We present a distinct mechanism for the formation of bound states in the
continuum (BICs). In chiral quantum systems there appear zero-energy states in
which the wave function has finite amplitude only in one of the subsystems
defined by the chiral symmetry. When the system is coupled to leads with a
continuum energy band, part of these states remain bound. We derive some
algebraic rules for the number of these states depending on the dimensionality
and rank of the total Hamiltonian. We examine the transport properties of such
systems including the appearance of Fano resonances in some limiting cases.
Finally, we discuss experimental setups based on microwave dielectric
resonators and atoms in optical lattices where these predictions can be tested.Comment: 9 pages, 8 figures. v2: includes results specific to honeycomb
  lattice; matches published versio

Molina, Rafael A.

Mur-Petit, Jordi

English

arXiv

9 pags. ; 8 figs. ; PACS number(s): 73.63.−b, 05.60.Gg, 42.70.Qs, 37.10.GhWe present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems, there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by the chiral symmetry. When the system is coupled to leads with a continuum energy band, part of these states remain bound. We derive some algebraic rules for the number of these states depending on the dimensionality and rank of the total Hamiltonian. We examine the transport properties of such systems including the appearance of Fano resonances in some limiting cases. Finally, we discuss experimental setups based on microwave dielectric resonators and atoms in optical lattices where these predictions can be tested. © 2014 American Physical Society.This work was supported by Spanish MINECO project Nos. FIS2012-33022 and FIS2012-34479, ESF Programme POLATOM, and the JAE-Doc program (CSIC and European Social Fund).Peer Reviewe

Digital.CSIC

Chiral bound states in the continuum

Institut für Quantenoptik, Leibniz Universität Hannover, December 1st to 5th, 2014We have studied the structure and dynamics of open discrete quantum systems, such as cold atoms in optical lattices, photons in photonic crystals, or electrons in semiconductor hetero-structures. We have identified a class of states (lattice scars) at the band center of bipartite lattices-such as the square or honeycomb lattices-which are resilient to local dissipative processes [1]. When such bipartite lattice systems are coupled to leads, lattice scarred states may remain bound within the system even when the energy-band center is embedded in the continuum spectrum of lead states-they become bound states in the continuum (BICs) [2,3]. We have shown how these states can have a dramatic impact on the transport properties through the system, enabling one to design the system-lead coupling so as to block all transmission in an energy range around the band center, introduce a Fano antiresonance, or a broad transmission peak, cf. Fig. 1 and Ref. [3]. Intriguing open questions remain as to the transport at energies where lattice symmetries imply a large density of states (van Hove singularities) [4].This work was supported by Spanish MINECO projects Nos. FIS2012-33022 and FIS2012-34479, ESF Programme POLATOM, and the JAE-Doc program (CSIC and European Social Fund).Peer Reviewe

References [1] J. von Neumann and E.P. Wigner, Phys. Z. 30, 465 (1929). [2] Plotnik et al., PRL (2011); Hsu et al., Nature 499, 188 (2013). [3] V. Fernández-Hurtado, J. Mur-Pett, J.J. García-Ripoll, and R.A. Molina, New J. Phys. 16, 035005 (2014). [4] J. Mur-Pett and R.A. Molina, Phys. Rev. B 90, 035434 (2014). [5] C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, arXiv:1407.3703 (2014). [6] J.-P. Brantut et al., Science 337, 1069 (2012); ibid. 342, 713 (2013); arXiv:1404.6400 (2014).Acknowledgements We acknowledge fruitul discussions with V. Fernández-Hurtado, J.J. García-Ripoll, and L. Tarruell. This work was supported by Spanish MINECO projects Nos. FIS2012-33022 and FIS2012-34479, ESF Programme POLATOM, and the JAE-Doc program (CSIC and European Social Fund).Chiral Bound States in the ContnuumJordi Mur-Pett & Rafael A. MolinaInst. Estructura de la Materia, IEM-CSIC, Madrid, Spain – jordi.mur@csic.esIntroducton – What are BICs?Bound states in the contnuum are square-integrable solutons of the Schrödinger equaton with an eigenenergy above the potental threshold. Hence, they are embedded in the contnuum of scatering states but, in contrast to Fano resonances, they are not coupled to it. First discovered by von Neuman and Wigner [1], they have only recently been observed in optcal setups [2]. No direct detecton in atomic or solid-state systems has been reported so far. Here we provide a framework to describe them in fnite latces, and propose two experiments to observe them in cold-atom & microwave-resonator setups.ResultsPartcle current ?VQuasi-1D leads(λ transverse modes)2D channel = bipartte latceTop viewsource drainLaser toimprint2D channelmaskhigh NAlensdichroicmirrorobjectve2D channelLaser foroptcallatceSide viewExperimental proposalsDetecton of chiral BICs requires (i) a fnite latce system; (ii) measuring its conductance for varying lead sizes. We discuss two possibilites [4]: microwave resonators, where similar 1D non-propagatng states have been observed very recently [5], and a cold-atom setup analogous to [6] with an optcal latce added to the 2D conducton channel.mw antenna(emission)mw antenna(measure)dielectricresonators metallic platesThe bipartte character of the latce corresponds to a chiral symmetry of the Hamiltonian:This implies a ‘partcle-hole’ symmetry between eigenstates with opposite eigenenergies:Hence, eigenstates with E=0 are localized on only one sublatce [3,4]. These zero-energy modes correspond to eigenvectors in the kernel of the Hamiltonian. The rank-nullity theorem from matrix algebra allows us to determine how many exist on each sublatce by calculatng the rank of the hopping matrix C:Closed system: Zero-energy modesA localized leak in the latce leads to a loss of populaton:However, in most cases populaton stays trapped for arbitrarily long tmes. It corresponds to components of the wavefuncton in zero-energy modes localized in one sublatce. We call them latce scars by analogy with Heller’s scarred wave functons from the theory of quantum chaos in contnuous systems [3].Dynamics in dissipatve latcesLong-tme surviving populaton in a regular (lef) and chaotc (right) domain. The corresponding wave functons are superpositons of zero-energy modes localized in the two sublatces. See Ref. [3] for details.Conductance measurementsWhat happens when we couple the latce to quasi-1D leads?Zero-energy modes split into [4]:● Modes that couple to the leads: They acquire a width Γ~V; Their energy shifs away from E=0.● Modes that remain bound: chiral BICs! They keep E=0=Γ. Generally, one zero-energy mode islost per each site linked to the leads. Hence, the density of states (DOS) and conductance (G) around E=0 become probes of the existence of BICs. Interestngly, a small breaking of chiral symmetry transforms BICs into Fano resonances in G.DOS and G of a 10x10 square latce (supportng 10 zero modes) for various lead sizes, calculated with the Landauer-Bütker formalism [4]: As long as the number of links to leads is <10, G(Vg=0)=0. When λ=5, there is a Fano antresonance, but stll G(0)=0. For larger leads, G~DOS.t2 /t=0.01A small hopping to 2ndneighbours, which breakschiral symmetry, convertsBICs into narrow Fanoresonances.

Chiral Bound States in the Continuum

INT Program INT-15-1, Institute for Nuclear Theory,Seattle (USA),March 30 - April 2, 2015Peer Reviewe

Chiral bound states in the continuum

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