High-dimensional entanglement with larger Hilbert spaces enable an encoding of more bits per photon and thus promise increased communication capacities over quantum channels. Quantum frequency combs, which are intrinsically multimode in the temporal and frequency degrees of freedom within a single spatial mode, naturally facilitating the generation and measurement of high-dimensional entanglement. Current challenges include the extension of well-known methods for two qubits to high-dimensional quantum systems and their application in entanglement experiments with photons. More specifically, the major challenge is the certification of high-dimensional entanglement by a number of accessible experimental measurements. In this paper, we increase the Hilbert space dimensionality and provide versatile tools for quantifying and certifying high-dimensional entanglement in a biphoton frequency comb. We quantify the time binned Schmidt number up to 18 and certify entanglement of formation with 1.89 ebits. We have demonstrated a 648- dimensional Hilbert spaces with time-frequency entanglement in a biphoton frequency comb, enabling a computational space up to 13 photonic qubits, and 6.28 bits/photon classical information capacity. This high-dimensional time frequency multimode quantum states of biphoton frequency comb significantly boosting the photon information capacity that is critical for large-scale quantum information processing. Biphoton frequency comb has indeed demonstrated an attractive and powerful approach towards achieving this fundamental goal with applications in high-dimensional quantum information processing, time-frequency cluster-state quantum computation, high-dimensional encoding in quantum networks, and high-dimensional quantum simulations.
Amorphous photonic materials offer an alternative to photonic crystals as a building block for photonic integrated circuits due to their shared short-range order. By using the inherent disorder of amorphous photonic materials, it is possible to design flexible-shaped waveguides that are free from restrictions of photonic crystals at various symmetry axes. Effects of disorder on photonic crystal waveguide boundaries have examined before, and it is shown that flexible waveguides with high transmission are possible by forming a wall of equidistant scatterers around the defect created inside amorphous material configuration. Based on this principle, waveguides with various flexible shapes are designed and fabricated for planar circuit applications. A silicon-on-insulator (SOI) slab with random configuration of air hole scatterers is used. The amorphous configuration is generated through realistic Monte Carlo simulations mimicking crystalline-to-amorphous transition of semiconductor crystals via an assigned Yukawa potential to individual particles. The design parameters such as average hole distance, slab thickness and hole radius are adjusted so that the waveguide is utilizable around 1550 nm telecommunications wavelength. Such waveguides on slab structures are characterized here and the level of randomness and band gap properties of amorphous configurations are analyzed in detail. These efforts have the potential to lead easier design of a wide range of components including but not limited to on-chip Mach-Zehnder interferometers, splitters, and Y-branches.
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