超導穿隧接合元件於電路量子電動力學中的量子冷凍機之應用

Superconducting Tunnel Junctions for Refrigeration Applications in Circuit Quantum Electrodynamics

張佑誠(Yu-Cheng Chang)

指導教授 ： 管希聖 ； 陳啟東

國立臺灣大學/理學院/物理學研究所/博士(2019年)

https://doi.org/10.6342/NTU201901972

摘要

近年來電路量子電動力學的蓬勃發展，提供了一個研究基礎物理的平台，並使得積體電路的製程、設計及整合概念得到延伸，進而發展多樣且具實用性的感測元件，甚至於目前備受矚目的超導量子電腦。然而這些元件需操作於低溫環境下，任一造成電子溫度上升的熱源，將導致元件給予錯誤的訊息，因此供給額外電子冷卻能力的量子冷凍機將在電路量子電動系統中扮演極其重要的角色。為實現量子冷凍機，我們明確製訂出一步步待完成的階段性研究，一、光量子熱閥，二、熱儲與超導共振腔耦合能之設計，三、光子熱整流器，四、量子奧圖冷凍動機之實現。本論文將討論已實現的光量子熱閥及熱儲與超導共
振腔耦合能之設計。在此論文中，我們研究電路設計的人工原子經由電容式耦合至左右兩個相同且與有限容積熱儲耦合的超導微波共振腔，藉由調變人工原
子的能階可以改變左右熱儲間的熱傳輸量，形同可控制熱傳輸的閥門，並在共振腔-熱儲與共振腔-人工原子，兩耦合能的互相較勁下，構成兩種截然不同的傳輸機制，最後實驗結果與理論計算彼此相互呼應。實驗上，將電子束微影技術所製作的三種超導穿隧接合設計成上述的各個元件：一、超導體-一般金屬-超導體接合作為有限熱容積的熱儲，結合四分之一波長的共平面波導共振腔，形成在特定頻譜的微波接受器及發射器，二、一般金屬-絕緣體-超導體接合可作為具有高靈敏度的電子溫度計，偵測熱儲溫度可計算其吸收或是釋放的熱量，三、並聯的超導體-絕緣體-超導體接合構成可調變能階的人工原子，在本實驗中，暨為目前廣泛應用於超導量子電腦中的量子位元(transmon)。其熱的傳輸途徑是由熱儲經電子-光子的交互作用激發共振腔內的光子，間接激發人工原子，釋放光子傳遞至另一個熱儲，光子能量與人工原子內能階的差距及光子的數量會影響光子傳輸的數量，同時影響熱傳輸量，形同一個可調的光子熱傳輸的量子熱閥，並在量子冷凍機中，扮演操控熱傳輸的重要角色。
此外，為了解實際的人工原子和共振腔之間的耦合能，及避免熱儲的高電性損耗特性，消耗掉可觀測的光子，實驗上移除了熱儲並設計了第三個共振腔，以微弱的電容式耦合到人工原子，在以非破壞性測量的條件下，窺探人工原子能階的調變及與超導共振腔間的交互作用。共振腔和熱儲間的耦合能可決定兩熱儲間的最大熱傳輸功率，以及熱傳輸的調變量，但在與熱儲強耦合的共振腔，微波訊號表徵微小，藏身於背景訊號中，在擷取技術上相當難度。實驗上，我們利用鈮超導體作為四分之一波長共平面波導共振腔的主體，波導中心線在電壓波節點處以鋁-銅-鋁結構取代，並藉由分別量測穿透係數在元件溫度高於及低於鋁超導相變溫度，來分析其共振特性。量測銅厚度為50 奈米到150 奈米不同的元件，得到品質因子為10~67，考量超導耦合與安德烈夫反射在微波電流下的電性反應，量測結果在合理的理論預測範圍。

關鍵字

電路量子電動力學 ； 量子冷凍機 ； 超導微波共振腔 ； 超導轉變 ； 低品質因子

並列摘要

Circuit quantum electrodynamics has flourished in recent years. It provides a platform for studying fundamental physics that helps to extend the concept of process, design and integration of integrated circuits. It has been applied to the areas of versatile quantum sensing as well as superconducting quantum computing. However, these applications require an ultralow temperature environment – any heat source that raises the electron temperature can induce error. Therefore, a quantum refrigerator capable of proving electron cooling plays a crucial role in the circuit quantum electrodynamic system. To realise the quantum refrigerator, we propose and demonstrate a clear, step-bystep scheme. Step I, tunable photonic heat transport in a quantum heat valve. II, design of the coupling between the heat reservoir and superconducting coplanar waveguide (CPW) resonator. III, photonic heat rectifier. IV, Implantation of Otto refrigerator. In this thesis, we will discuss the realisation of this scheme, including step I and II.
We study heat transport through an assembly consisting of a superconducting qubit capacitively coupled between two nominally identical coplanar waveguide resonators, each equipped with a heat reservoir in the form of a normal-metal mesoscopic resistor termination. We report the observation of tunable photonic heat transport through this resonator–qubit–resonator assembly, and find that the reservoir-reservoir heat flux depends on the ratio of the qubit–resonator and the resonator–reservoir coupling strengths. The assembly displays qualitatively different behaviours in different coupling regimes. Our quantum heat valve is relevant for the realisation of quantum heat engines and refrigerators, which can be obtained, for example, by exploiting the time-domain dynamics and coherence of driven superconducting qubits. This effort would ultimately bridge the gap between the fields of quantum information and thermodynamics of mesoscopic systems.
Characterisation of the coupling strength between a coplanar waveguide resonator and the heat reservoir is a prerequisite for understanding and implementation of this hybrid assembly. Due to the need of a highly dissipative channel, the quality factor of the resonator is inevitably low. In this thesis, we also present a method for determination of the quality factor of a resonator coupled strongly to the heat reservoir and experiments on λ/4 superconducting niobium CPW resonators terminated at the antinode by a dissipative copper microstrip via an aluminium lead. The dissipation of these resonators is high so that it is not possible to determine their very low quality factors using the conventional transmission spectrum analysis technique. Our method involves a comparison of the transmission characteristics above and below the superconducting transition of the aluminium lead, which enable us to identify the resonance. This method is experimentally verified with increasing thicknesses of the copper microstrips from 50 nm to 150 nm, which results in quality factors of 10~67, as expected from our calculations.

並列關鍵字

circuit quantum electrodynamics ； quantum refrigerator ； superconducting microwave resonator ； superconducting transition ； low quality factor

參考文獻

[1] Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature, 398(6730):786–788, April 1999.

[2] D. Vion. Manipulating the Quantum State of an Electrical Circuit. Science, 296(5569):886–889, May 2002.

[3] John Clarke and Frank K. Wilhelm. Superconducting quantum bits. Nature, 453(7198):1031–1042, June 2008.

[4] A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature, 431(7005):162–167, September 2004.

[5] M. H. Devoret and R. J. Schoelkopf. Superconducting Circuits for Quantum Information: An Outlook. Science, 339(6124):1169–1174, March 2013.