arXiv subjects

Lavi K. Upreti

Publications and source records attributed to Lavi K. Upreti.

9 recordsLinked to original sources

arXiv2026

Topological non-Abelian gauge structures in Cayley-Schreier lattices

Crystalline constructions known as Cayley-Schreier lattices have been suggested as a platform for realizing arbitrary gauge fields in synthetic crystals with real hopping amplitudes. Here, we reveal that Cayley-Schreier lattices can naturally give rise to implementable lattice systems that incorporate non-Abelian gauge structures transforming into a space-group symmetry. We show that their symmetry sectors can be interpreted as blocks of pseudospin models---some of which correspond to true spinors---that can realize a wealth of different topological invariants in a single setup. We underpin these general results with concrete models and illustrate how they can be implemented in technologically available experimental platforms. Our work sets the stage for a systematic investigation of topological insulators and metals with non-Abelian gauge structures.

cond-mat.mes-hall↗

arXiv2026

Engineering symmetry-protected topological states in waveguide arrays

The topological classification of a system depends on the discrete symmetries of its Hamiltonian. In Floquet photonic waveguide arrays, the abstract symmetries of the Altland--Zirnbauer (AZ) scheme -- chiral, particle-hole, and time-reversal (for photonics, $z$-reversal) -- arise from structural properties of the lattice, yet a systematic correspondence has not been established. Here, we illustrate this correspondence for a simpler system of one-dimensional waveguide arrays with real coupling coefficients, showing how bipartite structure and $z$-reflection symmetry alone determine the whole AZ class. We further demonstrate that non-bipartite networks -- lacking conventional particle-hole symmetry, chiral symmetry, and $z$-reversal symmetry -- can nonetheless support topologically protected boundary states at quasienergy $\varepsilon = π$, even in one dimension. The protecting symmetry -- \textit{shifted}-particle-hole symmetry -- applies equally to higher-dimensional Floquet waveguides.

physics.optics↗

arXiv2023

Realizing efficient topological temporal pumping in electrical circuits

Quantized adiabatic transport can occur when a system is slowly modulated over time. In most realizations however, the efficiency of such transport is reduced by unwanted dissipation, back-scattering, and non-adiabatic effects. In this work, we realize a topological adiabatic pump in an electrical circuit network that supports remarkably stable and long-lasting pumping of a voltage signal. We further characterize the topology of our system by deducing the Chern number from the measured edge band structure. To achieve this, the experimental setup makes use of active circuit elements that act as time-variable voltage-controlled inductors.

cond-mat.other↗

arXiv2023

Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states.

cond-mat.mes-hall↗

arXiv2023

Topological properties of Floquet winding bands in a photonic lattice

The engineering of synthetic materials characterised by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a two-coupled ring system we engineer an anomalous Floquet metal that is gapless in the bulk and shows simultaneously two different topological properties. On the one hand, this synthetic lattice presents bands characterised by a winding number. The winding emerges from the breakup of inversion symmetry and it directly relates to the appearance of Bloch suboscillations within its bulk. On the other hand, the Floquet nature of the lattice results in well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enrich the variety of topological phases available in lattices subject to Floquet driving and suggest the possible emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries.

physics.optics↗

arXiv2022

Simulating hyperbolic space on a circuit board

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a "hyperbolic drum", and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter.

cond-mat.other↗

arXiv2022

Observation of cnoidal wave localization in non-linear topolectric circuits

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of non-linearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a non-linear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the non-linear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the non-linear regime, where the cnoidal eccentricity decreases from edge to bulk.

cond-mat.mes-hall↗

arXiv2022

Universality of Hofstadter butterflies on hyperbolic lattices

Motivated by recent experimental breakthroughs in realizing hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. By utilizing large hyperbolic lattices with periodic boundary conditions, we obtain the true hyperbolic bulk spectrum that is unaffected by contributions from boundary states. Our results reveal that the butterfly spectrum with large extended gapped regions prevails and that its shape is universally determined by the number of edges of the fundamental tile, while the fractal structure is lost in such a non-Euclidean case. We explain how these intriguing features are related to the nature of Landau levels in hyperbolic space, and how they could be verified experimentally.

cond-mat.mes-hall↗

arXiv2020

Topological chiral interface states beyond insulators

We show how to engineer a chiral spectral flow of interface states in a gapless system. Although the bulk bands touch -- thus making the topological indices of the bands ill-defined -- this spectral flow has a topological origin that makes it robust even when it coexists with the bulk bands. This phenomenon is illustrated with an adiabatically modulated photonic quantum walk.

cond-mat.mes-hall↗