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Getting Started in Quantum Optics
ISBN-13: 9783031124341 / Angielski / Miękka / 2022 / 258 str.
Getting Started in Quantum Optics
ISBN-13: 9783031124341 / Angielski / Miękka / 2022 / 258 str.
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This book, based on classroom-tested lecture notes, provides a self-contained one semester undergraduate course on quantum optics, accessible to students (and other readers) who have completed an introductory quantum mechanics course and are familiar with Dirac notation and the concept of entanglement. The book covers canonical quantization, the harmonic oscillator, vacuum fluctuations, Fock states, the single photon state, quantum optical treatment of the beam splitter and the interferometer, multimode quantized light, and coherent and incoherent states. Metrology is a particular area of emphasis, with the book culminating in a treatment of squeezed light and its use in the laser interferometer gravitational-wave observatory (LIGO). The Heisenberg limit is described, along with NOON states and their application in super-sensitivity, super-resolution and quantum lithography. Applications of entanglement and coincidence measurements are described including ghost imaging, quantum illumination, absolute photodetector calibration, and interaction-free measurement. With quantum optics playing a central role in the so-called “second quantum revolution,” this book, equipped with plenty of exercises and worked examples, will leave students well prepared to enter graduate study or industry.
This book, based on classroom-tested lecture notes, provides a self-contained one semester undergraduate course on quantum optics, accessible to students (and other readers) who have completed an introductory quantum mechanics course and are familiar with Dirac notation and the concept of entanglement. The book covers canonical quantization, the harmonic oscillator, vacuum fluctuations, Fock states, the single photon state, quantum optical treatment of the beam splitter and the interferometer, multimode quantized light, and coherent and incoherent states. Metrology is a particular area of emphasis, with the book culminating in a treatment of squeezed light and its use in the laser interferometer gravitational-wave observatory (LIGO). The Heisenberg limit is described, along with NOON states and their application in super-sensitivity, super-resolution and quantum lithography. Applications of entanglement and coincidence measurements are described including ghost imaging, quantum illumination, absolute photodetector calibration, and interaction-free measurement. With quantum optics playing a central role in the so-called “second quantum revolution,” this book, equipped with plenty of exercises and worked examples, will leave students well prepared to enter graduate study or industry.
Chapter 1: Canonical Quantization x
1.1. Hamiltonian Mechanics x
1.2. Canonical Quantization
1.3. Commutation Relations
Chapter 2: The Harmonic Oscillator x
2.1. Classical Harmonic Oscillator x
2.2. Quantum Harmonic Oscillator x
2.3. Dirac Formalism x
2.4. Number Operator x
2.5. Annihilation Operator x
2.6. Creation Operator x
2.6. Creating Excited States from the Ground State x
2.7. Expectation Values x
2.8. Heisenberg Uncertainty Relation x
Chapter 3: Canonical Quantization of Light x
3.1. Single Mode of Radiation x
3.2. Quadrature Components x
3.3. Classical Hamiltonian x
3.4. Canonical Quantization x
3.5. Time-Dependence x
3.5. Quadrature Operators x
3.6. Physical Observables x
3.7. Photons x
Chapter 4: Vacuum Fluctuations x
4.1. Photon Number x
4.2. Electric Field of Fock State x
4.3. Vacuum Fluctuations x
4.4. Experimental Evidence of Vacuum Fluctuations x
Chapter 5: Single Photon State x
5.1. Single Photon State x
5.2. Photodetection x
5.3. Single Photon Sources and Detectors x
Chapter 6: Single Photon on a Beam Splitter x
6.1. Classical Beam Splitter x
6.2. Quantum Beam Splitter x
6.3. Input/Output Transformation x
6.4. Single Photon on a Beam Splitter x
6.5. Coincident Measurements x
6.6. Correlation Function x
6.7. Entangled State x
6.8. Hanbury Brown-Twiss Experiment x
Chapter 7: Single Photon in an Interferometer x
7.1. Classical Light Interference x
7.2. Quantum Light Interference x
7.3. Wave-particle Duality x
Chapter 8: Multimode Quantized Radiation x
8.1. Multimode Radiation x
8.2. Quantized Multimode Radiation x
8.3. Vacuum Energy x
8.4. Single Photon Wavepacket x
8.5. Spontaneous Emission x
Chapter 9: Coherent States x
9.1. Coherent States x
9.2. Coherent States as a Superposition of Fock States x
9.3. Photon Number x
9.4. Poisson Distribution x
9.5. Time-dependence of Coherent States x
9.6. Electric Field x
9.7. Phasor Representation x
9.8. Quadratures x
9.9. Number-phase Uncertainty Relation x
Chapter 10: Coherent State on a Beam Splitter x
10.1. Coherent State on a Beam Splitter x
10.2. Coincidence Measurements x
Chapter 11: Incoherent States x
11.1. Incoherent States x
11.2. Average Electric Field x
11.3. Average Photon Number x
11.4. Photon Number Distribution x
11.5. Comparison of Different Types of Light x
11.6. Uncertainty x
11.7. Correlations x
Chapter 12: Homodyne and Heterodyne Detection x
12.1. Homodyne Detection x
12.2. Heterodyne Detection x
Chapter 13: Coherent State in an Interferometer x
13.1. Coherent Light Interference x
13.2. Coincident Detection x
13.3. Coherent homodyne signal in an interferometer x
13.4. Uncertainty in Homodyne Signal x
Chapter 14: Squeezed Light x
14.1. Classical Description of Non-linear Optics x
14.2. Quantum Description x
14.3. Squeezing Operator x
14.4 Electric Field x
14.5. Quadratures x
14.6. Power in the Beam x
14.7. Fragility of Squeezing x 14.8. Squeezed Vacuum xChapter 15: Squeezed Light in an Interferometer x
15.1. Squeezed Light in an Interferometer x
15.2. Laser Interferometer Gravitational-wave Observatory (LIGO) x
Chapter 16: Heisenberg Limit x
16.1. Heisenberg Limit x
16.2. Phase Shifter x
16.3. NOON State x
16.4. Super-sensitivity x16.5. Super-resolution and Quantum Lithography x
16.6. Producing NOON States x
Chapter 17: Quantum Imaging x
17.1. Non-local Interference x
17.2. Ghost Imaging x
17.3. Quantum Illumination x
17.4. Absolute Photodetector Calibration x
17.5. Interaction-free Measurement x
Chapter 18: Light-matter Interaction x
18.1. Jaynes-Cummings Hamiltonian x
18.2. Spontaneous Emission x
18.3. Rabi Oscillations x
18.4. Making Large x
Further Reading x
Ray LaPierre attended Dalhousie University, Canada, where he obtained a B.Sc. degree in Physics in 1992. He then completed his M.Eng. degree in 1994 and Ph.D. degree in 1997 in the Engineering Physics Department at McMaster University, Canada. His graduate work involved development of molecular beam epitaxy of compound semiconductor alloys for laser diodes in telecom applications. Upon completion of his graduate work in 1997, he joined JDS Uniphase, Canada, where he developed dielectric coatings for wavelength division multiplexing devices. In 2004, he rejoined McMaster University as an Assistant Professor in the Engineering Physics Department. He is currently Professor in the Engineering Physics Department at McMaster with interests in III-V nanowires, molecular beam epitaxy, and applications in photovoltaics, photodetectors and quantum information processing.
This book, based on classroom-tested lecture notes, provides a self-contained one semester undergraduate course on quantum optics, accessible to students (and other readers) who have completed an introductory quantum mechanics course and are familiar with Dirac notation and the concept of entanglement. The book covers canonical quantization, the harmonic oscillator, vacuum fluctuations, Fock states, the single photon state, quantum optical treatment of the beam splitter and the interferometer, multimode quantized light, and coherent and incoherent states. Metrology is a particular area of emphasis, with the book culminating in a treatment of squeezed light and its use in the laser interferometer gravitational-wave observatory (LIGO). The Heisenberg limit is described, along with NOON states and their application in super-sensitivity, super-resolution and quantum lithography. Applications of entanglement and coincidence measurements are described including ghost imaging, quantum illumination, absolute photodetector calibration, and interaction-free measurement. With quantum optics playing a central role in the so-called “second quantum revolution,” this book, equipped with plenty of exercises and worked examples, will leave students well prepared to enter graduate study or industry.
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