Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices

Accessing Beyond-Light Line Dispersion and High-Q Resonances of Dense Plasmon Lattices by Bandfolding

Dense plasmon lattices are promising as experimentally accessible implementations of seminal tight-binding Hamiltonians, but the plasmonic dispersion of interest lies far beyond the light line and is thereby inaccessible in far-field optical experiments. In this work, we make the guided mode dispersion of dense hexagonal plasmon antenna lattices visible by bandfolding induced by perturbative scatterer size modulations that introduce supercell periodicity. We present fluorescence enhancement experiments and reciprocity-based T-matrix simulations for a systematic variation of perturbation strength. We evidence that folding the K-point into the light cone gives rise to a narrow plasmon mode, achieving among the highest reported quality factors for plasmon lattice resonances in the visible wavelength range despite a doubled areal density of plasmon antennas. We finally show K-point lasing and spontaneous symmetry breaking between the bandfolded K- and K'-modes, signifying that intrinsic symmetry properties of the dense plasmon lattice are maintained and can be observed upon band folding.

Landau Rainbow Induced by Artificial Gauge Fields

The ability to generate Landau levels using a pseudomagnetic field (PMF), also called an artificial gauge field, opens up new pathways for exploring fundamental physics and developing novel applications based on topological protection. In this Letter, we simultaneously realize a PMF and a pseudoelectric field (PEF) on a photonic crystal platform and observe a rainbow effect of the Landau zeroth modes. While a PMF induces a series of discretized Landau levels of photons in a similar way as the quantum Hall effect for electrons, a PEF breaks the degeneracy of the flat band of Landau levels over a broad range. Thus, different frequencies of the Landau modes can be dispersed into different spatial positions, leading us to term this phenomenon the "Landau rainbow." The Landau rainbow, induced by the joint action of PMFs and PEFs, features robustness, broadband capability, and scalability, and may find applications in areas such as slow-light effect, multifrequency divider, and optical information multiplexing.

Phonon Landau Quantization and Enhanced Lifetime in Deformed Graphene

The pseudomagnetic field effect may offer unique opportunities for the emergence of intriguing phenomena. To date, investigations into pseudomagnetic field effects on phonons have been limited to sound waves in metamaterials. The revelation of this exotic effect on the atomic vibration of natural materials remains elusive. Our simulations of twisted graphene nanoribbons reveal well-defined Landau spectra and sublattice polarization of phonon states, mimicking the behavior of Dirac Fermions in magnetic fields. Both valley-specified helical edge currents and snake orbits are obtained. Analysis of dynamics indicates that phonon Landau states have extended lifetimes, which are crucial for the realization of Landau-level lasing. Our findings demonstrate the occurrence of the phonon pseudomagnetic field effect in natural materials, which has important implications for the mechanical tuning of phonon quantum states at the atomic scale.

Photonic Dirac waveguide in inhomogeneous spoof surface plasmonic metasurfaces

The metamaterial with artificial synthetic gauge field has been proved as an excellent platform to manipulate the transport of the electromagnetic wave. Here we propose an inhomogeneous spoof surface plasmonic metasurface to construct an in-plane pseudo-magnetic field, which is generated by engineering the gradient variation of the opened Dirac cone corresponding to spatially varying mass term. The chiral zeroth-order Landau level is induced by the strong pseudo-magnetic field. Based on the bulk state propagation of the chiral Landau level, the photonic Dirac waveguide is designed and demonstrated in the experimental measurement, in which the unidirectionally guided electromagnetic mode supports the high-capacity of energy transport. Without breaking the time-reversal symmetry, our proposal structure paves a new way for realizing the artificial in-plane magnetic field and photonic Dirac waveguide in metamaterial, and have potential for designing integrated photonic devices in practical applications.

Polaritonic states trapped by topological defects

The miniaturization of photonic technologies calls for a deliberate integration of diverse materials to enable novel functionalities in chip-scale devices. Topological photonic systems are a promising platform to couple structured light with solid-state matter excitations and establish robust forms of 1D polaritonic transport. Here, we demonstrate a mechanism to efficiently trap mid-IR structured phonon-polaritons in topological defects of a metasurface integrated with hexagonal boron nitride (hBN). These defects, created by stitching displaced domains of a Kekulé-patterned metasurface, sustain localized polaritonic modes that originate from coupling of electromagnetic fields with hBN lattice vibrations. These 0D higher-order topological modes, comprising phononic and photonic components with chiral polarization, are imaged in real- and Fourier-space. The results reveal a singular radiation leakage profile and selective excitation through spin-polarized edge waves at heterogeneous topological interfaces. This offers impactful opportunities to control light-matter waves in their dimensional hierarchy, paving the way for topological polariton shaping, ultrathin structured light sources, and thermal management at the nanoscale.

Pseudomagnetic suppression of non-Hermitian skin effect

It has recently been shown that the non-Hermitian skin effect can be suppressed by magnetic fields. In this work, using a two-dimensional tight-binding lattice, we demonstrate that a pseudomagnetic field can also lead to the suppression of the non-Hermitian skin effect. With an increasing pseudomagnetic field, the skin modes are found to be pushed into the bulk, accompanied by the reduction of skin topological area and the restoration of Landau level energies. Our results provide a time-reversal invariant route to localization control and could be useful in various classical wave devices that are able to host the non-Hermitian skin effect but inert to magnetic fields.

Surface potential-adjusted surface states in 3D topological photonic crystals

Surface potential in a topological matter could unprecedentedly localize the waves. However, this surface potential is yet to be exploited in topological photonic systems. Here, we demonstrate that photonic surface states can be induced and controlled by the surface potential in a dielectric double gyroid (DG) photonic crystal. The basis translation in a unit cell enables tuning of the surface potential, which in turn regulates the degree of wave localization. The gradual modulation of DG photonic crystals enables the generation of a pseudomagnetic field. Overall, this study shows the interplay between surface potential and pseudomagnetic field regarding the surface states. The physical consequences outlined herein not only widen the scope of surface states in 3D photonic crystals but also highlight the importance of surface treatments in a photonic system.

Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal

When electrons moving in two dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels (LLs). LLs can also arise from pseudomagnetic fields (PMFs) induced by lattice distortions. In three-dimensional (3D) systems, there has been no experimental demonstration of LLs  as a type of flat band thus far. Here, we report the experimental realization of a flat 3D LL in an acoustic crystal. Starting from a lattice whose bandstructure exhibits a nodal ring, we design an inhomogeneous distortion corresponding to a specific pseudomagnetic vector potential (PVP). This distortion causes the nodal ring states to break up into LLs, including a zeroth LL that is flat along all three directions. These findings suggest the possibility of using nodal ring materials to generate 3D flat bands, allowing access to strong interactions and other attractive physical regimes in 3D.

Realization of all-band-flat photonic lattices

Flatbands play an important role in correlated quantum matter and have promising applications in photonic lattices. Synthetic magnetic fields and destructive interference in lattices are traditionally used to obtain flatbands. However, such methods can only obtain a few flatbands with most bands remaining dispersive. Here we realize all-band-flat photonic lattices of an arbitrary size by precisely controlling the coupling strengths between lattice sites to mimic those in Fock-state lattices. This allows us to go beyond the perturbative regime of strain engineering and group all eigenmodes in flatbands, which simultaneously achieves high band flatness and large usable bandwidth. We map out the distribution of each flatband in the lattices and selectively excite the eigenmodes with different chiralities. Our method paves a way in controlling band structure and topology of photonic lattices.

Photonic Realization of a Generic Type of Graphene Edge States Exhibiting Topological Flat Band

Cutting a honeycomb lattice (HCL) ends up with three types of edges (zigzag, bearded, and armchair), as is well known in the study of graphene edge states. Here, we propose and demonstrate a distinctive twig-shaped edge, thereby observing new edge states using a photonic platform. Our main findings are (i) the twig edge is a generic type of HCL edge complementary to the armchair edge, formed by choosing the right primitive cell rather than simple lattice cutting or Klein edge modification; (ii) the twig edge states form a complete flat band across the Brillouin zone with zero-energy degeneracy, characterized by nontrivial topological winding of the lattice Hamiltonian; (iii) the twig edge states can be elongated or compactly localized at the boundary, manifesting both flat band and topological features. Although realized here in a photonic graphene, such twig edge states should exist in other synthetic HCL structures. Moreover, our results may broaden the understanding of graphene edge states, as well as new avenues for realization of robust edge localization and nontrivial topological phases based on Dirac-like materials.

Experimental realization of chiral Landau levels in two-dimensional Dirac cone systems with inhomogeneous effective mass

Chiral zeroth Landau levels are topologically protected bulk states. In particle physics and condensed matter physics, the chiral zeroth Landau level plays a significant role in breaking chiral symmetry and gives rise to the chiral anomaly. Previous experimental works on such chiral Landau levels are mainly based on three-dimensional Weyl degeneracies coupled with axial magnetic fields. Their realizations using two-dimensional Dirac point systems, being more promising for future applications, were never experimentally realized before. Here we propose an experimental scheme for realizing chiral Landau levels in a two-dimensional photonic system. By introducing an inhomogeneous effective mass through breaking local parity-inversion symmetries, a synthetic in-plane magnetic field is generated and coupled with the Dirac quasi-particles. Consequently, the zeroth-order chiral Landau levels can be induced, and the one-way propagation characteristics are experimentally observed. In addition, the robust transport of the chiral zeroth mode against defects in the system is also experimentally tested. Our system provides a new pathway for the realization of chiral Landau levels in two-dimensional Dirac cone systems, and may potentially be applied in device designs utilizing the chiral response and transport robustness.

Antichiral surface states in time-reversal-invariant photonic semimetals

Besides chiral edge states, the hallmark of quantum Hall insulators, antichiral edge states can exhibit unidirectional transport behavior but in topological semimetals. Although such edge states provide more flexibility for molding the flow of light, their realization usually suffers from time-reversal breaking. In this study, we propose the realization of antichiral surface states in a time-reversal-invariant manner and demonstrate our idea with a three-dimensional (3D) photonic metacrystal. Our system is a photonic semimetal possessing two asymmetrically dispersed Dirac nodal lines. Via dimension reduction, the nodal lines are rendered a pair of offset Dirac points. By introducing synthetic gauge flux, each two-dimensional (2D) subsystem with nonzero k_z is analogous to a modified Haldane model, yielding a k_z-dependent antichiral surface transport. Through microwave experiments, the bulk dispersion with asymmetric nodal lines and associated twisted ribbon surface states are demonstrated in our 3D time-reversal-invariant system. Although our idea is demonstrated in a photonic system, we propose a general approach to realize antichiral edge states in time-reversal-invariant systems. This approach can be easily extended to systems beyond photonics and may pave the way for further applications of antichiral transport.

Observing the quantum topology of light

Topological photonics provides a powerful platform to explore topological physics beyond traditional electronic materials and shows promising applications in light transport and lasers. Classical degrees of freedom are routinely used to construct topological light modes in real or synthetic dimensions. Beyond the classical topology, the inherent quantum nature of light provides a wealth of fundamentally distinct topological states. Here we implement experiments on topological states of quantized light in a superconducting circuit, with which one- and two-dimensional Fock-state lattices are constructed. We realize rich topological physics including topological zero-energy states of the Su-Schrieffer-Heeger model, strain-induced pseudo-Landau levels, valley Hall effect, and Haldane chiral edge currents. Our study extends the topological states of light to the quantum regime, bridging topological phases of condensed-matter physics with circuit quantum electrodynamics, and offers a freedom in controlling the quantum states of multiple resonators.

Inhibition and Reconstruction of Zener Tunneling in Photonic Honeycomb Lattices

Quantum coherence is the central element of particle states, and it characterizes the overall performance of various quantum materials. Bloch oscillation is a fundamental coherent behavior of particles under a static potential, which can be easily destroyed by Zener tunneling in multiband 2D lattice materials. The control of Zener tunneling therefore plays the key role in quantum engineering for complicated physical systems. Here, the inhibition and reconstruction of Zener tunneling in photonic honeycomb lattices are experimentally demonstrated.  Deformed honeycomb lattices are integrated and an effective static potential is realized on the 2D lattice materials. Zener tunneling disappears in stretch-type lattices and wave packets stay in the dispersionless upper energy band. On the contrary, Zener tunneling is greatly enhanced in compression-type lattices and wave packets exhibit directional oscillations without branches, which manifest the preserved coherence of the wave packets. The results demonstrate the protection of photonic coherence by structurally controlling the Zener tunneling, representing a step toward flexible quantum engineering for large-scale artificial quantum materials.

Pattern-tunable synthetic gauge fields in topological photonic graphene

We propose a straightforward and effective approach to design, by pattern-tunable strain-engineering, photonic topological insulators supporting high quality factors edge states. Chiral strain-engineering creates opposite synthetic gauge fields in two domains resulting in Landau levels with the same energy spacing but different topological numbers. The boundary of the two topological domains hosts robust time-reversal and spin-momentum-locked edge states, exhibiting high quality factors due to continuous strain modulation. By shaping the synthetic gauge field, we obtain remarkable field confinement and tunability, with the strain strongly affecting the degree of localization of the edge states. Notably, the two-domain design stabilizes the strain-induced topological edge state. The large potential bandwidth of the strain-engineering and the opportunity to induce the mechanical stress at the fabrication stage enables large scalability for many potential applications in photonics, such as tunable microcavities, new lasers, and information processing devices, including the quantum regime.

Strain induced localization to delocalization transition on a Lieb photonic ribbon lattice

Ribbon lattices are kind of transition systems in between one and two dimensions, and their study is crucial to understand the origin of different emerging properties. In this work, we study a Lieb ribbon lattice and the localization-delocalization transition occurring due to a reduction of lattice distances (compression) and the corresponding flat band deformation. We observe how above a critical compression ratio the energy spreads out and propagates freely across the lattice, therefore transforming the system from being a kind of insulator into a conductor. We implement an experiment on a photonic platform and show an excellent agreement with the predicted phenomenology. Our findings suggest and prove experimentally the use of compression or mechanical deformation of lattices to switch the transport properties of a given system.

Modified Bose-Einstein condensation in an optical quantum gas

Open quantum systems can be systematically controlled by making changes to their environment. A well-known example is the spontaneous radiative decay of an electronically excited emitter, such as an atom or a molecule, which is significantly influenced by the feedback from the emitter's environment, for example, by the presence of reflecting surfaces. A prerequisite for a deliberate control of an open quantum system is to reveal the physical mechanisms that determine its state. Here, we investigate the Bose-Einstein condensation of a photonic Bose gas in an environment with controlled dissipation and feedback. Our measurements offer a highly systematic picture of Bose-Einstein condensation under non-equilibrium conditions. We show that by adjusting their frequency Bose-Einstein condensates naturally try to avoid particle loss and destructive interference in their environment. In this way our experiments reveal physical mechanisms involved in the formation of a Bose-Einstein condensate, which typically remain hidden when the system is close to thermal equilibrium.

Observation of supersymmetric pseudo-Landau levels in strained microwave graphene

Using an array of coupled microwave resonators arranged in a deformed honeycomb lattice, we experimentally observe the formation of pseudo-Landau levels in the whole crossover from vanishing to large pseudomagnetic field strengths. This result is achieved by utilising an adaptable setup in a geometry that is compatible with the pseudo-Landau levels at all field strengths. The adopted approach enables us to observe the fully formed flat-band pseudo-Landau levels spectrally as sharp peaks in the photonic density of states and image the associated wavefunctions spatially, where we provide clear evidence for a characteristic nodal structure reflecting the previously elusive supersymmetry in the underlying low-energy theory. In particular, we resolve the full sublattice polarisation of the anomalous 0th pseudo-Landau level, which reveals a deep connection to zigzag edge states in the unstrained case.