Quantum Mechanics in the Single Photon Laboratory

Description

Arising from a series of laboratory class experiments developed by the authors, this book provides an overview of fundamental experiments that can be used to practically demonstrate the underlying principles of quantum physics and quantum information science. Designed with multiple readerships in mind, it will be essential for the professor who would like to recreate a similar suite of experiments for their students as well as students of physics, who would like to learn how such experiments are conducted. Computer scientists, photonics engineers and electrical engineers who would like to foray into quantum technologies would also find this narrative useful to learn about the terminology, key postulates of quantum physics, the collapse of states on measurement and how quantum computers could be implemented. Key Features Accompanied by downloadable code and data from real experiments for readers to manipulate, plot and compute expectation values, errors and density matrices. Includes worked examples demonstrating basic calculations on computing probabilities from projective measurements, effect of unitary operators on states, computing density matrices, and expectation values, fidelities and purities. Features end-of-chapter problems Incorporates overviews and learning objectives for each chapter Essential reading for students of quantum physics and modern optics PRELIMS.pdf Preface Acknowledgments Author biographies Muhammad Hamza Waseem Faizan-e-Ilahi Dr Muhammad Sabieh Anwar Abbreviations List of quantum optics experiments CH001.pdf Chapter 1 Introduction References CH002.pdf Chapter 2 Classical nature of light 2.1 Electromagnetic waves 2.2 Polarization 2.2.1 The polarization ellipse 2.2.2 Polarization manipulation 2.2.3 Jones calculus 2.2.4 Stokes parameters 2.3 Experimental explorations 2.3.1 Light source and detection 2.3.2 Understanding, manipulating and measuring polarization using Jones calculus 2.3.3 Fourier analysis and peanut plots 2.3.4 Interference and erasure of which-way information References CH003.pdf Chapter 3 Quantum nature of light 3.1 Quantum mechanical states 3.2 Qubits 3.3 Transforming quantum states 3.4 Measuring quantum states 3.5 Composite systems and entangled states 3.6 Mixed states and the density matrix 3.7 Photon statistics References CH004.pdf Chapter 4 Experiments related to the quantum nature of light 4.1 General components of the lab 4.1.1 Light source 4.1.2 Light detection 4.1.3 Coincidence counting unit 4.2 Q1: Spontaneous parametric downconversion 4.2.1 The downconversion crystal and phase-matching 4.2.2 Optical alignment 4.2.3 Accidental coincidence counts 4.2.4 The experiment 4.3 Q2: proof of existence of photons 4.3.1 Photodetection and degree of second-order coherence 4.3.2 Accidental coincidences 4.3.3 The optical setup 4.3.4 The experiment 4.4 Q3: Estimating the polarization state of single photons 4.4.1 Reconstructing the single-photon polarization state 4.4.2 Generating and measuring polarization states 4.4.3 The experiment 4.5 Q4: Visualizing the polarization state of single photons 4.5.1 Antenna polarimetry and the polarization pattern method 4.5.2 Polarization pattern of single photons 4.5.3 The experiment 4.6 Q5: Single-photon interference and quantum eraser 4.6.1 The polarization interferometer and quantum erasure 4.6.2 Aligning the interferometer 4.6.3 The experiment References CH005.pdf Chapter 5 Experiments related to entanglement and nonlocality 5.1 Entanglement and local realism 5.2 The proverbial Alice and Bob experiment 5.3 Generating polarization-entangled photons 5.4 NL1: Freedman’s test of local realism 5.4.1 Freedman’s inequality 5.4.2 Quantum mechanical prediction for Freedman’s test 5.4.3 Tuning the Bell state 5.4.4 The experiment 5.5 NL2: Hardy’s test of local realism 5.5.1 The Hardy inequality 5.5.2 Quantum mechanical prediction for Hardy’s test 5.5.3 The experimental setup 5.5.4 Aligning the detectors 5.5.5 Tuning the Hardy state 5.5.6 Measuring probabilities with four detectors 5.5.7 The experiment 5.6 NL3: CHSH test of local realism 5.6.1 The CHSH inequality 5.6.2 Quantum mechanical prediction for the CHSH test 5.6.3 Tuning the Bell state 5.6.4 The experiment References CH006.pdf Chapter 6 Quantum state tomography 6.1 Qubits, Stokes parameters and tomography 6.1.1 The Bloch sphere for pure states 6.1.2 The Bloch sphere for density matrices 6.1.3 Stokes parameters as projections of the state on the Bloch sphere 6.2 Single-qubit tomography 6.3 Two-qubit tomography 6.4 Nonideal measurements and compensation of errors 6.5 Maximum likelihood estimation 6.6 The experiment References CH007.pdf Chapter 7 Conclusion References APP1.pdf Chapter Optical elements Mechanical elements Actuators and controllers Detection and coincidence counting unit Testing of FPGA Q1: Spontaneous parametric downconversion Q2: Proof of existence of photons Q3: Estimating the polarization state of single photons Q4: Visualizing the polarization state of single photons Q5: Single-photon interference and quantum eraser NL1: Freedman’s test of local realism NL2: Hardy’s test of local realism NL3: CHSH test of local realism QST: Quantum state tomography APP2.pdf Chapter B.1 Introduction B.2 Architecture B.3 Configuring the FPGA B.3.1 Designing the system B.3.2 Implementing the design APP3.pdf Chapter