Study On Flat-band Localization And Topology In Optomechanical Arrays

Along with the miniaturization and integration of artificial quantum devices,people have realized many metamaterials for lots of platforms,such as,photonic crystals,phononic crystals,superconducting quantum circuits and cold atoms,etc.The purity,controllability of the structures and tunability of parameters of systems are the advantages of the artificial metamaterials comparing with solid materials,which leads to realization(observation)of many physical phenomena in theory.Cavity optomechanical systems are a class of hybrid quantum devices,which focus on the interaction between cavity and mechanical resonator via radiations–they combine the photonic and phononic devices.The researches on cavity optomechanics mostly are single-body,however,the realization of optomechanical crystals gives a platform to study the propagation of light and sound simultaneously.This thesis will study the many-body effects of light and sound with the optomechanical arrays,i.e.,photonic and phononic flat-band localization and topology.The flat-band is a perfect dispersionless band,its macroscopic degeneracy directly related the strong correlation physics in the presence of interactions.Moreover,the photonic and phononic non-trivial topological phases induce chiral edge mode,which can be directly observed in experiments.The robustness to the perturbations and disorders gives it broad application prospects.Here our study can be specifically divided into three parts:1.The flat-band localization is the perfect platform to investigate the strong correlation physics.Since the configuration of Lieb lattice has the path interference,which is the reason of the emergence of the flat-band.Via optomechanical arrays in which the optomechanical coupling results in polarization of photons and phonons,one can investigate the photonic and phononic flat-bands in the Lieb lattice.Here we find the polaritons in the flat-bands.Due to the tunability of bands–the advantage of optomechanical arrays,we can easily obtain photonic and phononic flat-bands as well as the transition between their roles.Finally,we numerically calculate the flat-band localization effect,the accessible parameters show the feasibility on experiments.Our study might has a potential application in quantum devices.2.Here we propose a bipartite lattice to investigate the flat-band.Based on the optomechanical arrays,we find a novel flat-band.We show it is general in a certain extent,which can be obtained in one-dimensional,two-dimensional tight-binding models.Here we show three examples–one dimensional lattice,two dimensional(honeycomb and Lieb)lattices– to strength our argument.Physically,it is induced by the hybrid-interference in the bipartite lattice,which is different from the reason of geometry-induced flat-band of lattice.Moreover,the flat-band is fixed when the lattice has been constructed generally,however,this novel flat-band is controllable,i.e.,we can control its emergence and disappearance of this flat-band.Further,the localization of this novel flat-band is also different from others,we have shown the differences in the main text.Besides,when the dissipation is included,the flat-band localization can still been presented.This might inspire the study on cavity optomechanics and many-body physics.3.Here we study the topological phases of light and sound,Ref.[V.Peano,et al.,Phys.Rev.X,5,031011(2015)] mostly shows the nontrivial photonic and phononic topological phases,basically reduplicate the quantum Hall effects in condensed matter physics.Here,we investigate not only the photonic and phononic topological phases,but also the study the parameter-amplifier terms which has been neglected in most cases.These terms will result in particles non-conserved,which is total different from the pairs in superconducting of fermions.These parameter-amplifier terms will induce the hole and particle type bands,implying the existence of inelastic chiral edge modes companying with the elastic chiral edge modes.Moreover,the tunability of bands can give rise to multiple topological phase transitions.Because of directly observation of propagation of the sound and light and topological protection,our work might inspire the study on the artificial quantum networks.In a summary,based on the optomechanical arrays(hybrid quantum devices platform),we will study the controllable photonic and phononic flat-band localization,hybrid-interference-induced flat-band localization and topological phases of light and sound.Our work might have the inspiration and promising future in artificial quantum devices.