Топологические состояния высокого порядка и квантово-запутанные состояния фотонных пар в резонансных наноструктурах Олехно Никита Андреевич

brief description

Олехно, Никита Андреевич.
Топологические состояния высокого порядка и квантово-запутанные состояния фотонных пар в резонансных наноструктурах : диссертация ... кандидата физико-математических наук : 1.3.6. / Олехно Никита Андреевич ; [Место защиты: ФГАОУ ВО «Национальный исследовательский университет ИТМО»]. - Санкт-Петербург, 2021. - 175 с. : ил.; 14,5х20,5 см.
Оглавление диссертациикандидат наук Олехно Никита Андреевич
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Synopsis
Introduction
1 Generation of entangled surface plasmon-polariton pairs via SPDC of light by a nanoparticle
1.1 Theoretical model
1.1.1 General formalism
1.1.2 Dipole approximation
1.1.3 Generation of entangled surface plasmon-polaritons
1.2 Generation of SPP N00N-states with a GaAs nanoparticle
1.2.1 N00N-state generation via degenerate SPDC at normal pump incidence
1.2.2 Robustness of the N00N-state generation
1.3 Outlook
1.4 Scientific statement
2 Topological edge states of entangled photon pairs in coupled cavity arrays
2.1 Theory
2.1.1 Two-photon Bose-Hubbard model with on-site interaction
2.1.2 Equivalent two-dimensional tight-binding model
2.1.3 Classification of two-photon excitations
2.2 Equivalent electrical circuit
2.2.1 Circuit derivation
2.2.2 Experimental realization
2.2.3 Excitation of the modes in the electrical circuit
2.2.4 Doublon spectroscopy
2.2.5 Eigenmode reconstruction
2.3 Topological properties
2.4 Effects of disorder
2.5 Outlook
2.6 Scientific statement
3 Statistics-induced topological edge states of anyons in coupled cavity arrays
3.1 Theoretical model
3.1.1 Particle number conservation
3.1.2 Wave function symmetry
3.1.3 Tight-binding equations
3.2 Two -anyon states in the model
3.3 Equivalent electrical circuit
3.3.1 Electrical circuit derivation
3.3.2 Numerical model of equivalent electrical circuit
3.4 Numerical simulations of the equivalent circuit
3.5 Outlook
3.6 Scientific statement
4 Higher-order topological states in two-dimensional cavity arrays with D4 symmetry and next-nearest neighbor couplings
4.1 Theoretical description
4.1.1 Extended Su-Schrieffer-Heeger model
4.1.2 Generalized chiral symmetry
4.1.3 Bulk, edge, and corner excitations in the extended 2D SSH model
4.1.4 Bound states in the continuum
4.2 Electrical circuit realization
4.2.1 Circuit derivation
4.2.2 Numerical simulations of the circuit
4.2.3 Experimental setup and measurements
4.3 Topological properties
4.3.1 Theoretical evaluation
4.3.2 Retrieval of the topological invariant in experiments
4.4 Outlook
4.5 Scientific statement
Conclusion
Acknowledgements
Acronyms
References
Appendix A. Texts of author's main publications
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