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Topological photonics is the study of how the geometries and topologies of devices can be used to manipulate the behavior of photons. Many topological models exhibit edge states, a defining feature of these models, which travel around the perimeter of the lattice and are not affected by disorder. These edge states can help create scalable delay lines, quantum sources of light, and lasers all of which are robust against fabrication-induced disorder and bends in photonic structures. This research proposal is structured into two parts.

In the first half of this thesis, we investigate a topological model and study some of its quantum applications. First, we realize the anomalous quantum Hall effect in a photonic platform using a 2D array of ring resonators with zero flux threading the lattice. The lattice implements a Haldane model by using the next-nearest couplings in lattice to simulate a nonzero local gauge flux while having a net flux of zero. The lattice hosts edge states, which are imaged through a CCD camera and show robustness against missing site-defects, 90 degree bends and fabrication-induced disorder. We also demonstrate a topological non-trivial to trivial phase transition by simply detuning the ring resonances. Next, we show degenerate photon pair creation in an anomalous quantum Hall device using a dual-pump spontaneous fourwave mixing process. The linear dispersion in the edge band results in an efficient phase matching and shows up as maximum counts in spectral correlations. The flatness of edge band also allows us to tune the bandwidth of the quantum source by changing the pump frequencies. Furthermore, we verify the indistinguishability of the photons using a Hong-Ou-Mandel (HOM) experiment. Finally, we simulate the transport of time-bin entangled photons in an integer quantum Hall device. The edges states preserve the temporal correlations and are robust against fabrication induced disorder. In contrast, the bulk states in the device exhibit localization, which is manifested in bunching/anti-bunching behavior.

In the second part, we explore a few experimental quantum optics techniques developed as a part of investigating quantum transport in topological devices. We

demonstrate two experimental techniques:

  1. We use an EOM-based time-lens technique to resolve temporal correlations of time-bin entangled photons, which would have been otherwise inaccessible due to the limited temporal resolution of single photon detectors. Our time-lens also maps temporal correlations to spectral correlations and provides a way of manipulating frequency-bin entangled photons.

  2. We show frequency-resolved interference of two and three photons distinguishable in time, which would not have interfered in a standard Hong-Ou-Mandel (HOM) setup. Our setup can be extended to implement temporal boson sampling using phase modulators. Furthermore, we demonstrate time-reversed HOM-like interference using time-bin entangled photon pairs and show that the spectral correlations are sensitive to phase between photons.

Lastly, we demonstrate some miscellaneous experimental techniques, such as the design of the electronics used for time-lens, optimal spontaneous parametric down conversion parameters, measuring joint spectral intensity using a chirped bragg grating, and simultaneous measurement of Hong-Ou-Mandel interference for different frequencies.