Topological Effects in Bosonic Lattices

Project Information

TEBLA

Grant agreement ID: 101025211

DOI

10.3030/101025211

Project closed

EC signature date 11 March 2021

Start date 1 June 2021

End date 31 May 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 190 680,96

EU contribution

€ 190 680,96

Coordinated by

AALTO KORKEAKOULUSAATIO SR
Finland

Periodic Reporting for period 1 - TEBLA (Topological Effects in Bosonic Lattices)

Reporting period: 2021-06-01 to 2023-05-31

Summary of the context and overall objectives of the project

Topology is a branch of mathematics that investigates geometric shapes that withstand deformation, like a coffee mug that retains the hole in its handle no matter how you deform it. In the last few decades, topology has been explored in the physical properties of many quantum systems. The project studied emergent topological effects in bosonic lattices seeking to unveil novel lasing phenomena and topological fluids. Specifically, the research focussed on the exploration of topology and quantum geometry in the context of non-Hermitian bosonic systems.
The significance of this research lies in its potential impact on various technological and scientific domains. The comprehension and the control of topological nanoplasmonic lattice systems can lead to the development of highly efficient nanolasers and ultrasensitive sensors. Such advancements have far-reaching implications, revolutionizing fields such as communication or environmental monitoring. Furthermore, the exploration of topological phenomena in plasmonic lattices opens up the way for topological photonics, offering robust and efficient means of information transport and processing. Advancements in these areas hold the promise of improving the quality of life, driving economic growth, and promoting sustainable and innovative technologies.
The overall objectives of the project are twofold:
a) Investigate models of interacting bosons in a lattice with non-trivial quantum geometry.
b) Examine the effects of topology and quantum geometry on non-Hermitian bosonic systems, with a focus on their lasing properties.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The primary focus of this project was to explore the impact of topology and quantum geometry in diverse bosonic systems, including ultracold atoms in optical lattices and photonic systems. A Bose-Hubbard model was investigated in weakly interacting regimes, and Bose-Einstein condensates in flat band systems were analyzed using Bogoliubov theory, where mean-field interactions play a crucial role in dictating the condensate momentum, which can differ from non-flat band systems. The research demonstrated that the speed of sound and excitation fraction in flat band condensates are connected to orbital-independent generalization of the quantum metric, which reduces to the usual quantum metric (Fubini-Study metric) and the Hilbert-Schmidt quantum distance only in special cases. Further investigation focused on the superfluid properties of a many-body bosonic system in 1D, specifically a Bose-Hubbard model on a two-leg ladder (Creutz ladder) with two flat bands. The research provided insights into the different behaviors of the single-particle quantum metric (defined in momentum space) and the many-body quantum metric (defined in the twisted-boundary condition space) with regards to the Drude response. This work showed that the many-body quantum metric tends to decrease an upper bound of the superfluid weight, whereas prior studies associated the single-particle quantum metric with an increase in superfluid weight and extended our understanding of many-body topological and quantum geometrical effects in bosonic lattices.
In addition, the project applied topological and quantum geometrical concepts to a specific bosonic system, namely a lattice of nanoparticles arrays hosting plasmonic modes. In such plasmonic lattices, the project studied how topological modes known as bound states in the continuum (BICs) are affected by non-Hermitian losses and geometry of the system. Collaborating closely with experiments in my host institution, the research theoretically predicted and experimentally demonstrated a lasing mode topological transition with various topological charges, emphasizing the significance of light polarization winding in plasmonic modes.
The project's results were effectively disseminated through a diverse array of channels, reaching both the scientific community and the general public. These dissemination efforts included presentations at conferences, seminars, and the publication of scientific papers. Notably, the research yielded successful publications in peer-reviewed journals during the project, with additional preprints submitted for peer review, showcasing the wide reach of the research findings. Moreover, the researcher actively engaged in outreach activities to popularize their work on topological matter. Through talks, posters, and seminars, they fostered scientific exchange and promoted awareness and understanding of their research in topological matter, both within the scientific community and among the broader public. These efforts not only contributed to the advancement of scientific knowledge but also played a crucial role in disseminating important scientific insights to a wider audience.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The project has made progress beyond the state of the art in several areas related to quantum geometry and topology in bosonic systems. By studying the effect of quantum geometry on various bosonic systems, including ultracold atoms in optical lattices and plasmonic systems, the research has explored novel phenomena that were previously not fully understood. The identification and analysis of a topological transition in the lasing from bound states in the continuum (BICs) affected by non-Hermitian losses in nanoplasmonic lattice systems represents an advancement in the field. These BICs have practical implications in the development of novel nanophotonic devices, such as highly efficient nanolasers and ultra-sensitive sensors.
The project's investigation into the superfluid properties of a many-body bosonic system in 1D, specifically a Bose-Hubbard model on a two-leg ladder known as the Creutz ladder with two flat bands, represents progress beyond the state of the art in the field of the quantum geometry in bosonic lattices. The state-of-the-art had mainly focused so far on the single-particle quantum metric, defined in momentum space from Bloch sates, and had associated the effect of the single-particle quantum metric with an increase in superfluid weight. This project revealed the remarkable significance of the many-body quantum metric, which is defined in the parameter space of the twist boundary conditions, that was not previously understood. The many-body quantum metric of the system’s Hamiltonian tends to decrease an upper bound of the superfluid weight.
Further research will continue to explore and understand topological phenomena and quantum geometrical effects in bosonic lattices. The potential impacts of the project extend beyond the scientific community. The discoveries made in this research could have practical implications in the design of new nanophotonic devices, which have the potential to revolutionize fields such as communication and monitoring. The development of highly efficient nanolasers and ultra-sensitive sensors has significant socio-economic implications, leading to technological advancements and potential economic growth, while the insights gained through this research can have wider societal implications by contributing to fundamental research in condensed matter physics and nanophotonics.

A topological transition in lasing from nanophotonic lattices