Floquet bound states in the continuum

Quantum mechanics predicts that certain stationary potentials can sustain bound states with an energy buried in the continuous spectrum of scattered states, the so-called bound states in the continuum (BIC). Originally regarded as mathematical curiosities, BIC have found an increasing interest in recent years, particularly in quantum and classical transport of matter and optical waves in mesoscopic and photonic systems where the underlying potential can be judiciously tailored. Most of our knowledge of BIC is so far restricted to static potentials. Here we introduce a new kind of BIC, referred to as Floquet BIC, which corresponds to a normalizable Floquet state of a time-periodic Hamiltonian with a quasienergy embedded into the spectrum of Floquet scattered states. We discuss the appearance of Floquet BIC states in a tight-binding lattice model driven by an ac field in the proximity of the dynamic localization regime.

[1]  Alexander Szameit,et al.  Photonic Floquet Topological Insulators , 2013, CLEO 2013.

[2]  Nöckel.  Resonances in quantum-dot transport. , 1992, Physical review. B, Condensed matter.

[3]  M. Holthaus,et al.  Collapse of minibands in far-infrared irradiated superlattices. , 1992, Physical review letters.

[4]  J. M. Zhang,et al.  Bound states in the continuum realized in the one-dimensional two-particle Hubbard model with an impurity. , 2012, Physical review letters.

[5]  M. Holthaus,et al.  Quantum wells and superlattices in strong time-dependent fields. , 1993, Physical review. B, Condensed matter.

[6]  Frank H. Stillinger,et al.  Bound states in the continuum , 1975 .

[7]  G. Bahir,et al.  Electronic bound states in the continuum above (Ga,In)(As,N)/(Al,Ga)As quantum wells , 2012 .

[8]  S. Longhi,et al.  Tamm–Hubbard surface states in the continuum , 2013, Journal of physics. Condensed matter : an Institute of Physics journal.

[9]  A. Tünnermann,et al.  Observation of defect-free surface modes in optical waveguide arrays. , 2008, Physical review letters.

[10]  Yuri S. Kivshar,et al.  Light propagation and localization in modulated photonic lattices and waveguides , 2012 .

[11]  Friedrich,et al.  Interfering resonances and bound states in the continuum. , 1985, Physical review. A, General physics.

[12]  Driven quantum transport on the nanoscale , 2004, cond-mat/0409251.

[13]  J. Faist,et al.  Observation of an electronic bound state above a potential well , 1992, Nature.

[14]  M. L. L. D. Guevara,et al.  Electronic transport through a parallel-coupled triple quantum dot molecule : Fano resonances and bound states in the continuum , 2005, cond-mat/0508727.

[15]  R. Friedman,et al.  Conical intersections and bound molecular states embedded in the continuum. , 2003, Physical review letters.

[16]  P. Hänggi,et al.  Driven quantum tunneling , 1998 .

[17]  Gil Refael,et al.  Floquet topological insulator in semiconductor quantum wells , 2010, 1008.1792.

[18]  E. Bulgakov,et al.  Bound states in the continuum in open quantum billiards with a variable shape , 2006 .

[19]  O. Olendski,et al.  Fano resonances of a curved waveguide with an embedded quantum dot , 2003 .

[20]  P. Laporta,et al.  Observation of dynamic localization in periodically curved waveguide arrays. , 2005, Physical review letters.

[21]  C. Chu,et al.  Localized states in continuum in low-dimensional systems , 2006, cond-mat/0609214.

[22]  J. Neumann,et al.  Über merkwürdige diskrete Eigenwerte , 1993 .

[23]  C Sias,et al.  Dynamical control of matter-wave tunneling in periodic potentials. , 2007, Physical review letters.

[24]  Bohm-Jung Yang,et al.  Topological protection of bound states against the hybridization , 2012, Nature Communications.

[25]  J. González,et al.  Bound states in the continuum in graphene quantum dot structures , 2010, 1009.2711.

[26]  A. Borisov,et al.  Bound States in the continuum in photonics. , 2008, Physical review letters.

[27]  Y. Kivshar,et al.  Defect-free surface states in modulated photonic lattices. , 2007, Physical review letters.

[28]  Hsin Lin,et al.  Electronic structure of the metallic ground state of La2-2xSr1+2xMn2O7 for x≈0.59 and comparison with x=0.36, 0.38 compounds as revealed by angle-resolved photoemission , 2008 .

[29]  Friedrich,et al.  Physical realization of bound states in the continuum. , 1985, Physical review. A, General physics.

[30]  E. Bulgakov,et al.  Bound states in the continuum in photonic waveguides inspired by defects , 2008 .

[31]  Dunlap,et al.  Dynamic localization of a charged particle moving under the influence of an electric field. , 1986, Physical review. B, Condensed matter.

[32]  M. Segev,et al.  Experimental observation of optical bound states in the continuum. , 2011, Physical review letters.

[33]  Scattering theory on graphs: II. The Friedel sum rule , 2001, cond-mat/0112225.

[34]  G. Platero,et al.  Floquet-Bloch theory and topology in periodically driven lattices. , 2013, Physical review letters.

[35]  Y. Kivshar,et al.  Surface bound states in the continuum. , 2011, Physical review letters.