Hamiltonian Engineering inIntegrated Photonics

QC 2026-09-11

Abstract

This dissertation investigates the emulation of complex wave dynamics, topologicalphases, and non-Hermitian systems using integrated photonic circuits,addressing the limitations of traditional static and energy-conservingoptical systems through passive and reconfigurable architectures.The experimental foundation relies on two complementary platforms: passivesilicon nitride circuits for simulating static spatial propagation, and programmablesilicon-on-insulator Mach-Zehnder interferometer (MZI) meshes.Utilizing singular value decomposition, the active meshes synthesize discretetimeevolution operators to dynamically tune coupling amplitudes and onsitepotentials.Within the Hermitian framework, the passive circuits provide observationalevidence of the Topological Anderson Phase and a reentrant metal-insulatortransition driven by spatially correlated disorder. Additionally, the activeMZI mesh is employed to emulate the Bloch-Siegert shift. By mapping thediscrete time evolution of a driven two-level system onto spatial propagation,the system demonstrates resonance jumps and the conversion of bidirectionalRabi oscillations into unidirectional transport.The experimental scope is subsequently expanded into the non-Hermitianregime. Employing the unitary dilation method, ancillary modes on the programmablemesh introduce controlled dissipation to synthesize non-unitaryoperators. This approach enables the realization of a non-Hermitian Hamiltonianon a Klein bottle parameter space, yielding experimental signaturesconsistent with paired exceptional points. Furthermore, implementing rowstochasticMarkov matrices demonstrates dissipation-induced multimode phasesynchronization, with synchronization rates governed by the spectral gapand operating independently of absolute optical attenuation.In summary, this thesis explores Hamiltonian engineering on integrated photonicplatforms as a method to simulate topological and non-Hermitian phenomena.The investigated architectures and dissipative mechanisms offera framework for studying fundamental wave physics, suggesting potential pathways for future applications in exceptional-point-enhanced optical neuralnetworks and high-bandwidth optical interconnects.

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