بررسي اثر هاي خميدگي فضا بر برخي فرآيند هاي اپتيك كوانتومي و امكان سنجي برپايي چيدمان تجربي طيف سنجي كوانتومي

Investigation of the spatial curvature effects on some quantum optical processes an‎d the feasibility of implementing an experimental setup of quantum spectroscopy

فيزيك

In this thesis, we first review the properties of stan‎dard coherent states an‎d their generalization to curved spaces. We then turn to one of the most fundamental processes in quantum optics: parametric down-conversion. As a key application of this process, quantum spectroscopy is introduced. Next, we investigate the effects of spatial curvature on induced parametric down-conversion, employing coherent states defined on curved manifolds. In particular, we analyze the quantum statistical properties of the output states of this process an‎d their dependence on spacetime curvature. The subsequent step of this research involves incorporating thermal effects. After a brief introduction to the thermo-field dynamics formalism—used to include temperature in quantum optical processes—we define temperature-dependent coherent states on the circular manifold an‎d examine their essential quantum statistical features. Building on this, we adopt a combined approach: using these new states, we study the simultaneous influence of spatial curvature an‎d temperature on atom–field interactions within the Jaynes–Cummings model. Finally, by applying the Gilmore–Perelomov approach, we introduce a novel family of coherent states on the circle an‎d propose a unique experimental method for their laboratory realization.

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