Floquet bound states in the continuum

Stefano Longhi,Giuseppe Della Valle

doi:10.1038/srep02219

Stefano Longhi, Giuseppe Della Valle

Open Access

https://doi.org/10.1038/srep02219

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Abstract

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.

Highlights

Dipartimento di Fisica- Politecnico di Milano and Istituto di Fotonica e Nanotecnologie - Consiglio Nazionale delle Ricerche Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy
We introduce a new kind of bound states in the continuum (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 introduce a new kind of BIC, referred to as Floquet BIC, which correspond to breathing normalizable Floquet states of a time-periodic Hamiltonian with a quasienergy embedded into the spectrum of Floquet scattered states

Summary

Introduction

Dipartimento di Fisica- Politecnico di Milano and Istituto di Fotonica e Nanotecnologie - Consiglio Nazionale delle Ricerche Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy. A t the birth of quantum mechanics, von Neumann and Wigner[1] suggested rather surprisingly that certain spatially oscillating attractive potentials can sustain normalizable states at a positive energy, i.e. embedded into the spectrum of scattered states. Because of their unusual geometry, such potentials were earlier regarded as mathematical curiosities with low physical relevance, and for many years BIC did not attract the interest of the scientific community. Time periodic Hamiltonians are found in a wide range of different physical fields and describe important physical phenomena, for example driven quantum tunneling, scattering from oscillating potentials and quantum transport on the nanoscale[24,25]. In the high-frequency limit, such states can be explained as a result of selective destruction of tunneling

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