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.
Author(s): Ray LaPierre
Series: Undergraduate Texts in Physics
Publisher: Springer
Year: 2022
Language: English
Pages: 241
City: Cham
Preface
Reference
Acknowledgments
How to Use This Book
Contents
Chapter 1: Canonical Quantization
1.1 Hamiltonian Mechanics
1.2 Canonical Quantization
1.3 Commutation Relations
Reference
Chapter 2: Quantum Harmonic Oscillator
2.1 Classical Harmonic Oscillator
2.2 Quantum Harmonic Oscillator
2.3 Dirac Formalism
2.4 Number Operator
2.5 Annihilation Operator
2.6 Creation Operator
2.7 Creating Excited States from the Ground State
2.8 Expectation Value and Uncertainty
2.9 Heisenberg Uncertainty Relation
2.10 Some Important Relations
References
Chapter 3: Canonical Quantization of Light
3.1 Single Mode of Radiation
3.2 Quadrature Components
3.3 Classical Hamiltonian
3.4 Canonical Quantization
3.5 Time-Dependence
3.6 Quadrature Operators
3.7 Physical Observables
3.8 Photons
References
Chapter 4: Fock States and the Vacuum
4.1 Photon Number
4.2 Electric Field of the Fock State
4.3 Vacuum Fluctuations
4.4 Experimental Evidence of Vacuum Fluctuations
References
Chapter 5: Single Photon State
5.1 Single Photon State
5.2 Photodetection Signal
5.3 Single Photon Sources
5.4 Single Photon Detectors
References
Chapter 6: Single Photon on a Beam Splitter
6.1 Classical Beam Splitter
6.2 Quantum Beam Splitter
6.3 Input/Output Transformation
6.4 Single Photon on a Beam Splitter
6.5 Coincident Measurements
6.6 Second-Order Correlation Function
6.7 Entangled State
6.8 Hanbury Brown-Twiss Experiment
References
Chapter 7: Single Photon in an Interferometer
7.1 Classical Light Interference
7.2 Quantum Light Interference
7.3 Wave-Particle Duality
Reference
Chapter 8: Entanglement
8.1 Entangled States
8.2 EPR Paradox and Hidden Variables
8.3 CHSH Inequality
8.4 Testing the CHSH Inequality
8.5 Quantum Key Distribution
References
Chapter 9: Multimode Quantized Radiation
9.1 Multimode Radiation
9.2 Quantized Multimode Radiation
9.3 Vacuum Energy
9.4 Single Photon Wavepacket
9.5 Spontaneous Emission
Reference
Chapter 10: Coherent State
10.1 Coherent State
10.2 Coherent State as a Superposition of Fock States
10.3 Photon Number
10.4 Poisson Distribution
10.5 Electric Field of Coherent State
10.6 Phasor Representation
10.7 Time-Dependence of Coherent State
10.8 Quadratures
10.9 Displacement Operator
10.10 Number-Phase Uncertainty Relation
10.11 Revisiting the Fock State
Reference
Chapter 11: Coherent State on a Beam Splitter
11.1 Photodetection Probability
11.2 Coincidence Measurements
Chapter 12: Incoherent State
12.1 Incoherent State
12.2 Electric Field of Incoherent State
12.3 Photodetector Signal
12.4 Photon Number Distribution
12.5 Photon Number Uncertainty
12.6 Comparison of Different Types of Light
Reference
Chapter 13: Homodyne and Heterodyne Detection
13.1 Homodyne Detection
13.2 Heterodyne Detection
Chapter 14: Coherent State in an Interferometer
14.1 Coherent Light Interference
14.2 Coincident Detection
14.3 Homodyne Signal
14.4 Uncertainty in the Homodyne Signal
Chapter 15: Squeezed Light
15.1 Classical Description of Nonlinear Optics
15.2 Quantum Description of Squeezing
15.3 Squeezing Operator
15.4 Electric Field of Squeezed Light
15.5 Quadratures
15.6 Squeezed Power
15.7 Fragility of Squeezing
15.8 Squeezed Vacuum
15.9 Photon Number Distribution of Squeezed Light
References
Chapter 16: Squeezed Light in an Interferometer
16.1 Homodyne Signal Using Squeezed Light
16.2 Laser Interferometer Gravitational-Wave Observatory (LIGO)
References
Chapter 17: Heisenberg Limit
17.1 Heisenberg Limit
17.2 Phase Shifter
17.3 NOON States
17.4 Super-sensitivity
17.5 Super-resolution and Quantum Lithography
17.6 Producing a NOON State
17.7 Hong-Ou-Mandel Effect
17.8 High NOON State
17.9 Quantum State Engineering
References
Chapter 18: Quantum Imaging
18.1 Nonlocal Interference
18.2 Ghost Imaging
18.3 Quantum Illumination
18.4 Absolute Photodetector Calibration
18.5 Interaction-Free Measurement (Elitzur-Vaidman Bomb Problem)
References
Chapter 19: Light-Matter Interaction
19.1 Jaynes-Cummings Hamiltonian
19.2 Spontaneous Emission
19.3 Cavity Quantum Electrodynamics
19.4 Circuit QED
19.5 Rydberg Atoms
19.6 Rabi Oscillations
19.7 Collapse and Revival of Rabi Oscillations
19.8 Example of a CQED Experiment
19.9 Dressed Atom-Cavity States and Vacuum Rabi Splitting
References
Chapter 20: Atomic Clock
20.1 Quartz Oscillators-Before Atomic Time
20.2 Resonance Frequency in the Cs Atom
20.3 Stern-Gerlach Apparatus
20.4 Thermal Atomic Clock
20.5 Improvements to the Atomic Clock
20.6 Applications of the Atomic Clock
References
Chapter 21: Atom Cooling and Trapping
21.1 Paul Trap
21.2 Laser Cooling
21.3 Magneto-optical Trap
21.4 Sisyphus Cooling
21.5 Dipole Trap, Optical Tweezers, and Optical Lattice
References
Further Reading
Appendix 1: Derivation of Lamb Shift
Appendix 2: Derivation of Casimir Formula
Appendix 3: Derivation of Normalization Constant in Single Photon Wavepacket
Appendix 4: Derivation of Planck´s Distribution Law
Index
