Dipole-dipole interactions mediated by a photonic flat band

Enrico Di Benedetto; Alejandro Gonzalez-Tudela; Francesco Ciccarello

doi:10.22331/q-2025-03-25-1671

Dipole-dipole interactions mediated by a photonic flat band

Enrico Di Benedetto^1,4, Alejandro Gonzalez-Tudela², and Francesco Ciccarello^1,3,4

¹Università degli Studi di Palermo, Dipartimento di Fisica e Chimica-Emilio Segrè, Via Archirafi 36, 90123 Palermo (Italy)
²CSIC – Instituto de Fisica Fundamental, C. de Serrano 113, 28006 Madrid (Spain)
³NEST, Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, 56127 Pisa (Italy)
⁴Dipartimento di Fisica e Chimica-Emilio Segrè (UNIPA), Via Archirafi 36, 90123 Palermo (Italy)

Published:	2025-03-25, volume 9, page 1671
Editor:	Mark Mitchison
Eprint:	arXiv:2405.20382v4
Doi:	https://doi.org/10.22331/q-2025-03-25-1671
Citation:	Quantum 9, 1671 (2025).

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Updated after initial publication: This publication was updated to version v4 after the initial publication. The authors left the following comment on the arXiv:

18 pages, 6 figures

Abstract

Flat bands (FBs) are energy bands with zero group velocity, which in electronic systems were shown to favor strongly correlated phenomena. Indeed, a FB can be spanned with a basis of strictly localized states, the so called $\textit{compact localized states}$ (CLSs), which are yet generally non-orthogonal. Here, we study emergent dipole-dipole interactions between emitters dispersively coupled to the photonic analogue of a FB, a setup within reach in state-of the-art experimental platforms. We show that the strength of such photon-mediated interactions decays exponentially with distance with a characteristic localization length which, unlike typical behaviours with standard bands, saturates to a finite value as the emitter's energy approaches the FB. Remarkably, we find that the localization length grows with the overlap between CLSs according to an analytically-derived universal scaling law valid for a large class of FBs both in 1D and 2D. Using giant atoms (non-local atom-field coupling) allows to tailor interaction potentials having the same shape of a CLS or a superposition of a few of these.

Flat Bands are dispersionless energy bands, feature causing a quenching of kinetic energy, making such systems extremely sensitive to small perturbations and non-linearities. Here, we examine the case in which the non-linearity is introduced through the coupling of two-level emitters (almost) resonant to the Flat Band. We find several features depending heavily on the orthogonality of the Flat Band basis, such as the emergence of compact bound states. We show that these compact states can be used to induce effective spin-Hamiltonians with exact finite-ranged interactions. Furthermore, in the non-orthogonal case we are able to observe the emergence of an exotic new class of bound states which, although resulting from the coupling in the bandgap of dispersive energy bands, can be completely studied through the Flat Band projector only. The localization length of these states is frequency-independent and is related to the overlap between states in the Flat Band basis. Finally, we also show that it is possible to engineer any shape of the bound state by controlling the coupling of a giant atom to the system.

Flat bands (FBs) are band structures featuring zero-group velocity along the whole band, which in electronic systems have been shown to be source of strongly correlated phenomena. Here, we study the emergent photon-mediated interactions when emitter are tuned to the photonic analogue of FBs, a setup becoming within reach of state-of-art platforms In particular, we find that, unexpectedly, dispersive interactions between atoms are mediated by exponentially localized atom-photon bound states (BSs), whose range remains finite even for vanishing detuning from the FB. This represents a notable difference with respect to the cavity-QED case in which the presence of non-dispersive cavity modes does not lead to this kind of behaviour. We link this BS to a set of compact localized states (CLSs) spanning the FB eigenspace, which are generally non-orthogonal, and work out analytically the BS localization length as a function of the CLS non-orthogonality parameter for a large class of 1D and 2D lattices.

We also show that photon-mediated interactions can be tailored in an exact way if giant atoms are coupled to the system in the vicinity of a FB.

Featured image: Comparison between bound states in the quasi-1D sawtooth lattice. While bound states seeded by the dispersive band have a well-known dependency on the detuning between the qubit and the bandedge frequencies, bound states due to the flat band are insensitive to detuning, and they show a well-defined localization length that can be related to the overlap of the compact states spanning the flat band eigenspace.

Popular summary

Flat bands (FBs) can be understood in different ways. In a system of non-interacting particles, a flat band can be thought as the set of states associated to particles with a quenched kinetic energy. Another possible approach is seeing a flat band as an energy level with a massive degeneracy, infinite in the thermodynamic limit. Those two complementary features attracted the attention of scientists for two main reasons i.e., (1) the possibility to witness non-Markovian effects due to the quenching of kinetic energy and (2) the study of many-body phases of matter when particle-particle interactions or other non-linear elements are added to the system. Here, we study what happens upon coupling one or several qubits to such systems, showing the emergence of an atom-photon bound state seeded by the FB. This bound state is insensitive to the qubit's frequency and inherits the localization properties of the FB itself which, in this particular case, give rise to an exponential envelope with a localization length that depends on intrinsic features of the flat band. In particular, we show that this localization length can be related to the overlap between compact localised states, a core concept of the FB theory.

► BibTeX data

@article{DiBenedetto2025dipoledipole,
  doi = {10.22331/q-2025-03-25-1671},
  url = {https://doi.org/10.22331/q-2025-03-25-1671},
  title = {Dipole-dipole interactions mediated by a photonic flat band},
  author = {Di Benedetto, Enrico and Gonzalez-Tudela, Alejandro and Ciccarello, Francesco},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1671},
  month = mar,
  year = {2025}
}

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[1] Vincent Jouanny, Simone Frasca, Vera Jo Weibel, léo Peyruchat, Marco Scigliuzzo, Fabian Oppliger, Franco De Palma, Davide Sbroggiò, Guillaume Beaulieu, Oded Zilberberg, and Pasquale Scarlino, "High kinetic inductance cavity arrays for compact band engineering and topology-based disorder meters", Nature Communications 16 1, 3396 (2025).

[2] Jia-Qiang Chen, Peng-Bo Li, Álvaro Gómez-León, and Alejandro González-Tudela, "Photon-mediated interactions by Floquet photonic lattices", Physical Review A 112 5, 053710 (2025).

[3] Yu-Tong Wang, Qi-Hang Ye, Jun-Yong Yan, Yufei Qiao, Yu-Xin Liu, Yong-Zheng Ye, Chen Chen, Xiao-Tian Cheng, Chen-Hui Li, Zi-Jian Zhang, Cheng-Nian Huang, Yun Meng, Kai Zou, Wen-Kang Zhan, Chao Zhao, Xiaolong Hu, Clarence Augustine T. H. Tee, Wei E. I. Sha, Zhixiang Huang, Huiyun Liu, Chao-Yuan Jin, Lei Ying, and Feng Liu, "Moiré cavity quantum electrodynamics", Science Advances 11 21, eadv8115 (2025).

[4] Yeongjun Kim, Sergej Flach, and Alexei Andreanov, "Real-space decay of flat-band projectors from compact localized states", Physical Review B 113 23, 235110 (2026).

[5] Seokju Lee, Seung Hun Lee, and Bohm-Jung Yang, "Embedding Independent Length Scale of Flat Bands", Physical Review Letters 137 1, 016401 (2026).

[6] E. M. Broni, A. M. C. Souza, M. L. Lyra, F. A. B. F. de Moura, and G. M. A. Almeida, "Resonant cavity QED with chiral flat bands", Physical Review A 113 4, 043727 (2026).

[7] Kellen O'Brien, Maya Amouzegar, Won Chan Lee, Martin Ritter, and Alicia J. Kollár, "Circuit-QED Lattice System with Flexible Connectivity and Gapped Flat Bands for Photon-Mediated Spin Models", PRX Quantum 7 1, 010321 (2026).

[8] Rodrigo A. Vicencio, Fabiola G. L. Cárcamo-Macaya, Diego Román-Cortés, and Pablo Solano, "Observation of Non-Markovian Radiative Phenomena in Structured Photonic Lattices", Physical Review Letters 135 1, 013601 (2025).

[9] R.A. Silva, H.R. Publio, A.J.F. de Souza, G.M.A. Almeida, A.L.R. Barbosa, and F.A.B.F. de Moura, "Atomic decay in a coupled-cavity system with Gaussian-correlated hopping", Physics Letters A 560, 130953 (2025).

[10] Matija Tečer, Giuseppe Calajó, and Marco Di Liberto, "Flat-band-mediated photon-photon interactions in two-dimensional waveguide QED networks", Physical Review A 113 1, 013701 (2026).

[11] Zhiyong Liu, Yue Sun, and Ying Hu, "From flat to narrow bands: Engineering quantum emission in a one-dimensional Lieb lattice", Physical Review A 113 5, 053713 (2026).

[12] Mauro Cirio, Pengfei Liang, and Neill Lambert, "Input-output hierarchical equations of motion", Physical Review A 112 1, 012211 (2025).

[13] Tomonari Mizoguchi, Mina Maruyama, Yasuhiro Hatsugai, and Susumu Okada, "Evolution of flat bands in a two-dimensional fused pentagon network", Physical Review B 112 8, 085421 (2025).

[14] Ying Xia, Jia-Qi Li, and Xin Wang, "Selective band interaction and long-range hopping in a structured environment with giant atoms", Physical Review A 111 5, 053706 (2025).

[15] Yu-Tong Wang, Qi-Hang Ye, Jun-Yong Yan, Yufei Qiao, Chen Chen, Xiao-Tian Cheng, Chen-Hui Li, Zi-Jian Zhang, Cheng-Nian Huang, Yun Meng, Kai Zou, Wen-Kang Zhan, Chao Zhao, Xiaolong Hu, Clarence Augustine T H Tee, Wei E. I. Sha, Zhixiang Huang, Huiyun Liu, Chao-Yuan Jin, Lei Ying, and Feng Liu, "Cavity-Quantum Electrodynamics with Moiré Flatband Photonic Crystals", arXiv:2411.16830, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-10 16:21:39) and SAO/NASA ADS (last updated successfully 2026-08-10 16:21:41). The list may be incomplete as not all publishers provide suitable and complete citation data.

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