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.

We investigate the emission of a qubit weakly coupled to a one-band coupled-cavity array where, due to an engineered gradient in the cavity frequencies, photons are effectively accelerated by a synthetic force F. For strong F, a reversible emission described by an effective Jaynes-Cummings model occurs, causing a chiral time-periodic excitation of an extensive region of the array, either to the right or to the left of the qubit depending on its frequency. For weak values of F instead, a complex non-Markovian decay with revivals shows up. This is reminiscent of dynamics induced by mirrors in standard waveguides, despite the absence of actual mirrors, and can be attributed to the finite width of the energy band which confines the motion of the emitted photon. In a suitable regime, the decay is well described by a delay differential equation formally analogous to the one governing the decay of an atom in a multi-mode cavity where the cavity length and time taken by a photon to travel between the two mirrors are now embodied by the amplitude and period of Bloch oscillations, respectively.

Newton’s constant is the least well-measured among the fundamental constants of Nature, and, indeed, its accurate measurement has long served an experimental challenge. Levitated mechanical systems are attracting growing attention for their promising applications in sensing and as an experimental platform for exploring the intersection between quantum physics and gravitation. Here we propose a mechanical interferometric scheme of interacting levitated oscillators for the accurate estimation of Newton’s constant. Our scheme promises to beat the current standard by several orders of magnitude.

We investigate the entanglement properties in the symmetric subspace of N-partite d-dimensional systems (qudits). As it happens already for bipartite diagonal symmetric states, also in the multipartite case the local dimension d plays a crucial role. Here, we demonstrate that there is no bound entanglement for d = 3, 4 and N = 3. Using different techniques, we present strong analytical evidence that no bound entanglement exist for any N if d ≤ 4. Interestingly, bound entanglement of diagonal symmetric states exist for any number of parties, N ≥ 2, and local dimensions d ≥ 5.