Getting Started in Quantum Optics

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.

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 x







Chapter 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 x



16.5. 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