本篇論文利用超導量子位元(superconducting transmon qubit)實現量子光學。
首先我們利用強且與量子位元共振的驅動光照在置於一微傳輸線末端的單 顆超導量子位元上,使其產生莫洛三重態(Mollow triplet),再利用微弱的探測光 探測量子位元的狀態。我們發現在莫洛三重態(Mollow triplet)的頻率之間,反 射的探測光有 7%的放大現象。一般來說,在光學或微波領域要產生光放大的機 制,必須有很強的驅動光使材料產生居量反轉,進而產生受激放射。但這裡的光 放大機制並非由於居量反轉,也非描述於裸量子位元(bare qubit state)基底,更 非描述於綴飾態(dressed state)基底,而是利用四光子過程(four-photon process) 機制,將強驅動光的能量轉換成弱探測光的能量。我們的元件可以在量子資訊過 程和量子極限量測有所應用。由於我們的元件只由單一的二能階量子位元組成, 可以被視為極限微型化的四波混合參數放大器。
再來我們將兩顆超導量子位元鑲在半開放的一維傳輸線上,一個量子位元置 於傳輸線的末端,永遠處在微波電場的腹點,另一個量子位元遠離傳輸線末端的 鏡子,我們可以調控該量子位元處於微波電場的腹點或節點,故可以調控量子位 元與光場交互作用的大小,進而改變量子位元處於環境之真空漲落(vacuum fluctuation)。我們實現量子位元間透過真實光子與虛光子的光媒介交互作用 (photon-mediated interaction)。一方面,由於透過真實光子的交互作用,兩個量 子位元的特徵態會重新組合成新的特徵態,稱為亮態(bright state)與暗態(dark state),或稱超幅射(superradiant)與次幅射(subradiant)。另一方面,透過虛光 子的交互作用可以觀察到能譜分裂的現象。由於破壞性干涉效應,我們觀測到兩 顆量子位元之間的不去相干交互作用,即使一顆量子位元不會鬆弛,還是能透過 虛光子經由傳輸線與另外一顆量子位元交換激發態。最後在我們的系統觀察到亮 態與暗態(超幅射與次輻射)的對稱轉換。

In this thesis we study quantum optics with superconducting qubit (transmon). Firstly, we demonstrate reflective amplification of a weak probe, using a resonantly pumped superconducting qubit, placed at the end of a transmission line. When driv- ing the qubit strongly on resonance such that a Mollow triplet appears, we observe a 7% amplitude gain for a weak probe at frequencies in-between Mollow triplet. In general, amplification of optical or microwave fields is often achieved by strongly driv- ing a medium to induce population inversion such that a weak probe can be amplified through stimulated emission. This amplification is not due to population inversion, neither in the bare qubit basis nor in the dressed-state basis, but instead results from a four-photon process that converts energy from the strong drive to the weak probe. The device demonstrated in this thesis may have applications in quantum information processing and quantum-limited measurements. Since it consists of a single two-level artificial atom, it can be viewed as the ultimate miniaturization of a four-wave-mixing parametric amplifier.
Secondly, we embed two transmons in a half open transmission line. One qubit sits at the end of transmission line, where is voltage antinode, the other qubit is far away from the mirror, which can be tuned in and out of the node of the field, we can change the spatial structure of modes of the vacuum fluctuations, so that one can tune the coupling strength between the qubit and field. We demonstrate both real and virtual photon- mediated interaction between this two superconducting qubits. On the one hand, due to real photon-mediated interaction, the eigenstates of two transmon qubits recombined into new eigenstates, which is bright (superradiant) and (subradiant) dark state. On the other hand, virtual photon-mediated interaction exhibits the splitting in our system. Due to the destructive interference effect, one can see the decoherence-free interaction between two qubits in our system, i.e. even if the qubit can not relax into the transmis- sion, one can still exchange excitations via virtual photons in the transmission line to the other qubit. We also demonstrate symmetry transition of the bright state (superradiant) and dark state (sub radiant).

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