Topological Photonics
Topological Photonics
As a sub-field of optics, photonics places particular emphasis on interdisciplinary analogies with electronic materials and condensed matter physics. This field is driven by recent advances in nanofabrication such as laser-writing and lithography, which offer unprecedented flexibility in device geometries and precision down to the nanoscale. The main challenge today is how to exploit emerging nanofabrication technologies to improve the performance of optical devices such as waveguides, resonators, lasers, and sensors, which form key components of light-based technologies in the communication, data processing, and environmental sensing industries.
Topology has emerged as a powerful new paradigm for the design and characterization of electronic systems and beyond, with the 2016 Physics Nobel Prize awarded for the discovery of topological phases of matter. The spread of these ideas to photonics has given rise to the sub-field of topological photonics, which offers systematic ways to design reliable and fault-tolerant optical components based on topologically-protected edge modes. Originally demonstrated with microwaves in 2008, the last few years have seen the first implementations of topological photonic waveguides and lasers in nanoscale optical systems and their integration with nonlinear and quantum optical effects. Interest and investment continue to grow as efforts move from proofs of concept at microwave frequencies towards optical device applications.
I have been interested in the design of reconfigurable and nonlinear topological photonic systems scalable to the technologically-important optical frequency range, including generalizing the theory of ideal (lossless) topological phases to realistic (lossy) systems [Phys. Rev. Lett.118, 040401 (2017)] and the first experimental demonstration of topologically-protected Weyl point degeneracies at optical frequencies [Nature Phys. 13, 611 (2017)]. More broadly, my research interests include exploiting other analogies between electrons and photons, such as light propagation photonic lattices of waveguide arrays mimicking graphene [Phys. Rev. Lett., 121, 033904 (2018)], related 2D materials [Phys. Rev. Lett. 116, 183902 (2016)], and frustrated spin systems [APL Photon. 3, 070901 (2018)], which offer novel ways to control the flow of light.
There are two dominant approaches to designing photonic circuits and devices: Discrete tight binding models that are directly analogous to certain electronic systems, and full wave simulations of photonic crystals using commercial finite element modelling software such as COMSOL. The former requires a weak coupling approximation, limited to arrays of weakly coupled optical waveguides or resonators, while the latter is computationally intensive and relies on group theoretical principles to guide designs. I have pioneered hybrid approaches based on numerical simulations of Schrodinger-like equations, which enable tractable computations without being limited to the tight binding approximation. This allowed me to not only design strongly-coupled waveguide arrays supporting novel classes of “Floquet” topological phases [Phys. Rev. Lett. 117, 013902 (2016)] and nonlinearly-induced topological edge states [Phys. Rev. Lett. 117, 143901 (2016)], but also develop simplified models to understand the behaviour of weakly-guiding leaky-wave lattices [Nature Phys. 17, 632 (2021)]. For these designs, fabrication and experimental techniques were already well-established; the key was my ability to numerically characterize and optimize novel designs.
In the longer term, engineered quantum systems are attracting increasing investment from government and industry, with particular focus on developing a quantum computer. The manipulation and transmission of quantum states of light is essential for transmission of information encoded in qubits, and will likely be the only practical way to create quantum computers capable of operating at room temperature. Thus, I have become interested in how ideas from topological photonics may be useful for improving the performance of quantum photonic devices. For example, we recently showed how certain entangled photon states can be robustly transported using topological resonator arrays [Phys. Rev. Lett. 122, 066601 (2019)].
While I am a theorist, I am passionate about bringing recent discoveries towards real world applications benefiting wider society by collaborating with experimental groups in China (Prof. Zhigang Chen, Nankai University), the USA (Prof. Mikael Rechtsman, Pennsylvania State University), and Australia (Prof. Yuri Kivshar, Australian National University).
Quantum processors currently being developed on the road to a large-scale fault-tolerant quantum computer offer new opportunities for how we do materials science. Indeed, quantum algorithms promise the ability to simulate the certain properties of complex materials that are intractable using existing classical computers. One area of active research is the development of quantum algorithms for first-principles simulation of large complex molecules. We have been studying the potential capabilities and limitations of quantum algorithms capable of running on near-term quantum hardware, including the design of shallow circuits to compute the ground state energies of small molecules [Phys. Rev. A 108, 022416 (2023), Quantum Sci. and Technol. 9, 025003 (2024)]. One area we are currently exploring is to generalize these results to finite-temperature systems and periodic (crystalline) materials.
It is interesting to note that despite a lot of hype regarding the potential capabilities of quantum computers, very few quantum algorithms have been rigorously proven to offer useful speed-ups compared to the best classical algorithms, the most famous example being Shor's algorithm for factoring large numbers. In fact, most quantum algorithms currently being explored today are expected to not be useful in practice. One interesting exception is quantum algorithms for topological data analysis, which have been discovered only in the last few years [Adv. Phys.: X 8, 2202331 (2023)]. Thanks to the nature of topological data analysis methods (computing combinatorial properties of relatively small input datasets), there can be an exponential quantum speedup compared to the best classical algorithms in certain limits. I would like to benchmark these newly-developed algorithms on large-scale data analysis problems in quantum chemistry, materials science, and photonics.
There is growing interest in applying machine learning techniques to not only better understand complex physical systems, including topological and correlated quantum phases of matter, but to solve a variety of practical problems including the inverse design of materials such as photonic crystals with desired properties, processing of experimental data, and even optimal control of complex experiments. Popular techniques such as artificial neural networks require big data and computational resources. Moreover, it becomes difficult understand how the trained model works and when it may fail. These limitations motivate studies of explainable machine learning techniques based on easily-interpretable features of the input data.
Topological data analysis is a powerful approach for understanding complex datasets which attracts growing interest in the physical sciences. One approach taken by topological data analysis, known as persistent homology, is to study the persistence of various topological features of the data (e.g. clusters and cycles) across a range of scales in order to infer its shape in a manner which is robust to noise. The most significant features persist over a wide range of scales. This information can be encoded in a persistence diagram which tracks the birth and death scales of the topological features. Topological data analysis has already been fruitfully applied to diverse fields, including feature detection in complex biochemical datasets and even analysis of voting patterns of USA Congress members. I am interested in applying topological data analysis techniques such as this to better understand the properties of complex physical systems and materials.
Our preliminary work has focused on how persistent homology can be used to understand the behaviour of widely-used toy models in condensed matter physics. Applications we have considered include the characterization of topological phase transitions in tight binding models [APL Photonics 6, 030802 (2021)] and the detection of order-disorder and localization transitions in the Aubry-Aubry-Harper model [Phys. Rev. B 106, 054210 (2022)]. Our ongoing research is aiming to apply these methods to better understand the dynamics of complex quantum systems, including many-body quantum scars.
More broadly, I am interested in how other techniques developed by the machine learning community can change the way we do physics and materials science. For example, automatic differentiation has been integral to speeding up the training of large-scale artificial neural networks. Automatic differentiation libraries now exist for popular programming languages such as Python and Julia. One application is tocombine these libraries with multiphysics modelling or materials design codes to rapidly optimize the design of devices. Another potential application is the efficient mesh-free numerical simulation of complex systems by training highly flexible variational models, an approach known as physics-inspired neural networks.