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 show that weak hopping disorder induces a delocalization of the lifted mode whereas the effective emitter-field coupling strength, and the associated mode volume experienced by the emitter, remains protected against structural fluctuations. We illustrate our approach using selected flat band lattices. Our findings provide a route to flat band state preparation via quench dynamics and robust cavity-QED control.
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 show that weak hopping disorder induces a delocalization of the lifted mode whereas the effective emitter-field coupling strength, and the associated mode volume experienced by the emitter, remains protected against structural fluctuations. We illustrate our approach using selected flat band lattices. Our findings provide a route to flat band state preparation via quench dynamics and robust cavity-QED control.
Abstract We investigate qubits coupled to the boundary of a two-dimensional photonic lattice that supports dispersionless edge modes—unlike conventional edge modes that sustain propagating photons. As a case study, we consider a honeycomb lattice ( photonic graphene ) of coupled resonators with a zigzag edge, where the edge modes form a flat band defined only over a restricted region of momentum space. We show that light–matter interactions are effectively captured by a dissipative cavity-QED model, wherein the emitter coherently couples to a localized mode emerging as a superposition of edge modes. This mode has support on only one sublattice and displays an unconventional power-law localization around the qubit—yet remaining normalizable in the thermodynamic limit—with a spatial range that can be tuned by introducing lattice anisotropy. We predict the occurrence of vacuum Rabi oscillations and state transfer between distant emitters. An experimental demonstration using superconducting circuits is proposed.
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.
Engineering the on-site frequencies of a photonic lattice provides a powerful route to endow emitted photons with non-trivial dynamical and topological properties, reshaping the way a coupled qubit decays. This thesis investigates the emission dynamics of a qubit weakly coupled to photonic lattices hosting such synthetic potentials, showing how the resulting band structure dictates qualitatively distinct regimes of light-matter interaction.In the first part, we study a qubit coupled to a one-dimensional coupled-cavity array with a linear gradient in the cavity frequencies, which acts on photons as a synthetic force F. For strong F, emission becomes reversible and is captured by an effective Jaynes--Cummings model, producing a chiral, time-periodic excitation of an extended region of the array, either to the right or to the left of the qubit depending on its frequency. For weak F, the decay is non-Markovian and exhibits revivals reminiscent of atoms between mirrors, even though no mirrors are present: the finite bandwidth confines the emitted photon, and the dynamics is well described by a delay differential equation in which the amplitude and period of Bloch oscillations play the role of cavity length and round-trip time.In the second part, we move to two dimensions and couple a giant atom, a qubit with multiple, spatially separated coupling points, non-locally to a honeycomb lattice of resonators with detuned sublattice frequencies. By suitably arranging the coupling points, the giant atom selectively addresses a single valley, a capability unattainable with a local emitter. This valley-selective coupling endows the emitted photons with an effective valley-polarized Berry curvature, giving rise to valley-polarized edge modes at domain walls between regions of opposite sublattice detuning. As a consequence, a giant atom placed near such a domain wall exhibits chiral emission of valley-polarized photons without breaking time-reversal symmetry, suggesting a natural implementation in circuit QED.Together, these results establish synthetic potentials in photonic lattices as a versatile tool for controlling qubit emission, linking waveguide QED to Bloch-oscillation physics and to valleytronics.
Circuit QED systems provide an ideal platform for exploring the strong-coupling regime of multimode cavity QED. Here we present two new phenomena from multimode strong coupling: a circuit Lagrangian analysis which captures beyond tight-binding effects of strong photon-photon coupling and experimental observation of strong wave-mixing resonances in the qubit response. Our circuit analysis reveals qualitatively new features such as emergent band gaps, lifted degeneracies, broadened flat bands, and frequency-dependent hopping. Within the multimode photon environment, strong qubit-photon coupling in turn gives rise to multiphoton processes involving multiple normal modes. We demonstrate a strong four-wave-mixing process involving excitation of a qubit and simultaneous frequency conversion between modes. Notably, this wave-mixing process is dominated by localized flat-band modes of the photonic lattice, which exhibit the strongest coupling to the transmon qubit.
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 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.
The concept of flat band plays an important role in strongly correlated many-body physics. However, the demonstration of the flat band physics is highly nontrivial due to intrinsic limitations in conventional condensed-matter materials. Here we propose a circuit quantum electrodynamics simulator of the two-dimensional (2D) Lieb lattice exhibiting a flat middle band. By exploiting the parametric conversion method, we design a photonic Lieb lattice with in situ tunable hopping strengths in a 2D array of coupled superconducting transmissionline resonators. Moreover, the flexibility of our proposal enables the incorporation of both the artificial gauge field and the strong photon-photon interaction in a time- and site-resolved manner. To unambiguously demonstrate the synthesized flat band, we further investigate the observation of the flat band localization of microwave photons through the pumping and the steady-state measurements of only a few sites on the lattice. Requiring only current level of technique and being robust against imperfections in realistic circuits, our scheme can be readily tested in experiment and may pave a new way towards the realization of exotic photonic quantum Hall fluids including anomalous quantum Hall effect and bosonic fractional quantum Hall effect without magnetic field.