arXiv subjects

Mikael C. Rechtsman

Publications and source records attributed to Mikael C. Rechtsman.

At least 19 recordsLinked to original sources

arXiv2026

Weyl Points and Fermi Arc Surface States in a Self-assemblable Zinc-Blende Photonic Crystal

Colloidal self-assembly has long been proposed as a method for growing large-scale three-dimensional photonic crystals with important optical properties in visible and near-infrared wavelength regimes, where top down lithographic fabrication fails. While much of the focus in these systems has been on producing a photonic band gap, such lattices can also give rise to topological features of photonic bands. To date, there has been no proposal for realizing topological photonic features in photonic crystals that may be self-assembled. In 3D, Weyl points are topological band degeneracies that are of particular interest due to their robustness to perturbations and their corresponding Fermi arc surface states. In order to realize Weyl points, either time-reversal or inversion symmetry must be broken, and no previous self-assembled colloidal photonic crystal has exhibited either property. Here, we propose a new zinc-blende structure, built off of recent progress in self-assembling diamond photonic crystals, which lacks inversion symmetry and supports photonic Weyl points. Furthermore, we show that the geometry can be optimized to make the Weyl point and its Fermi arc surface states experimentally observable in the photonic crystal's projected band structure. Finally, we perform molecular dynamics simulations to demonstrate that the geometry we propose for observing Weyl points is capable of being self-assembled with realistic interparticle interactions. Together, these results provide a platform for the assembly of large-scale photonic crystals supporting topological degeneracies and robust Fermi arc surface states in the visible and near-infrared.

physics.optics↗

arXiv2026

Extreme sensitivity of nonlinear trajectories enhances optical spectral broadening

The generation of a wide spectrum of light in highly nonlinear optical fibers has broad application in spectroscopy, microscopy and medical imaging. To generate such a 'supercontinuum', an ultrashort pulse of light is injected into a highly nonlinear fiber. Then, in a process called self-phase modulation, the nonlinearity of the fiber causes the spectrum to start broadening as the pulse becomes chirped during propagation, seeding further cascaded nonlinear processes. The dynamics associated with supercontinuum generation are captured mathematically as a pulse profile evolving in time and occupying a single spatial mode. Here, we theoretically and experimentally demonstrate that a waveguide composed of multiple coupled cores - a photonic molecule' - rather than just a single core, gives rise to greater self-phase modulation for a given input power. This is perhaps counterintuitive because it may be naively expected that the strongest nonlinear effects would be achieved by concentrating all optical power in one waveguide. The increased broadening arises due to the extreme sensitivity of trajectories near a separatrix of the nonlinear dynamics. This sensitivity leads to a distortion of the temporal shape of the pulse, resulting in a broader spectrum. The effect is reminiscent of the sensitivity associated with exceptional points in coupled-resonator systems, but does not suffer in the same way from the parasitic effects of noise. This suggests that by including multiple cores, a straightforward modification of conventional nonlinear fiber design, supercontinuum sources seeded by self-phase modulation can generate a significantly wider spectrum. More broadly, this demonstrates that the sensitivity to initial conditions associated with nonlinear dynamics may be utilized to generate stronger nonlinear effects in optics.

physics.optics↗

arXiv2026

Quantum Geometry in the Continuum: Solitons in Shallow Lattices

The quantum geometry of electronic, photonic, and atomic lattice systems quantifies the distance in Hilbert space between Bloch states at neighboring lattice momenta. This quantity has profound implications for flat-band systems especially, characterizing surprising behavior such as superfluidity and superconductivity when the group velocity is zero and no transport would be expected for non-interacting particles. However, when the band is not flat, the effects of quantum geometry are often intertwined with and partly masked by the band dispersion. Here, we show that in weakly interacting bosonic systems in the critical dimension (i.e., two dimensions for Kerr nonlinearity), the deviation from critical behavior due to the presence of the lattice is governed by the quantum geometry, which is directly proportional to the fourth-order dispersion. Furthermore, we identify the family of continuous lattice potentials that saturates the bound on the quantum metric for a given effective mass tensor.

cond-mat.quant-gas↗

arXiv2026

Topological Pumping Through a Localized Bulk in a Photonic Hofstadter System

Photonic systems provide a highly tunable platform for emulating quantum Hall physics. This tunability enables probing of the interplay between strong disorder and robust topological transport that remains difficult to access in solid-state systems. Here we realize a photonic version of the Harper-Hofstadter and Aubry-André models using a one-dimensional multilayer photonic crystal (Bragg stack) with a synthetic dimension encoded in its geometry. By modulating the layer thicknesses, we observe the Hofstadter butterfly and its chiral edge states from a family of one-dimensional multilayer structures, consistent with the Thouless pump picture. Exploiting the quasiperiodicity in this model, we show that increasing quasiperiodic modulation induces a wavelength-selective localization transition: specific Chern bands become fully localized along one dimension, while chiral edge states persist and continue to wind across the gap. We confirm this behavior through numerical simulations and experiments, and eigenmode analysis reveals that edge transport in this regime proceeds via a sequence of Landau-Zener transitions between localized states. These results demonstrate a crossover from adiabatic Thouless pumping under weak quasiperiodic modulation to a Landau-Zener-mediated topological pump at strong modulation, realized in a a compact and easily tunable photonic system.

physics.optics↗

arXiv2025

Quantized pumping in disordered nonlinear Thouless pumps

We investigate the dynamics of nonlinear optical Thouless pumps in the presence of disorder, using optical waveguide arrays. It was previously known that the displacement of solitons in Thouless pumps is quantized and may exhibit integer and fractional transport over the course of the pump cycle. Here, we demonstrate that, in disordered nonlinear pumps, quantization may be maintained despite the presence of disorder, even though it would not be in the linear domain. Moreover, nonlinearity allows pumps to be executed more quickly (i.e., less adiabatically). This may serve as a design principle for integrated non-reciprocal devices based on temporal modulation.

cond-mat.mes-hall↗

arXiv2025

Effective delocalization in the one-dimensional Anderson model with stealthy disorder

We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical transparency properties of stealthy hyperuniform layered media, we compute the localization length using a perturbative expansion of the self-energy. We find that, for fixed energy and small but finite disorder strength $W$, there exists for any finite length system a range of stealthiness $χ$ for which the localization length exceeds the system size. This kind of "effective delocalization" is the result of the novel kind of correlated disorder that spans a continuous range of length scales, a defining characteristic of stealthy systems. Unlike uncorrelated disorder, for which the localization length $ξ$ scales as $W^{-2}$ to leading order for small W, the leading order terms in the perturbation expansion of $ξ$ for stealthy disordered systems vanish identically for a progressively large number of terms as $χ$ increases such that $ξ$ scales as $W^{-2n}$ with arbitrarily large $n$. Moreover, we support our analytical results with numerical simulations. Our results introduce stealthy disorder into quantum tight-binding models and show that enforcing a low-$k$ spectral gap markedly alters the scattering landscape, enabling localization lengths that exceed the system size at fixed disorder strength. Since this mechanism relies only on the spectral properties of the disorder, it carries over directly to photonic and phononic wave systems.

cond-mat.dis-nn↗

arXiv2025

Airy Resonances in Photonic Crystal Superpotentials

Airy wavefunctions are associated with one of the simplest scenarios in wave mechanics: a quantum bouncing ball. In other words, they are the eigenstates of the time-independent Schrodinger equation with a linear potential. In the domain of optics, laser beams that are spatially shaped as Airy functions (`Airy beams') have been shown to exhibit a prominent lobe that follows a curved path, rather than propagating in a straight line, and which has self-healing properties in the presence of obstacles. Here, we observe the presence of Airy resonances in two-dimensional photonic crystals composed of a lattice of holes in a silicon slab. Analogously to electrons in a linear potential, these Airy resonances arise due to a linear spatial variation in the lattice constant of the holes. We map the electromagnetic description of the photonic crystal onto a 2D non-Hermitian Schrodinger equation with a linear potential, which we call a `superpotential'. The non-Hermiticity appears in the form of a complex effective mass due to out-of-plane radiation and fundamentally alters the collective optical response of the Airy resonances.

physics.optics↗

arXiv2025

Multi-band fractional Thouless pumps

Quantization of particle transport lies at the heart of topological physics. In Thouless pumps - dimensionally reduced versions of the integer quantum Hall effect - quantization is dictated by the integer winding of single-band Wannier states. Here, we show that repulsive interactions can drive a transition from an integer- to a fractional-quantized Thouless pump (at fixed integer filling) by stabilizing a crystal of multi-band Wannier states, each with fractional winding. We numerically illustrate the concept in few-particle systems, and show that a dynamical Hartree-Fock ansatz can quantitatively reproduce the pumping phase diagram.

cond-mat.str-el↗

arXiv2025

Stealthy-Hyperuniform Wave Dynamics in Two-Dimensional Photonic Crystals

Hyperuniform structures are spatial patterns whose fluctuations disappear on long length scales, making them effectively homogeneous when observed from afar. Mathematically, this means that their spectral density, $\tildeρ({\bf k})$, approaches zero for low wavenumber, $|\textbf{k}|$. Crystalline lattices are hyperuniform, as are certain quasicrystals, maximally random jammed packing of spheres, and electrons in the fractional quantum Hall state. Stealthy-hyperuniformity is an even stronger constraint on the spectral density: it requires that $\tildeρ({\bf k})$ is strictly zero in a finite range of wavevectors around $\mathbf{k}=\mathbf{0}$, called the stealthy regime, or exclusion region. Since the degree of scattering by disorder is, to leading order, proportional to $\tildeρ({\bf k})$, waves propagating through such structures may do so without scattering for sufficiently long wavelengths and short distances. Here, we measure scattering by disorder in photonic crystal slabs with stealthy-hyperuniform disorder by measuring the linewidths of the photonic bands. We observe the transition between the stealthy and non-stealthy regimes, marked by a sharp increase in linewidth. We also observe the effects of multiple scattering in the stealthy regime, which implies diminishing transparency. Moreover, we show that residual single scattering in the stealthy regime arises from an intrinsically non-Hermitian effect: propagating light has a complex effective mass due to radiative loss out of the slab.

physics.optics↗

arXiv2025

Quantized dynamical pumping via dissipation in a mechanical Thouless pump

Thouless pumps are time-periodic one-dimensional systems that capture the physics of the two-dimensional quantum Hall effect via the quantized pumping of particles under adiabatic modulation. Recent work in photonics has shown that nonlinearity can act to quantize the displacement of light in the form of soliton motion. Here we use a mechanical system -- namely coupled pendulums described by the Frenkel-Kontorova model -- to propose and observe quantized non-adiabatic Thouless pumping using topological kink solitons. The pumping proceeds by a qualitatively different mechanism compared to Thouless' original proposal as the pump is non-adiabatic and dissipation is necessary. In the presence of an additional potential gradient along the pump, we predict and observe the emergence of quantized transport against the pumping direction as a function of the period and show the emergence of a rich plateau structure; this quantization is unique to dissipative systems and cannot be described by the Chern number. Finally, we experimentally demonstrate the robustness of the process by pumping the soliton through a tunable nonlinear defect.

nlin.PS↗

arXiv2024

Weyl points on non-orientable manifolds

Weyl fermions are hypothetical chiral particles that can also manifest as excitations near three-dimensional band crossing points in lattice systems. These quasiparticles are subject to the Nielsen-Ninomiya "no-go" theorem when placed on a lattice, requiring the total chirality across the Brillouin zone to vanish. This constraint results from the topology of the (orientable) manifold on which they exist. Here, we ask to what extent the concepts of topology and chirality of Weyl points remain well-defined when the underlying manifold is non-orientable. We show that the usual notion of chirality becomes ambiguous in this setting, allowing for systems with a non-zero total chirality. This circumvention of the Nielsen-Ninomiya theorem stems from a generic discontinuity of the vector field whose zeros are Weyl points. Furthermore, we discover that Weyl points on non-orientable manifolds carry an additional $\mathbb{Z}_2$ topological invariant which satisfies a different no-go theorem. We implement such Weyl points by imposing a non-symmorphic symmetry in the momentum space of lattice models. Finally, we experimentally realize all aspects of their phenomenology in a photonic platform with synthetic momenta. Our work highlights the subtle but crucial interplay between the topology of quasiparticles and of their underlying manifold.

cond-mat.mes-hall↗

arXiv2024

The effect of hyperuniform disorder on band gaps

The properties of semiconductors, insulators, and photonic crystals are defined by their electronic or photonic bands, and the gaps between them. When the material is disordered, Lifshitz tails appear: these are localized states that bifurcate from the band edge and act to effectively close the band gap. While Lifshitz tails are well understood when the disorder is spatially uncorrelated, there has been recent interest in the case of hyperuniform disorder, i.e., when the disorder fluctuations are highly correlated and approach zero at long length scales. In this paper, we analytically solve the Lifshitz tail problem for hyperuniform systems using a path integral and instanton approach. We find the functional form of the density-of-states as a function of the energy difference from the band edge. We also examine the effect of hyperuniform disorder on the density of states of Weyl semimetals, which do not have a band gap.

cond-mat.dis-nn↗

arXiv2024

Stability of topologically protected slow light against disorder

Slowing down light in on-chip photonic devices strongly enhances light-matter interaction, but typically also leads to increased backscattering and small-bandwidth operation. It was shown recently that, if one modifies the edge termination of a photonic Chern insulator such that the edge mode wraps many times around the Brillouin zone, light can be slowed to arbitrarily low group velocity over a large bandwidth, without being subject to backscattering. Here we study the robustness of these in-gap slow light modes against fabrication disorder, finding that disorder on scales significantly larger than the minigaps between edge bands is tolerable. We identify the mechanism for wavepacket breakup as disorder-induced velocity renormalization and calculate the associated breakup time.

physics.optics↗

arXiv2024

Optical control of topological end states via soliton formation in a 1D lattice

Solitons are self-consistent solutions of the nonlinear Schrödinger equation that maintain their shape during propagation. Here we show, using a pump-probe technique, that soliton formation can be used to optically induce and control a linear topological end state in the bulk of a Su-Schrieffer-Heeger lattice, using evanescently-coupled waveguide arrays. Specifically, we observe an abrupt nonlinearly-induced transition above a certain power threshold due to an inversion symmetry-breaking nonlinear bifurcation. Our results demonstrate all-optical active control of topological states.

physics.optics↗

arXiv2023

Direct Observation of Landau Levels in Silicon Photonic Crystals

We experimentally observe photonic Landau levels that arise due to a strain-induced pseudomagnetic field in a silicon photonic crystal slab. The Landau levels are dispersive (i.e., they are not flat bands) due to the distortion of the unit cell by the strain. We employ an additional strain which induces a pseudoelectric potential to flatten them.

physics.optics↗

arXiv2023

Artificial gauge fields in the t-z mapping for optical pulses: spatio-temporal wavepacket control and quantum Hall physics

We extend the $t-z$ mapping formalism of time-dependent paraxial optics by identifying configurations displaying a synthetic magnetic vector potential, leading to a non-trivial band topology in propagating geometries. We consider an inhomogeneous 1D array of coupled optical waveguides beyond the standard monochromatic approximation, and show that the wave equation describing paraxial propagation of optical pulses can be recast in the form of a Schrödinger equation, including a synthetic magnetic field whose strength can be controlled via the transverse spatial gradient of the waveguide properties across the array. We use an experimentally-motivated model of a laser-written waveguide array to demonstrate that this synthetic magnetic field can be engineered in realistic setups and can produce interesting observable effects such as cyclotron motion, a controllable Hall drift of the wavepacket displacement in space or time, and unidirectional propagation in chiral edge states. These results significantly extend the variety of physics that can be explored within propagating geometries and pave the way for exploiting this platform for higher-dimensional topological physics and strongly correlated fluids of light.

physics.optics↗

arXiv2023

Response to polarization and weak topology in Chern insulators

Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show that spatial or temporal differences in polarization within Chern insulators are well-defined and physically meaningful because they account for bound charges and adiabatic currents. We further show that the difference in polarization across Chern-insulator regions can be quantized in the presence of crystalline symmetries, leading to "weak" symmetry-protected topological phases. These phases exhibit charge fractional quantization at the edge and corner interfaces and with concomitant topological states. We also generalize our findings to quantum spin-Hall insulators and 3D topological insulators. Our work settles a long-standing question and deems the bulk polarization as the fundamental quantity with a "bulk-boundary correspondence", regardless of whether a Wannier representation is possible.

cond-mat.mes-hall↗

arXiv2023

Topological Phases of Photonic Crystals under Crystalline Symmetries

Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological bands in one- and two dimensional photonic crystals, with and without time-reversal symmetry. Our approach exploits the symmetry representations of field eigenmodes at high-symmetry points in momentum space, allowing for the efficient design of a wide range of topological PhCs. In particular, we show that the complete classification provided here is useful for diagnosing photonic crystal analogs of obstructed atomic limits, fragile phases, and stable topological phases that include bands with Dirac points and Chern numbers.

cond-mat.mes-hall↗