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(a) Structure of the 1D Kagomè model, featuring five sublattices with hopping rates ±J. A possible choice of CLS is higlighted in green. (b) Energy spectrum featuring four dispersive bands and a FB of energy ω FB = 2J. The FB touches the upper edge of one of the dispersive bands. (c) Bound state seeded by an atom in the dispersive regime δ FB ≫ g with δ FB = ω0 − 2J the detuning from the FB, which we report in the legend (we show only the BS wavefunction on sublattice a). We consider 100 cells with the emitter coupled to cavity a50. In contrast e.g. to the case in Fig. 1 (f)-(h), the localization length here does depend on δ FB (which is due to the band touching as explained later on in Section 6).
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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 compact localized states (CLSs), which are yet generally non-orthogonal. Here, we study emergent dipole-dipole interactions be...
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... order to make the reader familiarize with CLSs and their properties (especially non-orthogonality), we present next some examples of lattices exhibiting FBs [see Fig. 2 and Fig. 3]. In this section, we will only discuss 1D models, meaning that here the cell index n is an integer and the wavevector k a real number (see Appendix A for more details on those ...
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... 1D Kagomè model sketched in Fig. 3(a) is a lattice with five sublattices, representing the 1D version of the popular 2D Kagomè model [72]. In this model each cavity is coupled to its nearest neighbour with rate −J, except for pairs (a n , b n ) and (d n , e n ) which are coupled with rate J. This system differs from the previous instances in that there exists a FB (of ...
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... the 1D version of the popular 2D Kagomè model [72]. In this model each cavity is coupled to its nearest neighbour with rate −J, except for pairs (a n , b n ) and (d n , e n ) which are coupled with rate J. This system differs from the previous instances in that there exists a FB (of frequency 2J) which touches the edge of a dispersive band [see Fig. ...
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... from all the remaining bands [recall Eq. (26) where only the contribution of the FB is retained]. This rules out in particular those lattices where a FB arises on the edge of a dispersive band. In 1D, such band touching happens for example in the stub lattice for ∆ = 0 (see Section 4.2.3 and Fig. 2) and in the Kagomè model (see Section A.4 and Fig. 3). Indeed, it turns out that in this case, an atom dispersively coupled to the FB seeds a BS with features analogous to typical BSs close to the band edge of an isolated dispersive band [e.g. as in Fig. 1 (c)-(e)]. This is witnessed by Fig. 3(c) for the Kagomè model, which shows that the BS localization length gets larger and larger as ...
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... in the stub lattice for ∆ = 0 (see Section 4.2.3 and Fig. 2) and in the Kagomè model (see Section A.4 and Fig. 3). Indeed, it turns out that in this case, an atom dispersively coupled to the FB seeds a BS with features analogous to typical BSs close to the band edge of an isolated dispersive band [e.g. as in Fig. 1 (c)-(e)]. This is witnessed by Fig. 3(c) for the Kagomè model, which shows that the BS localization length gets larger and larger as the detuning from the FB decreases in contrast to the saturation behavior next to an isolated FB that occurs e.g. in Fig. 1 (f)-(h). Notice that in these 1D examples the dispersive band scales quadratically in the vicinity of the ...
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... five-partite lattice represents a sort of 1D counterpart of the Kagomè model [67], where the Hamiltonian parameters and sublattice indexes are defined in Fig. 3(c). The Bloch Hamiltonian H k is calculated as the 5 × 5 matrix given ...
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... number Figure 7: Population of the atom-photon bound state on sublattice a of the lattice in Fig. 3(d) of Ref. [67] (the behavior is similar on other sublattices). There is a good agreement between the BS as obtained from exact diagonalization (blue line) and the one predicted by our theory (orange ...
Citations
... In particular, when the atomic frequency falls within a photonic bandgap, it becomes possible to induce coherent atom-atom interactions with tunable ranges [48][49][50][51]. Further control over these interactions can be achieved by coupling the atoms to topological photonic lattices [52][53][54][55] or photonic flat bands [56][57][58]. A fundamentally different approach to engineering coherent and dissipative interaction properties involves leveraging the collective emission of ordered atomic arrays coupled to propagating photons. ...
We investigate a Lieb lattice of quantum emitters coupled to a two-dimensional waveguide network and demonstrate that this system supports an energetically isolated flat band, enabling localization despite the presence of long-range photon-mediated couplings. We then explore the two-excitation dynamics in both the softcore and hardcore interaction regimes, which arise from the nonlinearity of the emitters. In the softcore regime, we observe interaction-induced photon transport within the flat band, mediated by the formation of bound photon pairs. In the hardcore regime, corresponding to the two-level atom limit, we instead find the emergence of metastable exciton-like dressed states involving both flat and dispersive bands. Our findings highlight how the interplay between the collective behavior of emitters and effective photon-photon interactions can provide a platform for studying highly correlated photonic states in flat-band systems.
... Inspired by recent developments in photonic crystals [26][27][28][29][30], there has been growing interest in the role of flat bands in enhancing light-matter interactions [29][30][31][32][33]. The associated large DOS with zero bandwidth make flat bands functionally analogous to high-Q cavities with effectively small mode volumes. ...
... large tolerance to the atom's position. Within this context, the study in Ref. [33] characterizes atom-photon bound states arising when an emitter is dispersively coupled to a flat-band. As the detuning decreases, the localization length saturates to a level depending on the overlap between CLSs belonging to classes U > 1. ...
... Hence, | ψ⟩ assumes its form. We note that our findings are consistent with those of Ref. [33], valid for the offresonant coupling regime. In the examples that follow, we see that the spatial profile of | ψ⟩ reflects the lattice's inability to host U = 1 CLSs, the influence of Anderson localization, and the flat-band support on x 0 . ...
Flat bands exhibit high degeneracy and intrinsic localization, offering a promising platform for enhanced light-matter interactions. Here, we investigate the resonant interaction between a two-level emitter and a chiral flat band hosted by a photonic lattice. In the weak coupling regime, the emitter undergoes Rabi oscillations with a lifted photonic mode whose spatial structure reflects the nature of compact localized states and the onset of Anderson localization. We illustrate our approach using selected chiral quasi-1D lattices. Our findings provide a route to flat band state preparation via quench dynamics while preserving the structure of the flat band.
... In the simplest case, a singlemode cavity mediates an all-to-all interaction between qubits, leading to trivial connectivity. An interaction that generates a spin model with non-trivial connectivity requires the presence of multiple modes in a bandwidth set by the qubit-photon interaction strength [5][6][7][8]. In such cases, the dispersion relation and spatial profiles of the photon modes determine the interaction profile. ...
... The combination of the oscillatory photonic wave functions and the triangular plaquettes of the lattice can lead to a short-range frustrated magnetic interaction. Similar results have been shown theoretically for 1D sawtooth lattice [8], but CPW lattices provide a route to extending this type of behavior to 2D and non-Euclidean cases. ...
Quantum spin models are ubiquitous in solid-state physics, but classical simulation of them remains extremely challenging. Experimental testbed systems with a variety of spin-spin interactions and measurement channels are therefore needed. One promising potential route to such testbeds is provided by microwave-photon-mediated interactions between superconducting qubits, where native strong light-matter coupling enables significant interactions even for virtual-photon-mediated processes. In this approach, the spin-model connectivity is set by the photonic mode structure, rather than the spatial structure of the qubit. Lattices of coplanar-waveguide (CPW) resonators have been demonstrated to allow extremely flexible connectivities and can therefore host a huge variety of photon-mediated spin models. However, large-scale CPW lattices have never before been successfully combined with superconducting qubits. Here we present the first such device featuring a quasi-1D CPW lattice with a non-trivial band structure and multiple transmon qubits. We demonstrate that superconducting-qubit readout and diagnostic techniques can be generalized to this highly multimode environment and observe the effective qubit-qubit interaction mediated by the bands of the resonator lattice. This device completes the toolkit needed to realize CPW lattices with qubits in one or two Euclidean dimensions, or negatively-curved hyperbolic space, and paves the way to driven-dissipative spin models with a large variety of connectivities.
... Waveguide quantum electrodynamics (QED) [1,2] has emerged as a powerful paradigm for engineering lightmatter interactions, where emitters coupled to confined photonic modes exhibit collective phenomena like superradiance [3][4][5][6], subradiance [7], and photon-mediated spin models [8][9][10][11][12][13][14][15][16]. In traditional setups, the photonic bath is assumed to be non-interacting, enabling exact solutions. ...
Waveguide quantum electrodynamics (QED) studies the interaction between quantum emitters and guided photons in one-dimension. When the waveguide hosts interacting photons, it becomes a platform to explore many-body quantum optics. However, the influence of photonic correlations on emitter dynamics remains poorly understood. In this work, we study the collective decay and coherent interactions of quantum emitters coupled to a one-dimensional Bose-Hubbard waveguide, an array of coupled photonic modes with repulsive on-site interactions that supports superfluid and Mott insulating phases. We show that photon-photon interactions alone can trigger a superradiant burst, independent of emitter spacing and transition frequency. In the off-resonant regime, emitters exhibit two distinct types of mediated interactions: delocalized superfluid excitations yield distance-independent couplings, while Mott-insulator quasiparticles generate short-range interactions mediated by doublons and holons. Our work bridges many-body physics and waveguide QED, revealing how photonic many-body states shape emitter dynamics.
... We aim to leverage nonlinearities in CCAs to investigate drivendissipative phase transition 69,71,72 . Moreover, these lattices facilitate the creation of unique devices capable of hosting photons in curved spaces 19 , gapped flat band 73,74 , and enable alternative forms of qubitqubit interaction 20,75 . The high-impedance, ultracompact nature of our platform enables the realization of dense, multimode environments 7,8,41 , providing a pathway to study quantum many-body phenomena with a high degree of control. ...
Superconducting microwave metamaterials offer enormous potential for quantum optics and information science, enabling the development of advanced quantum technologies for sensing and amplification. In the context of circuit quantum electrodynamics, such metamaterials can be implemented as coupled cavity arrays (CCAs). In the continuous effort to miniaturize quantum devices for increasing scalability, minimizing the footprint of CCAs while preserving low disorder becomes paramount. In this work, we present a compact CCA architecture using superconducting NbN thin films manifesting high kinetic inductance. The latter enables high-impedance CCA (~1.5 kΩ), while reducing the resonator footprint. We demonstrate its versatility and scalability by engineering one-dimensional CCAs with up to 100 resonators and with structures that exhibit multiple bandgaps. Additionally, we quantitatively investigate disorder in the CCAs using symmetry-protected topological SSH edge modes, from which we extract a resonator frequency scattering of 0.2 2 − 0.03 + 0.04 % . Our platform opens up exciting prospects for analog quantum simulations of many-body physics with ultrastrongly coupled emitters.
Quantum emitters are a key component in photonic quantum technologies. Enhancing single-photon emissionby engineering their photonic environment is essential for improving overall efficiency in quantum informationprocessing. However, this enhancement is often limited by the need for ultraprecise emitter placement withinconventional photonic cavities. Inspired by the fascinating physics of moiré pattern, we propose a multilayermoiré photonic crystal with a robust isolated flatband. Theoretical analysis reveals that, with nearly infinite pho-tonic density of states, the moiré cavity simultaneously has a high Purcell factor and large tolerance over theemitter’s position, breaking the constraints of conventional cavities. We then experimentally demonstrate vari-ous cavity quantum electrodynamic phenomena with a quantum dot in moiré cavity. A large tuning range (upto 40-fold) of quantum dot’s radiative lifetime is achieved through strong Purcell enhancement and inhibitioneffects. Our findings open the door for moiré flatband cavity–enhanced quantum light sources and quantumnodes for the quantum internet.
