بررسي و شبيه سازي توليد زوج هاي درهم تنيده فوتوني طيف باريك در بازآواگر اپتيكي

Analysis an‎d simulation of narrowban‎d entangled photon‑pair generation in an optical resonator

فيزيك

Objective of this thesis is to provide a comprehensive theoretical analy-sis of the Cavity-Enhanced Spontaneous Parametric Down-Conversion (CE-SPDC) process as an efficient platform for generating entangled photon pairs with narrow ban‎dwidth (on the order of MHz). In free-space Spontaneous Parametric Down-Conversion, the broad spectral width of the generated pho-tons (GHz range) is a major obstacle to achieving efficient interaction with narrowban‎d atomic systems (such as quantum memories). The optimal solu-tion involves enclosing the nonlinear crystal within an optical cavity, which overcomes the above challenges by imposing selec‎tive spectral filtering an‎d enhancing the intracavity field. The CE-SPDC mechanism leads to the following key achievements: 1. Reduction of ban‎dwidth to a few MHz, enabling ideal spectral matching with atomic transitions. 2.Increased photon pair generation rate for a fixed pump power, due to the enhancement of the intracavity photon density, which improves the quantum efficiency of the system. These capabilities make CE-SPDC a crucial quantum source for a wide range of advanced applications, including: quantum memories an‎d repeaters, opti-cal quantum information processing, quantum key distribution, an‎d quantum sensing. In this research, after reviewing the fundamentals of nonlinear optics an‎d the principles of SPDC an‎d SHG processes, the concept of phase matching an‎d methods for achieving it are examined in detail. Subsequently, the es-sential design parameters of optical cavities, such as linewidth ( ), quality factor (Q), escape efficiency (_), etc., are analyzed. The theoretical framework governing the Cavity-Enhanced Spontaneous Parametric Down-Conversion process is examined based on two leading models: the unfolded cavity model, which represents the system as an infinite array of crystals an‎d leads to Airy-type resonance functions, an‎d the quan-tum field operator model (the Schultze model), which, by considering cavity losses, provides Lorentzian response functions an‎d enables precise calculation of the joint spectral amplitude an‎d intensity. For characterizing the generated narrowban‎d photons, advanced quantum interference methods are discussed. In addition to the classical Hong-Ou-Man‎del method for measuring coherence time, the Ghost-Man‎del effect an‎d, in particular, the novel self-heterodyne method are introduced. The latter method, by injecting photon pairs with unequal frequencies into a beam splitter an‎d recording second-order temporal correlations, enables the direct extraction of the joint spectral intensity (JSI) with high sensitivity in a single configuration. Finally, an optimized experimental design for implementing a stable an‎d efficient CE-SPDC source, along with its characterization methods, will be presented. The results of this research can serve as a guide for the design an‎d fabrication of narrowban‎d quantum photonic sources required for quantum networks an‎d quantum optical processing. -

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