The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

Dubček, Tena; Lelas, K.; Jukić, Dario; Pezer, Robert; Soljačić, Marin; Buljan, Hrvoje

doi:10.1088/1367-2630/17/12/125002

Cited by 15 publications

(12 citation statements)

References 51 publications

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“…In this issue, there are a number of important contributions, including theoretical analyses that apply to both condensed matter and photonic systems. For example, there are new proposed designs to achieve optical topological protection: Ma and Shvets [26] discuss an analogue of the valley hall effect in photonics; Jacobs et al [27] propose using tellegen metamaterial systems to break Lorentz reciprocity to realize Chern insulators; and Dubcek et al [28] present a novel design to realize the Harper-Hofstadter (i.e., integer quantum-Hall-like) Hamiltonian in waveguide arrays. In the realm of Floquet topological systems, Nathan and Rudner [29] show new theoretical insights by looking at the spectra of instantaneous Hamiltonians and relating their properties to the overall topology of the stroboscopic Floquet Hamiltonian; Sommer and Simon [30] cast their experimental effort on resonator-based realizations of fractional quantum Hall systems in terms of Floquet theory; Tauber and Delplace [31] use transfer matrices to gain new analytical insight into the Floquet problem.…”

Section: Topological Phases With Photonic Materialsmentioning

confidence: 99%

Focus on topological physics: from condensed matter to cold atoms and optics

et al. 2016

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The notions of a topological phase and topological order were first introduced in the studies of integer and fractional quantum Hall effects, and further developed in the study of topological insulators and topological superconductors in the past decade. Topological concepts are now widely used in many branches of physics, not only limited to condensed matter systems but also in ultracold atomic systems, photonic materials and trapped ions. Papers published in this focus issue are direct testaments of that, and readers will gain a global view of how topology impacts different branches of contemporary physics. We hope that these pages will inspire new ideas through communication between different fields.

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Section: Topological Phases With Photonic Materialsmentioning

confidence: 99%

Focus on topological physics: from condensed matter to cold atoms and optics

et al. 2016

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“…We estimate the effective hopping amplitude to be = K E 0.012 R . This is obtained by comparing the expansion of the initially localized single particle Gaussian wave packet in the total potential (13), with the expansion in the discrete lattice (14), and adjusting K until the two patterns coincide; this method was adopted from [48].…”

Section: Laser Assisted Tunneling In a Tonks-girardeau Gasmentioning

confidence: 99%

Laser assisted tunneling in a Tonks–Girardeau gas

et al. 2016

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We investigate the applicability of laser assisted tunneling in a strongly interacting one-dimensional (1D) Bose gas (the Tonks-Girardeau gas) in optical lattices. We find that the stroboscopic dynamics of the Tonks-Girardeau gas in a continuous Wannier-Stark-ladder potential, supplemented with laser assisted tunneling, effectively realizes the ground state of 1D hard-core bosons in a discrete lattice with nontrivial hopping phases. We compare observables that are affected by the interactions, such as the momentum distribution, natural orbitals and their occupancies, in the time-dependent continuous system, to those of the ground state of the discrete system. Stroboscopically, we find an excellent agreement, indicating that laser assisted tunneling is a viable technique for realizing novel ground states and phases with hard-core 1D Bose gases.

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“…These modes appear at the lattice’s edges with intensive localization of vibrational energy, when carefully designing the dynamical lattice to obey the BDI symmetry, and, hence, enjoying non-vanishing winding numbers of ±1 [44]. The second key example in this work is enabling the QVHE in a staggered square AIM with well-defined Dirac cones at high-symmetry points, inspired from similar photonic square lattices with alternating negative/positive coupling [52,53]. While acoustic-based square crystals may exhibit the QVHE by means of tilted (or tipped-over) Dirac cones away from high-symmetry points [59–61], a realization of the QVHE in square mechanical lattices remains, to our knowledge, an uncharted territory.…”

Section: Introductionmentioning

confidence: 99%

Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling

2021

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Mechanical topological insulators have enabled a myriad of unprecedented characteristics that are otherwise not conceivable in traditional periodic structures. While rich in dynamics, new developments in the domain of mechanical topological systems are hindered by their inherent inability to exhibit negative elastic or inertial couplings owing to the inevitable loss of dynamical stability. The aim of this paper is, therefore, to remedy this challenge by introducing a class of architected inertial metamaterials (AIMs) as a platform for designing mechanical lattices with novel topological and dispersion traits. We show that carefully coupling elastically supported masses via moment-free rigid linkages invokes a dynamically stable negative inertial coupling, which is essential for topological classes in need of such negative interconnection. The potential of the proposed AIMs is demonstrated via three examples: (i) a mechanical analogue of Majorana edge states, (ii) a square diatomic AIM that can sustain the quantum valley Hall effect (classically arising in hexagonal lattices), and (iii) a square tetratomic AIM with topological corner modes. We envision that the presented framework will pave the way for a plethora of robust topological mechanical systems.

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The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

Cited by 15 publications

References 51 publications

Focus on topological physics: from condensed matter to cold atoms and optics

Focus on topological physics: from condensed matter to cold atoms and optics

Laser assisted tunneling in a Tonks–Girardeau gas

Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling

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