation not explicitly encoded in the system's Hamiltonian.

## Key findings

- Quasicrystalline order emerges in the low-energy states during the phase transition.
- Strong interactions stabilize quasicrystalline order, while weak interactions lead to localization.
- The eight-fold symmetry appears solely in the low-energy states, not in the Hamiltonian.

## Abstract

The discovery of quasicrystals with crystallographically forbidden rotational symmetries has changed the notion of the ordering in materials, yet little is known about the dynamical emergence of such exotic forms of order. Here we theoretically study a nonequilibrium cavity-QED setup realizing a zero-temperature quantum phase transition from a homogeneous Bose-Einstein condensate to a quasicrystalline phase via collective superradiant light scattering. Across the superradiant phase transition, collective light scattering creates a dynamical, quasicrystalline optical potential for the atoms. Remarkably, the quasicrystalline potential is "emergent" as its eight-fold rotational symmetry is not present in the Hamiltonian of the system, rather appears solely in the low-energy states. For sufficiently strong two-body contact interactions between atoms, a quasicrystalline order is stabilized in the system, while for weakly interacting atoms the condensate is localized in one or few of the deepest minima of the quasicrystalline potential.