Multidimensional photonics in synthetic lattices
Creators: name: Wang, Kai
Publisher: name: The Australian National University
Year: 2019

description: Geometrical dimensionality is known to have a great impact on the fundamental characteristics of physical systems, from the stability of planetary orbits to the occurrence of Anderson localization. Importantly, accessing higher dimensions is central to the fundamental enhancement of performance in many applications, such as deep neural network and scalable quantum computation. Discrete photonic state is a potential candidate for information processing due to its well-maintained coherence at the room temperature. The manipulation of these states is typically based on periodic photonic structures interacting with light analogous to electrons in electronic lattices. However, the direct use of such usually planar structures restricts the physical behaviors of photonic states to be within low-dimensional regimes. Recently, synthetic lattices appear as an emerging and rapidly growing topic in photonics, where artificial engineering of discrete potentials are employed to lift up limitations imposed by the geometry. Yet it remains unknown in many aspects how such synthetic lattices can be utilized to facilitate multidimensional photonics. This thesis focuses on the theoretical and experimental study of multidimensional photonics that uses synthetic lattices for both classical and quantum light. More specifically, we focus on three key aspects in multidimensional photonics, i.e. forming multidimensional lattices, harnessing multidimensional properties and manipulating multidimensional states. We test the feasibility of our concepts on a variety of experimental platforms, including nanostructured metasurfaces, integrated waveguides, and nonlinear fibers. First, we introduce and experimentally demonstrate a controllable all-optical approach to synthetic frequency lattices in a nonlinear waveguide, which is suitable to implement long-range interactions and artificial gauge fields. This platform, based on coherent frequency conversion mediated by parametric nonlinearity, enables flexible implementation of synthetic lattices without complex electro-optic modulation. We employ such lattices to generalize the discrete Talbot effect to new instances, synthesize dimensions, and perform measurements of frequency combs. Secondly, we formulate and experimentally realize a new paradigm that utilizes a tailored isospectral transformation to map arbitrary dimensional networks to planar photonic structures while maintaining excitation dynamics. This facilitates our theoretical and experimental exploration of bound states at the edge of the continuum associated with a sharp transition in higher-dimensional defect localization, paving the way for versatile potential applications from quantum simulation to advanced sensing with the fundamental enhancement from higher dimensional physics. Thirdly, we focus on the manipulation and measurement of multidimensional photonic states spanned by entangled photons of quantum light. Specifically, we introduce a new concept with advanced imaging to map multiphoton quantum states to an optimized set of correlation measurements. Such a transformation is achieved by metagrating lattices interleaved on a nanostructured metasurface. We present the experimental observation of multiphoton interference on metasurfaces and reconstruction of single- and multi-photon quantum states using such flat imaging optics. Finally, we introduce the concept of inline detection and reconstruction of multiphoton quantum states in quantum-photonic circuits. While conventional quantum state measurements were at the output of devices, we make judicious use of integrated detectors for measuring quantum states inside circuits without changing the measured quantum state except for a small overall loss. We perform proof-of-principle experiments and utilize this scheme in the monitoring of coherence in parity-time symmetric couplers.