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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 管希聖 | |
| dc.contributor.author | Bai-Cian Ke | en |
| dc.contributor.author | 柯百謙 | zh_TW |
| dc.date.accessioned | 2021-05-20T20:09:24Z | - |
| dc.date.available | 2010-07-31 | |
| dc.date.available | 2021-05-20T20:09:24Z | - |
| dc.date.copyright | 2009-07-31 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-30 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9105 | - |
| dc.description.abstract | 最近，一種新型的放大器，稱為約瑟夫森分支放大 （JBA），用以測量超導量子位元（qubit），已經被提議和建造出來。JBA 解決了建構在傳統超導 Josephson junction 量子位元測量裝置的散熱問題，此惱人的散熱問題是由此裝置的電壓切換到 normal state 所引起 。本論文旨在模擬使用 JBA 測量量子位元的過程，並提供對理解量子測量問題所必需的相關知識。我們一開始回顧一些基本的超導量子電路元件，並介紹兩種不同類型的量子位元：flux qubit 和 charge qubit。由於 Josephson junction 的非線性電感，JBA 的數學模型可由驅動非線性振盪器所描述，此數學模型被稱為 Duffing 振子。因此，我們著重於量子 Duffing 振子的性質和介紹 JBA 的運作原理。測量量子位元的過程本身是一個開放量子系統的問題。為了來描述它的行為，我們推導了驅動 Duffing 振子和量子位元系統的縮減密度矩陣的 quantum master equation。我們區分了熱環境和測量裝置對系統的影響，並使用 Floquet formalism 處理時間上的週期性問題。並在最後提出一些 Duffing 振子和量子位元測量的模擬結果。 | zh_TW |
| dc.description.abstract | Recently, a new type of amplifier, called the Josephson bifurcation amplifier (JBA), to read out the state of a superconducting quantum bit (qubit), has been proposed and constructed. This JBA has solved the annoying dissipation problem of voltage switching to the normal state in traditional superconducting Josephson junction based qubit measurement devices. This thesis aims to model the qubit readout process by the JBA, and to provide the essential input toward the understanding of the quantum measurement problem. We first review some basic elements of superconducting quantum circuit, and introduce
two different types of qubits: flux qubits and charge qubits. Due to the nonlinear inductance of a Josephson junction, the mathematical model of the JBA can be linked to a driven non-linear oscillator, known as the Duffing oscillator. So we focus on the properties of the quantum Duffing oscillator and present the operation principles of the JBA. The qubit readout process is itself an open quantum system problem. To describe its dynamics, we derive the quantum master equation for the reduced density matrix of the combined driven quantum Duffing oscillator and qubit system. We distinguish the influence of the thermal environment on the combined system from that of the measurement device, and use the Floquet formalism to tackle the time-periodical driven problem. Simulation results of the Duffing oscillator and qubit measurement will be presented. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T20:09:24Z (GMT). No. of bitstreams: 1 ntu-98-R96222018-1.pdf: 1511224 bytes, checksum: 778ab74e83ec33a28691522bb76e2e1f (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Introduction to superconducting quantum bits . . . . . . . . . . . . . . . . 4 2.1 Josephson junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 The Josephson effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 A Josephson junction with a nonlinear inductance . . . . . . . . . . 8 2.1.3 The current-biased Josephson junction . . . . . . . . . . . . . . . . . .9 2.2 The Cooper-pair box and the SQUID . . . . . . . . . . . . . . . . . . . 11 2.2.1 The single cooper-pair box device . . . . . . . . . . . . . . . . . . . 11 2.2.2 The SQUID device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Charge qubits and flux qubits . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Charge qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Advanced charge qubits . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.3 Flux qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.4 Advanced flux qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 The quantronium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 The Josephson bifurcation amplier . . . . . . . . . . . . . . . . . . . . . 22 2.5.1 The quantronium with a JBA readout . . . . . . . . . . . . . . . . . 23 3 The Floquet formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1 The Flouqet theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1.1 General form of the solution . . . . . . . . . . . . . . . . . . . . . . 28 3.1.2 Some properties of quasienergy and QES . . . . . . . . . . . . . . 29 3.2 The extended Hilbert space . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.1 Operators in the extended Hilbert space . . . . . . . . . . . . . . . 32 3.2.2 The Floquet Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Driven two-level systems and oscillators in the Floquet picture . . . 35 3.3.1 Driven two-level systems . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.2 Driven oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3.3 The rotating wave approximation . . . . . . . . . . . . . . . . . . . 39 3.4 Time evolution operators . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4 Quantum dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1 The Density Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.1 Pure states and mixed states . . . . . . . . . . . . . . . . . . . . . . 44 4.1.2 Ensemble average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Derivation of the Master equation . . . . . . . . . . . . . . . . . . . . . 46 4.2.1 Equations of motion of the density matrix of closed systems . . 46 4.2.2 Integro-dierential form of the equation of motion for the density matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2.3 The Born approximation . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2.4 The Markovian approximation and bath correlation functions . . 51 4.3 Master equations of driven systems . . . . . . . . . . . . . . . . . . . . 53 4.3.1 The derivation of master equations . . . . . . . . . . . . . . . . . . 53 4.3.2 Microscopic models of dissipation . . . . . . . . . . . . . . . . . . . 55 5 The quantum Duffing oscillator . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1 Hamiltonian of quantum Dung oscillator . . . . . . . . . . . . . . . 59 5.2 The Floquet-Born-Markovian master equation . . . . . . . . . . . . . . 60 5.2.1 The driven weak-coupling master equation . . . . . . . . . . . . . 60 5.2.2 Complete set property of Floquet states . . . . . . . . . . . . . . . 61 5.2.3 The Floquet master equation . . . . . . . . . . . . . . . . . . . . . . 61 5.2.4 The rotating wave approximation . . . . . . . . . . . . . . . . . . . 63 5.2.5 Dynamics of the quantum Dung oscillator . . . . . . . . . . . . . 63 5.2.6 Expectation value of x(t) . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.3 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.3.1 Amplitude response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.3.2 Varying temperatures and the nonlinearity coefficients . . . . . . 68 5.3.3 Varying driving amplitudes . . . . . . . . . . . . . . . . . . . . . . . 68 5.3.4 Expansion in x space . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.4 Driven quantum Duffing oscillator coupled to a qubit . . . . . . . . 72 5.4.1 The JBA response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.4.2 Behaviors of the qubit . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 A Classical Duffing oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 | |
| dc.language.iso | en | |
| dc.title | 使用約瑟夫森分支放大器的量子測量之研究 | zh_TW |
| dc.title | Study of Quantum Measurement by a Superconducting Josephson Bifurcation Amplifier | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳岳男,周忠憲 | |
| dc.subject.keyword | 量子測量, | zh_TW |
| dc.subject.keyword | Josephson bifurcation amplifier,quantum measurement,josephson junction, | en |
| dc.relation.page | 90 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2009-07-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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