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研究生: 陳奕如
Chen, Yi-Ru
論文名稱: 利用加光子在壓縮真空態方式產生貓態
Generation of cat state via photon addition to the squeezed vacuum state
指導教授: 李瑞光
Lee, Ray-Kuang
口試委員: 陳應誠
Chen, Ying-Cheng
吳欣澤
Wu, Shin-Tza
賴暎杰
Lai, Yin-Chieh
林晏詳
Lin, Yen-Hsiang
學位類別: 博士
Doctor
系所名稱: 電機資訊學院 - 光電工程研究所
Institute of Photonics Technologies
論文出版年: 2023
畢業學年度: 112
語文別: 英文
論文頁數: 120
中文關鍵詞: 壓縮光先驅單光子源薛丁格貓量子態斷層掃描
外文關鍵詞: Squeezed light, heralded single photon sources, Schrödinger's cat, quantum state tomography
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  • 在通往光量子計算或量子資訊協議的道路上,準備離散變數(DV)和連續變數(CV)的混合式技術是必要的。 因此,配備高斯態和非高斯態以及進行高斯測量和非高斯測量,對於量子技術的未來應用是極重要的。 “薛丁格貓態”是混合離散變數和連續變數的產物之一,它是非高斯態,由兩個互相相反的相干態疊加。 除了基礎科學研究外,它還是量子計算、量子計量、量子隱形傳態或量子通訊的重要資源。

    在本論文中,我們是台灣第一個利用光參量振盪器(OPO)產生高斯態的壓縮光,並且開發出共模抑制比超過80 dB的平衡式零差偵測器。 此外,我們利用自發參數下轉換實現了非高斯態的單光子態,並且使用超導奈米線單光子偵測器來量測二階相關函數並且透過平衡式零差偵測器來重建維格納函數。

    很令我們有興趣的是混合 DV 和 CV 技術來產生薛丁格貓態。 我們沒有使用從壓縮光中減去光子的傳統方法,而是透過將一個單光子加入到壓縮真空態來首次實現光學“薛丁格貓”的實驗,從而產生高產生率。 這種突破性的技術可用來添加更多單光子,使大尺寸的貓成為可能。


    On the way toward the optical quantum computing or quantum communication protocols, it is essential to prepare the hybrid technique of discrete-variable (DV) and continuous-variable (CV). Thus, equipping the Gaussian state and non-Gaussian state and performing the Gaussian measurement and non-Gaussian measurement are crucial to apply in the future for the quantum technology. The ‘Schrödinger cat state’ which is a non-Gaussian state and a superposition of two opposite coherent states is one of the mixtures of DV and CV. Apart from fundamental science research, it is an important resource for quantum computation, quantum metrology, and quantum teleportation or quantum communication.

    In this thesis, we first generate the Gaussian state of squeezed light via an optical parametric oscillator (OPO) in Taiwan and develop the balanced homodyne detecter with more than 80 dB common mode rejection ratio. In addition, we implement the non-Gaussian state of a heralded single-photon state with spontaneous parametric down-conversion and perform the superconducting nanowire single-photon detector to measure the second-order correlation function and reconstruct the Wigner function via balanced homodyne detecter.

    It is of interest to us to combine DV and CV techniques to produce the Schrödinger cat state. Instead of using the traditional method of photon subtraction from squeezed light, we report the first experimental realization of optical ‘Schrödinger cats’ by adding one photon to a squeezed vacuum state, resulting in a high generation rate. This groundbreaking technique could be used to add more photons to pave the way toward a larger cat size.

    Acknowledgments ii 摘要vii Abstract ix 1 Introduction 1 2 Basics of quantum optics 5 2.1 Quantization of the electromagnetic field . . . . . . . . . . . . 5 2.1.1 Quadrature Operator . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Heisenberg Uncertainty Principle . . . . . . . . . . . . 7 2.2 Quantum state representations . . . . . . . . . . . . . . . . . . 8 2.2.1 Phase Space representation - Wigner function . . . . . 8 2.2.2 Ball-on-stick representation . . . . . . . . . . . . . . . . 9 2.2.3 Sideband representation . . . . . . . . . . . . . . . . . . 10 2.3 Quantum states of light . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 Fock state . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.2 Vacuum state . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.3 Coherent state . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.4 Squeezed state . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.5 Thermal state . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.6 Cat state . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Quantum measurement . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Positive operator valued measures (POVM) . . . . . . 20 2.4.2 Single photon detectors . . . . . . . . . . . . . . . . . . 21 2.4.3 Balanced homodyne detection (BHD) . . . . . . . . . . 21 2.5 Quantum States Tomography (QST) . . . . . . . . . . . . . . . 23 2.5.1 Maximum likelihood estimation (MaxLik) . . . . . . . 24 3 Generation and Detection of Squeezed State 27 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Experimental setups . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.2 Second harmonic generation (SHG) . . . . . . . . . . . 29 3.2.3 Optical parametric oscillator (OPO) . . . . . . . . . . . 31 3.2.4 Mach-Zehnder interferometer (MZ) . . . . . . . . . . . 32 3.2.5 Balanced homodyne detection (BHD) . . . . . . . . . . 33 3.3 Squeezing level . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.1 Optical loss . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3.2 Phase noise . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4 Squeezed state control . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.1 Pump phase . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.2 Measurement phase . . . . . . . . . . . . . . . . . . . . 41 3.5 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 42 3.5.1 Squeezing level . . . . . . . . . . . . . . . . . . . . . . . 43 3.5.2 Squeezed state tomography . . . . . . . . . . . . . . . . 44 Phase calibration . . . . . . . . . . . . . . . . . . . . . . 45 Normalization . . . . . . . . . . . . . . . . . . . . . . . . 45 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . 46 3.5.3 MaxLik vs. ML . . . . . . . . . . . . . . . . . . . . . . . 47 3.5.4 Wigner flow . . . . . . . . . . . . . . . . . . . . . . . . . 49 4 Generation and Detection of Single Photon State 53 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 Experimental setups . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.1 Spontaneous parametric down-conversion (SPDC) . . 55 4.2.2 Filter cavities (FCs) . . . . . . . . . . . . . . . . . . . . . 55 Sample and hold (S&H) . . . . . . . . . . . . . . . . . . 57 4.2.3 Superconducting nanowire single-photon detector (SNSPD) 59 4.2.4 Time-to-digital converter (TDC) . . . . . . . . . . . . . 61 4.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 62 4.3.1 Intensity cross-correlation function G(2)s,i (τ) . . . . . . . 62 4.3.2 Intensity auto-correlation function g(2)s,s (τ) . . . . . . . . 65 4.3.3 Single-photon state tomography . . . . . . . . . . . . . 68 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . 68 Data processing . . . . . . . . . . . . . . . . . . . . . . . 68 5 Generation and Detection of Cat State 75 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 Theory of cat state generation . . . . . . . . . . . . . . . . . . . 75 5.2.1 Photon subtraction from squeezed vacuum state . . . . 75 5.2.2 Photon addition to squeezed vacuum state . . . . . . . 77 5.3 Experimental setups . . . . . . . . . . . . . . . . . . . . . . . . 79 5.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4.1 Cat state tomography . . . . . . . . . . . . . . . . . . . 83 6 Conclusion and Outlook 89 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 6.2 Pathfinding research . . . . . . . . . . . . . . . . . . . . . . . . 90 A Programs 93 A.1 Arduino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 A.1.1 TTL signal . . . . . . . . . . . . . . . . . . . . . . . . . . 93 A.2 Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.2.1 Frequency filtering with Pykat . . . . . . . . . . . . . . 100 A.2.2 Get histogram for G(2)s,i measurement by QuTAG . . . . 103 A.2.3 Get timstamps for g(2)s,s 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