Topological Edge States in the Quantum Rabi Model Using Trapped-Ion Quantum Simulator = 갇힌 이온 양자 시뮬레이터를 사용한 양자 라비 모델의 토폴로지에지 상태 연구

다국어 초록 (Multilingual Abstract)

The quantum Rabi model(QRM) is the simplest and most fundamental model that de scribes the quantum light-matter interactions. However, because the coupling strength is much smaller than the atomic frequencies, the anti Janyes-Cumming(JC) term is often neglected, making it challenging to experimentally realize the model’s full rich ness. Recently, quantum simulation techniques using trapped ions, photonic wave guide system, and circuit QED have enabled the study of various physical phenomena of the QRM. In this work, we study the generalized resonant Rabi model (GRRM), a variant of the quantum Rabi model that exhibits nontrivial topological properties. In the GRRM, the JC and anti-JC couplings are treated independently, and both bosonic and spin frequencies are set to zero. This model exhibits parity symmetry, ˆ Π=eiˆ a†ˆ aˆ σz, which divides the Hilbert space into two decoupled parity chains, analogous to the Su–Schrieffer–Heeger (SSH) model. Using a trapped-ion quantum simulator, we realize the GRRM and prepare its topological edge state via adiabatic state preparation. The edge state, identified as a squeezed vacuum, is characterized by quadrature measurements and phonon-number distribution. Our results confirm squeezing, even-parity Fock state composition, and exponential localization—all signatures of a topological edge state

국문 초록 (Abstract)

양자Rabi 모델(QRM)은양자빛-물질상호작용을설명하는가장단순하고근본적 인모델이다.하지만일반적으로결합세기가전이주파수보다훨씬작기때문에,회 전파근사(rotating wave approximation)에서는 반 Jaynes–Cummings(anti-JC) 항을 종종생략하며,이로인해모델의풍부한특성을실험적으로구현하는것이어렵다. 최근에는트랩이온,광자도파로시스템,그리고회로QED를활용한양자시뮬 레이션기법을통해QRM의다양한물리현상을연구할수있게되었다. 이연구에서는비자명한위상특성을보이는변형된양자Rabi모델인일반화 공명Rabi모델(GRRM)을연구한다.GRRM에서는JC항과anti-JC항이독립적으 로다뤄지며,보손및스핀의주파수는모두0으로설정된다.이모델은다음과같은 파리티대칭성을가진다: ˆ Π=eiˆ a†ˆ aˆ σz, 이대칭성은힐베르트공간을두개의서로분리된파리티체인으로나누며,이는 Su–Schrieffer–Heeger (SSH) 모델과 유사하다. 트랩이온양자시뮬레이터를사용하여우리는GRRM을구현하고,g2/g1값을 점진적으로변화시켜그위상엣지상태를가역적으로준비하였다.이엣지상태는 압착진공상태로확인되며,포논수분포와사분면(quadrature)측정을통해특성화 되었다. 우리의결과는압착(squeezing), 짝수 파리티 폭 상태 구성, 그리고지수적 국소화등—위상엣지상태의모든특징을확인하였다

목차 (Table of Contents)

• Chapter 1. Introduction 1
• 1.1 Spin-Boson Model 2
• 1.2 Quantum Rabi Model 3
• 1.3 Generalized Resonant Rabi Model 4
•  1.3.1 Chiral Symmetry 6
• 1.4 Trapped-Ion Qubits 8
•  1.4.1 Advantages of Trapped-Ion Qubits 9
•  1.4.2 Motional Modes as Bosonic Degrees of Freedom 10
•  1.4.3 Stimulated Raman Transitions and Spin–Motion Coupling 10
•  1.4.4 Applications in Quantum Simulation 11
• Chapter 2. Ion Trap System & Experimental Setup 13
• 2.1 The 171Yb⁺ Ion Qubit 15
•  2.1.1 Ion Loading Procedure 19
• 2.2 Experimental Setup: Cryogenic Ion Trap System 20
•  2.2.1 Cryogenic Ion Trap System 22
•  2.2.2 Trap Structure Design 25
•  2.2.3 In-Chamber Components 28
•  2.2.4 In-Chamber Optical System 31
• Chapter 3. Stimulated Raman Transition 34
• 3.1 Introduction 34
• 3.2 Stimulated Raman Transition 35
•  3.2.1 Spin-dependent force 39
• 3.3 Simulation of Quantum Rabi Model 42
• 3.4 Experimental Setup 43
•  3.4.1 Optical Phase locking Loop 43
•  3.4.2 Raman Optical Setup 47
• 3.5 Raman Gate Operation 49
•  3.5.1 Co-Propagate Raman Operation 49
•  3.5.2 Counter-Propagate Raman Operation 51
• 3.6 Comparison between 370 nm CW Laser and 355 nm Mode-Locked Laser 53
• Chapter 4. Individual Addressing Using Multi-channel AOM 59
• 4.1 Introduction 59
• 4.2 Setup design 60
• 4.3 Intensity profile of focused Gaussian beam with finite aperture 67
• 4.4 Ray-tracing simulation 68
• 4.5 Results & Discussion 69
• Chapter 5. Topological Properties of Generalized Resonant Rabi Model 79
• 5.1 Introduction 79
• 5.2 Bogoliubov Transformation 81
•  5.2.1 Topological Edge State in GRRM 83
•  5.2.2 First Excited State in the Trivial Phase 84
• Chapter 6. Quantum Simulation of Topological Edge State in GRRM 88
• 6.1 Introduction 88
• 6.2 Adiabatic State Preparation 89
•  6.2.1 Expected Key Features of the Target State 91
•  6.2.2 Experimental Scheme 92
•  6.2.3 Numerical Simulation 94
• 6.3 Results 96
•  6.3.1 Spin-Boson Separability and Error Model Analysis 99
• 6.4 Symmetry Protection 103
• Chapter 7. Outlook 107
• 7.1 Summary 107
• 요약 119