此論文藉由理論、數值模擬和實驗方法，探討在一維微波波導管中設計超導人造原子選擇定則的手段。在此環境中，多個頻率的微波都參與作用。我們的目標是創造沒有自發輻射的亞穩態，用以實現微波波導管中的電磁誘發透明，並使其具有可調控頻率的性質。然而常見的 transmon 型超導人造原子在一維開放空間中並沒有亞穩態。透過費米黃金律，我們分別研究兩種通用的方法抑制自發輻射，並以 transmon 型人造原子為平台研究此一課題。

第一種方法是抑制介質的躍遷偶矩。我們使用兩個耦合的 transmon 型量子位元以形成超導人造「分子」。其第一激發態到基態有較小的躍遷偶矩，而第二激發態到基態的躍遷偶矩則較強。在兩個位元處於簡併態下，此系統自發形成一個孤立的亞穩態。藉由我們所提案的參數調制方法，其激發態和亞穩態之間能夠進行電場無法驅動的狀 態轉換。因此，此人造分子在參數調制下形成一個 Λ 型能階。我們並以數值模擬演示 此系統作為可調頻之電磁誘發透明介質的可行性。在實驗中，我們觀察到參數調制能夠驅動激發態與另一孤立能階之間的拉比振盪。然而，頻譜分析指出此系統是一個 Ξ 型能階，而非 Λ 型能階。另外，其時域反應指出了此一孤立能階和激發態具有相似的 去相干率。因此，電磁誘發透明並沒有在這個架設中被觀察到。

第二種方法是抑制波導管中特定頻率的真空擾動。我們研究一個具有單一邊界反射 的一維波導管。多個模態的電磁場以駐波形式存在於此空間中。我們將一個 transmon 放置在微波波導管中，並距離其邊界不遠處。人造原子所暴露真空擾動的振幅，取決 於其共振波長以及其在波導管中的位置。因此，原子所感受到的真空擾動在特定頻率 可以被抑制，我們將原子的共振頻率調控在真空擾動的駐波節點以抑制自發輻射，藉 此創造亞穩態。我們並在此架設中演示一種非典型的 Λ 型電磁誘發透明。

此論文闡述研究動機、理論背景、數值方法、元件設計與製作、量測方法及結果。

This thesis addresses our studies on engineering the selection rules of superconducting artificial atoms in the architecture of waveguide quantum electrodynamcis, in which a broadband of microwave comes into play. The goal is to create a meta-stable state free of spontaneous relaxation. It does not exist in a transmon-type artificial atom when embedded in an open space. The purpose is for realizing electromagnetically induced transparency (EIT) with frequency tunability in a microwave waveguide. We use transmon-type artificial atoms to study two universal approaches suggested by Fermi’s golden rule.

The first approach is by eliminating the inherent transition moment between certain levels in the media. Two frequency-tunable transmon qubits are paired up to form an artificial ”molecule”. The fi rst excited state |−⟩ of the molecule has a suppressed dipole moment, while the second excited state |+⟩ features an enhanced dipole moment. In particular, when the two qubits are biased on resonance, |−⟩ becomes an isolated meta-stable state |D⟩. Meanwhile, |+⟩ reaches a maximally dissipative state |B⟩. Parametric modulation on one of the qubits is able to activate the dipole-forbidden transition between |B⟩ and |D⟩. Therefore, the parametrically modulated transmon pair forms an effective Λ-system. We numerically demonstrate a frequency-tunable Λ-type EIT scheme through this approach. In the experimental study, the energy tunability and spontaneous relaxation of the |+⟩ state is characterized. We also observe that the dipole-forbidden transition between |B⟩ and |D⟩ is activated via our proposed parametric modulation. However, the spectroscopy implies that the system confi guresa Ξ-type level, instead of a Λ-type structure. In addition, the time dynamics infers a comparable decoherence rates between |−⟩ and | + ⟩. Therefore, EIT is missing in the device.

The second approach is by eliminating the vacuum fluctuation of certain frequency at specific position in a waveguide. A standing-wave-like multi-mode space is formed in a semi-infi nite waveguide, which is a regular waveguide interrupted by a boundary. In such a space, the magnitude of vacuum fluctuation depends both on the wavelength of the mode, and on the position in the waveguide. In particular, the wavelength of each mode specifies amplitude ”nodes” in certain positions. A typical tunable transmon is placed at a distance from the end of the waveguide. The frequency-dependent spontaneous relaxation is characterized. We selectively eliminate the vaccum fl uctuation at targeted transition in order to create a meta-stable state. An unconventional Λ-type EIT is experimentally demonstrated.

This thesis describes the motivation, theoretical background, numerical method, design, implementation and measurement results of the study.

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