波導量子電動力學中的超導人造原子波混頻研究

Abstract

在本論文中，我們以理論方式研究一維波導量子電動力學系統中的量子波混頻現象。該系統是由一個多能階 transmon 同時受到兩組相干微波場的驅動所組成。我們結合 Floquet 理論與 Dyson 展開，系統性地分析導致頻譜邊帶產生的多光子過程。本研究架構顯示，透過調控兩組驅動場的相對功率與失諧量，可以實現可調式頻率轉換，從而產生可調式頻率梳。進一步地，當我們將 transmon 的更高能階納入考量時，發現新的量子途徑會對頻譜響應產生顯著影響。根據本理論進行的數值模擬結果與實驗頻譜高度吻合，驗證了我們方法的正確性。本研究成果對於發展量子光子元件具有重要意義，包括頻率轉換器、具頻率選擇性的光子路由器，以及片上光源等。

In this thesis, we theoretically investigate quantum wave mixing in a one-dimensional waveguide quantum electrodynamics (QED) system comprising a multi-level transmon qubit driven by two coherent microwave fields. By combining Floquet theory with Dyson series formalism, we systematically analyze the multi-photon processes responsible for generating spectral sidebands. Our framework shows that frequency conversion can be engineered by tuning the relative powers and detunings of the driving fields, enabling the creation of tunable and symmetric frequency combs. By including higher energy levels of the transmon, we identify new quantum pathways that significantly affect the spectral response. Numerical simulations based on our theory show excellent agreement with experimental spectra, validating our approach. These findings provide valuable insights for the development of quantum photonic devices such as frequency converters, frequency-selective photon routers, and on chip light sources.