壹：液氦上准一維維格納晶體的雙穩態; 貳：超導共面波導共振腔

Abstract

在這本碩士論文的第一部份, 我們調查了液態氦表面電子晶體(維格納晶體Wigner Solid, 電子於液態氦表面形成二維晶格)從漣漪極化子(凹陷晶格Dimple Lattice, 液態氦表面上電子對鄰近的液態氦極化造成的凹陷晶格)中解偶的雙穩態。 我們於此實驗使用的樣品，其兩側有著微通道矩陣形成了儲存電子的電子庫，在兩個微通道矩陣中間隔著一個微通道，此中央微通道內的電子密度以及限制電子的靜電場強度被其兩側以及正下方的電極控制，其中正下方的電極於實驗中是低於液氦表面的，允許我們控制中央微通道內准一微電子晶體的排列行數，能控制的範圍由一行至數十行。 我們發現於重複的線性增加電壓下，維格納晶體的解偶力閥值並非一個常數，而是一個隨機的類高斯分佈。我們演示了於連續的正弦電壓驅動下，每個交流循環中整個電子系統會被鎖定於兩種傳輸模式的一種：耦合傳輸模式或是解偶傳輸模式，我們觀察到這種由於維格納晶體解偶力分佈造成的傳輸模式自發性類電報切換。 為了更進一步的調查如維格納晶體雙穩態的高頻電子動力學，我們採用了超導共面波導(Coplanar Waveguide)共振腔，共面超導共振腔能以千兆赫等級的共振頻率與電子作用，共振腔裝置近期也被多個研究團隊用於控制液態氦表面電子。 所以於論文的第二部分，我們討論了高品質因子超導共面波導共振腔的理論、設計及製程，品質因子表示著一個共振電路的損耗，高品質因子(Quality Factor)代表著低損耗以及高靈敏度，在這個論文著我們演示了如何製作一個共振腔有著五萬左右的品質因子。同時，我們也調查了共振腔對於環境（溫度以及液態氦覆蓋深度）的靈敏度。

In the first part of this thesis, we investigate the bistability of decoupling of an electronic crystal (Wigner solid, WS) from ripplonic polarons (or ‘dimple lattice’, DL) formed at the surface of liquid helium. In the device we used for this experiment, two arrays of microchannels form electron reservoirs, which are separated by a single microchannel. The electron density and the strength of the electrostatic confinement in this central microchannel are controlled by side gate electrodes, and a bottom gate electrode that is positioned underneath the helium. This allows us to control the number of electron rows in the quasi-one-dimensional electron lattice formed in the central microchannel, from one to several tens. We find that under repeated driving voltage ramps, the decoupling threshold force of the WS from the DL is not a constant but exhibits a Gaussian-like distribution. We then demonstrate that, under continuous sinusoidal driving voltage, the electron system can become locked in one of two transport modes: the decoupling transport mode (decoupling does occur) or coupling transport mode (decoupling does not occur). We observe a spontaneous telegraph-like switching between these transport modes that arises due to the distribution in the decoupling threshold force. To further investigate the high frequency electron dynamics such as the bistability of the WS, we adopt the superconducting coplanar waveguide (CPW) resonator, which can interact with electrons at GHz frequencies. These devices have recently been adopted by some research groups for the control of electrons on helium. So, in the second part of the thesis, we discuss the theory, design, fabrication and measurement of high quality-factor superconducting CPW resonators. We demonstrate the fabrication of resonators with quality factor around 105. Also, we investigate the sensitivity of these devices to temperature and the surrounding liquid helium.