Quasi-bound states in the continuum (QBICs) are Fano resonant states with long optical lifetimes controlled by symmetry-breaking perturbations. While conventional Fano responses are limited to linear polarizations and do not support tailored phase control, here we introduce QBICs born of chiral perturbations that encode arbitrary elliptical polarization states and enable geometric phase engineering. We thereby design metasurfaces with ultrasharp spectral features that shape the impinging wave front with near-unity efficiency. Our findings extend Fano resonances beyond their conventional limits, opening opportunities for nanophotonics, classical and quantum optics, and acoustics.In solid state physics, giant magnetoresistance is the large change in electrical resistance due to an external magnetic field. Here we show that giant magnetoresistance is possible in a spin chain composed of weakly interacting layers of strongly coupled spins. This is found for all system sizes even down to a minimal system of four spins. The mechanism driving the effect is a mismatch in the energy spectrum resulting in spin excitations being reflected at the boundaries between layers. This mismatch, and thus the current, can be controlled by external magnetic fields resulting in giant magnetoresistance. A simple rule for determining the behavior of the spin transport under the influence of a magnetic field is presented based on the energy levels of the strongly coupled spins.We report on novel exciton-polariton routing devices created to study and purposely guide light-matter particles in their condensate phase. In a codirectional coupling device, two waveguides are connected by a partially etched section that facilitates tunable coupling of the adjacent channels. This evanescent coupling of the two macroscopic wave functions in each waveguide reveals itself in real space oscillations of the condensate. This Josephson-like oscillation has only been observed in coupled polariton traps so far. Here, we report on a similar coupling behavior in a controllable, propagative waveguide-based design. By controlling the gap width, channel length, or propagation energy, the exit port of the polariton flow can be chosen. This codirectional polariton device is a passive and scalable coupler element that can serve in compact, next generation logic architectures.We report the observation of low-energy, low-momenta collective oscillations of an exciton-polariton condensate in a round "box" trap. The oscillations are dominated by the dipole and breathing modes, and the ratio of the frequencies of the two modes is consistent with that of a weakly interacting two-dimensional trapped Bose gas. The speed of sound extracted from the dipole oscillation frequency is smaller than the Bogoliubov sound, which can be partly explained by the influence of the incoherent reservoir. These results pave the way for understanding the effects of reservoir, dissipation, energy relaxation, and finite temperature on the superfluid properties of exciton-polariton condensates and other two-dimensional open-dissipative quantum fluids.We discuss the counting of Nambu-Goldstone (NG) modes associated with the spontaneous breaking of higher-form global symmetries. Effective field theories of NG modes are developed based on symmetry-breaking patterns, using a generalized coset construction for higher-form symmetries. We derive a formula of the number of gapless NG modes, which involves expectation values of the commutators of conserved charges, possibly of different degrees.Force reconstruction in dynamic force microscopy (DFM) is a nontrivial problem that requires the deconvolution of integrals. However, conventional reconstruction methods, which recover forces from single-frequency motion of the cantilever at its resonance, exhibit non-negligible error and reconstruction instability in the highly nonlinear force regime when the tip oscillates with its amplitude comparable to the decay length of the interaction. Here, we develop a theoretical platform of DFM based on multiharmonic signal analysis for exact and robust reconstruction of conservative and dissipative forces, valid for all oscillation amplitudes and entire tip-sample distances in both amplitude- and frequency-modulation atomic force microscopy. We achieve accuracy improvement by an order of magnitude for oscillation amplitudes comparable to or larger than the decay length, and by 2 orders of magnitude for smaller amplitudes at the force minimum, even in cases where conventional methods show poor accuracy (≳5%). Moreover, we obtain greater robustness with respect to the oscillation amplitude error, resulting in a fivefold increase in reconstruction precision. Our results demonstrate a fast and versatile reconstruction scheme for nanomechanical force characterization, with higher harmonics measured with sufficient signal-to-noise ratio, which provides unprecedented accuracy and stability beyond conventional methods.Weakly interacting Fermi gases simulate spin lattices in energy space, offering a rich platform for investigating information spreading and spin coherence in a large many-body quantum system. We show that the collective spin vector can be determined as a function of energy from the measured spin density, enabling general energy-space resolved protocols. We measure an out-of-time-order correlation function in this system and observe the energy dependence of the many-body coherence.We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sublattices are suppressed in the nearly adiabatic regime exponentially. Thus, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.We propose a novel mechanism to test time variation of the propagation speed of gravitational waves (GWs) in light of GWs astronomy. JH-RE-06 As the stochastic GWs experience the whole history of cosmic expansion, they encode potential observational evidence of such variation. We report that, one feature of a varying GWs speed is that the energy spectrum of GWs will present resonantly enhanced peaks if the GWs speed oscillates in time at high-energy scales. Such oscillatory behavior arises in a wide class of modified gravity theories. The amplitude of these peaks can be at reach by current and forthcoming GWs instruments, hence making the underlying theories falsifiable. This mechanism reveals that probing the variation of GWs speed can be a promising way to search for new physics beyond general relativity.