An international team of researchers reports on a new method that permits inducing symmetry-protected higher-order topology through a spontaneous symmetry-breaking mechanism in a two-dimensional system of ultra-cold bosonic atoms inside a cavity.
Symmetry-Protected Higher-Order Topology: Insights from Atom-Cavity Systems
Topology is a field of mathematics that studies the properties of geometric objects that are preserved under continuous deformations. In physics, topology provides a framework for understanding key properties of physical systems, which has led to the discovery of new materials with unique properties.
Atom-Cavity Dynamics: Breaking Symmetry, Unveiling Topology
Since discovering topological materials, researchers have focused on their unique non-local properties, making topology a central area in both fundamental and applied physics. In recent years, substantial progress has extended the existing paradigm of phases of matter to include the notion of topology and its relation to the underlying symmetries of quantum systems. This effort resulted in a thorough classification of non-interacting topological systems. Nevertheless, many examples of non-conventional topological phases still escape the current paradigm, presenting challenges and questions that demand new perspectives and solutions. These challenges include understanding the interplay of topology with interactions and studying higher-order topological insulators, which generalize the bulk-boundary correspondence. Currently, researchers propose and discover these phases in a wide range of systems, including electronic systems, photonics, and cold atoms in optical lattices, among others.
Peierls Transitions and Topological Phases: Atom-Cavity Experiments Explored
Quantum simulators made of cold atoms in optical lattices have not only been at the center of the study of topological materials because of their versatily, but are used to probe systems in which interactions between particles challenge the capabilities of available computational methods. In fact, the interplay between interactions and topology can result in interesting phenomena. For example, the combination of interaction-induced symmetry breaking and symmetry protection can give rise to delocalized fractional charges, absent in the non-interacting case. Cold atom experiments arise as perfect candidates to study interacting topological systems, but they still need to be benchmarked using advanced numerical methods.
Atom-cavity experimental setup: Ultracold bosonic atoms are trapped in the lowest band of a 2D optical lattice. The atoms couple to two cavity modes created by two optical cavities aligned in the x and y directions, and to a laser pump aligned in the z direction. In each direction, the chosen relative phase between the optical lattice and the cavity mode ensures that the nodes of the latter coincide with the sites of the lattice. In this configuration, the effective Hamiltonian describing the atom-cavity system includes correlated-tunneling terms, where atoms can tunnel between nearest neighbor sites by absorbing or emitting a photon from the cavity.
The recent study published in Physical Review Letters, ICFO researcher Joana Fraxanet, led by ICREA Prof. at ICFO Maciej Lewenstein, team member of Optologic project, in collaboration with Daniel Gonzalez-Cuadra from IQOQI, Alexandre Dauphin from PASQAL and Luca Barbiero from Politecnico de Torino, report on a readily available experimental protocol to induce symmetry-protected higher-order topology through a spontaneous symmetry-breaking mechanism in an atom-cavity system.
Adiabatic Preparation of Topological Phases: Atom-Cavity Protocol Revealed
In their study, the scientists used tensor-network-based numerical techniques to investigate a system of ultra-cold bosonic atoms coupled to two cavities. Firstly, trapping the atoms in the lowest energy band of an optical lattice, which counter-propagating laser beams generate, enhances the probability of photon-mediated interactions between the atoms by adding two optical cavities. Consequently, these interactions lead to effective infinite-range interactions. In the regimes of interest, these interactions subsequently induce a Peierls transition, which spontaneously breaks the translational symmetry of the system. As a result, the resulting pattern opens a topological gap, leading to a higher-order topological phase hosting corner states. Furthermore, the authors present a detailed protocol for the adiabatic preparation of this higher-order topological phase, which existing ultracold atom quantum simulators can readily implement, thereby opening the path toward realizing two-dimensional interaction-induced topological phases and observing Peierls transitions in dimensions larger than one.
Multimode Cavities and Topological Defects: Advancements in Atom-Photon Systems
Joana Fraxanet comments, “we would like to extend the setup to include multimode cavities, allowing us to generate atom-photon topological defects. These defects would generalize the topological solitons and fractionalized quasi-particles found in the Su-Schrieffer-Heeger model to two dimensions. Moreover, by exploring the regime of softcore bosons, we expect to find plaquette-ordered supersolid phases.” The results presented in this study represent a step forward in understanding interacting topological phenomena, which can have important applications in quantum information processing and the discovery of novel materials. Moreover, these results are relevant to a broad community of theoretical and experimental researchers working on topological matter, ultracold atoms experiments, quantum optics, and solid-state physics.
Reference article
Fraxanet, J., Dauphin, A., Lewenstein, M., Barbiero, L., González-Cuadra, D. (2023). Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System. Physical Review Letters, 131(26), 263001. https://doi.org/10.1103/PhysRevLett.131.263001
