We demonstrate the first experimental realization of a dispersionless state, in a photonic Lieb lattice formed by an array of optical waveguides. This engineered lattice supports three energy bands, including a perfectly flat middle band with an infinite effective mass. We analyze, both experimentally and theoretically, the evolution of well-prepared flat-band states, and show their remarkable robustness, even in the presence of disorder. The realization of flat-band states in photonic lattices opens an exciting door towards quantum simulation of flat-band models in a highly controllable environment.

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime.

Topological protection is a universal phenomenon that applies to electronic, photonic, ultracold atomic, mechanical, and other systems. The vast majority of research in these systems has explored the linear domain, where interparticle interactions are negligible. We experimentally observed solitons—waves that propagate without changing shape as a result of nonlinearity—in a photonic Floquet topological insulator. These solitons exhibited distinct behavior in that they executed cyclotron-like orbits associated with the underlying topology. Specifically, we used a waveguide array with periodic variations along the waveguide axis, giving rise to nonzero winding number, and the nonlinearity arose from the optical Kerr effect. This result applies to a range of bosonic systems because it is described by the focusing nonlinear Schrödinger equation (equivalently, the attractive Gross-Pitaevskii equation).

We report on the experimental realization of a uniform synthetic magnetic flux and the observation of Aharonov-Bohm cages in photonic lattices. Considering a rhombic array of optical waveguides, we engineer modulation-assisted tunneling processes that effectively produce nonzero magnetic flux per plaquette. This synthetic magnetic field for light can be tuned at will by varying the phase of the modulation. In the regime where half a flux quantum is realized in each plaquette, all the energy bands dramatically collapse into nondispersive (flat) bands and all eigenstates are completely localized. We demonstrate this Aharonov-Bohm caging by studying the propagation of light in the bulk of the photonic lattice. Besides, we explore the dynamics on the edge of the lattice and discuss how the corresponding edge states can be continuously connected to the topological edge states of the Creutz ladder. Our photonic lattice constitutes an appealing platform where the interplay between engineered gauge fields, frustration, localization, and topological properties can be finely studied.

We experimentally demonstrate the photonic realization of a dispersionless flat-band in a quasione-dimensional photonic lattice fabricated by ultrafast laser inscription. In the nearest neighbor tight binding approximation, the lattice supports two dispersive and a non-dispersive (flat) band. We experimentally excite superpositions of flat-band eigen modes at the input of the photonic lattice and show the diffractionless propagation of the input states due to their infinite effective mass. In the future, the use of photonic rhombic lattices, together with the successful implementation of a synthetic gauge field, will enable the observation of AharonovBohm photonic caging.Introduction The dynamics of electrons in a crystal reveals many interesting phenomena that depend on the lattice geometry, external fields, presence of disorders and inter-particle interactions. The propagation of light waves across a photonic lattice, a periodic array of coupled optical waveguides, mimics the time evolution of the electronic wavefunction in a periodic potential. Due to this mapping, the photonic analogue of various solidstate-phenomena [1][2][3][4][5] can be realized in the system of engineered waveguide-arrays. As with cold atoms in optical lattices [6][7][8], this artificial system allows us to engineer and access a desired Hamiltonian, and hence acts as a powerful platform for the study of various complex quantum mechanical effects in a clean environment. Indeed photonic lattices are ideal systems to study various effects in the absence of undesired excitations such as phonons in a real solid.

No abstract

We present measurements of the superBuid density and heat capacity of thin films of He adsorbed in aerogel glass. We find that the critical behavior of the super8uid density for films with transition temperatures between 50 mK and 1 K is similar to that seen for Alms adsorbed on Vycor. Power-law behavior is observed over at least one order of magnitude in reduced temperature with an exponent ( = 0.63 + 0.03. This exponent is much smaller than the value 0.811 + 0.004 found when the pores were filled with helium. We also find that the exponent is unchanged by the addition of small amounts of He. These results are consistent with the existence of a correlation length that diverges at the superfluid transition. Unlike for full-pore He aerogel, the correlation length is long compared with all structural length scales throughout the superQuid density power-law regime, thus leading to the more bulklike critical behavior. The heat capacity of He films in aerogel shows no singularity like that seen for full-pore He aerogel or for thin films adsorbed in Vycor. We show that this result is consistent with the predictions of hyperuniversality given the long correlation lengths implied by the super8uid density measurements.

Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological corner-localized modes of higher-order topological insulators can be symmetry protected bound states in the continuum; these states do not hybridize with the surrounding bulk states of the lattice even in the absence of a bulk bandgap. As such, this class of structures has potential applications in confining and controlling light in systems that do not support a complete photonic bandgap.