Topological Amplification in Photonic Lattices
arXiv:1812.01348 · doi:10.1103/PhysRevLett.122.143901
Abstract
We present a characterization of topological phases in photonic lattices. Our theory relies on a formal equivalence between the singular value decomposition of the non-Hermitian coupling matrix and the diagonalization of an effective Hamiltonian. By means of that mapping we unveil an application of topological band theory to the description of quantum amplification with non-reciprocal systems. We exemplify our ideas with an array of photonic cavities which can be mapped into a topological insulator Hamiltonian in the AIII symmetry class. We investigate stability properties and prove the existence of stable topologically non-trivial steady-state phases. Finally, we show numerically that the topological amplification process is robust against disorder in the lattice parameters.
arXiv comment9 pages. This new version has an Appendix with more details on the physical implementation of our ideas with an array of periodically modulated coupled cavities. Paper accepted for publication in Physical Review Letters
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