This book is a thoroughly modern and highly pedagogical graduate-level introduction to quantum optics, a subject which has witnessed stunning developments in recent years and has come to occupy a central role in the 'second quantum revolution'. The reader is invited to explore the fundamental role that quantum optics plays in the control and manipulation of quantum systems, leading to ultracold atoms, circuit QED, quantum information science, quantum optomechanics, and quantum metrology. The building blocks of the subject are presented in a sequential fashion, starting from the simplest physical situations before moving to increasingly complicated ones. This pedagogically appealing approach leads to quantum entanglement and measurement theory being introduced early on and before more specialized topics such as cavity QED or laser cooling. The final chapter illustrates the power of scientific cross-fertilization by surveying cutting-edge applications of quantum optics and optomechanics in gravitational wave detection, tests of fundamental physics, searches for dark matter, geophysical monitoring, and ultraprecise clocks. Complete with worked examples and exercises, this book provides the reader with enough background knowledge and understanding to follow the current journal literature and begin producing their own original research.
Author(s): Pierre Meystre
Series: Graduate Texts in Physics
Publisher: Springer
Year: 2021
Language: English
Pages: 385
City: Cham
Preface
Acknowledgement
Contents
1 Semiclassical Atom–Light Interaction
1.1 Multipole Expansion: A Brief Summary
1.2 The Lorentz Atom
1.3 Two-Level Atoms
1.3.1 Hamiltonian
1.3.2 Optical Bloch Equations
1.3.3 Relaxation Mechanisms
1.3.4 Density Matrix Equations
Problems
References
2 Electromagnetic Field Quantization
2.1 Quantum Harmonic Oscillator
2.2 Electromagnetic Field Quantization
2.2.1 Single-Mode Field
2.2.2 Multimode Field
2.3 States of the Field
2.3.1 Single-Mode Field in Thermal Equilibrium
2.3.2 Coherent States
2.3.3 Squeezed States
2.4 Photodetection and Correlation Functions
2.4.1 Detection by Absorption
2.4.2 Balanced Homodyne Detection
2.5 Quasiprobability Distributions
Problems
References
3 The Jaynes–Cummings Model
3.1 The Linchpin of Quantum Optics
3.2 Quantum Rabi Oscillations
3.3 Collapse and Revivals
3.4 Single-Mode Spontaneous Emission
3.5 Repeated Field Measurements
3.6 The Quantum Rabi Model
Problems
References
4 Composite Systems and Entanglement
4.1 The EPR Paradox
4.2 Quantum Entanglement
4.2.1 Schmidt Decomposition and Maximum Entanglement
4.2.2 Monogamy of Entanglement
4.3 Bell's Inequalities
4.4 Quantum Key Distribution
4.4.1 The BB84 Protocol
4.4.2 No-cloning Theorem
4.4.3 Quantum Teleportation
Problems
References
5 Coupling to Reservoirs
5.1 Spontaneous Emission in Free Space
5.1.1 Free Space Density of Modes
5.1.2 Weisskopf–Wigner Theory of Spontaneous Emission
5.1.3 Superradiance and Subradiance
5.2 Master Equation
5.2.1 Damped Harmonic Oscillator
5.2.2 Lindblad Form
5.2.3 Fokker–Planck Equation
5.3 Langevin Equations
5.4 Monte Carlo Wave Functions
5.4.1 Quantum Trajectories
5.5 Input–Output Formalism
Problems
References
6 Quantum Measurements
6.1 The von Neumann Postulate
6.2 Measurement Back Action
6.2.1 The Standard Quantum Limit
6.2.2 Quantum Non-demolition Measurements
6.3 Continuous Measurements
6.3.1 Continuous Projective Measurements
6.3.2 Positive Operator-Valued Measures
6.3.3 Weak Continuous Measurements
6.3.4 Continuous Field Measurements
6.4 The Pointer Basis
Problems
References
7 Tailoring the Environment—Cavity QED
7.1 Enhanced and Inhibited Spontaneous Emission
7.1.1 Master Equation for the Atom–Cavity System
7.1.2 Weak Coupling Regime
7.1.3 Strong Coupling Regime
7.2 The Micromaser
7.3 Dispersive Regime
7.4 Circuit QED
7.4.1 LC Circuit Quantization
7.4.2 Superconducting Qubits
7.4.3 Field–Qubit Coupling
7.5 The Casimir Force
Problems
References
8 Mechanical Effects of Light
8.1 Semiclassical Atom–Field Interaction Revisited
8.2 Gradient and Radiation Pressure Forces
8.3 Dissipation
8.4 Atomic Diffraction
8.4.1 Raman–Nath Regime
8.4.2 Bragg Regime
8.4.3 Stern–Gerlach Regime
8.5 Spontaneous Emission
8.6 Atom Interferometers
Problems
References
9 Laser Cooling
9.1 Doppler Cooling
9.2 Sisyphus Cooling
9.3 Subrecoil Cooling
9.4 Cavity Cooling
9.5 Sideband Cooling
9.6 Evaporative Cooling
Problems
References
10 Bose–Einstein Condensation
10.1 Phenomenology
10.2 BEC in Traps
10.3 Schrödinger Field Quantization
10.3.1 The Hartree Approximation
10.3.2 Quasiparticles
10.4 Ultracold Atoms on Optical Lattices
10.4.1 The Bose–Hubbard Model
Problems
References
11 Quantum Optomechanics
11.1 Classical Analysis
11.1.1 Static Phenomena: Optical Spring Effect
11.1.2 Effects of Retardation: Cold Damping
11.2 Quantum Theory
11.3 Beyond the Ground State
11.3.1 Linearized Coupling
11.3.2 Quadratic Coupling
11.3.3 Polariton Spectrum
11.4 Standard Quantum Limit of Optomechanical Detection
11.5 Ultracold Atoms
11.6 Functionalization and Hybrid Systems
Problems
References
12 Outlook
12.1 Gravitation
12.1.1 Gravitational Wave Detection
12.1.2 Tests of the Equivalence Principle
12.1.3 Testing the Inverse Square Law
12.1.4 Gravitationally Induced Decoherence
12.2 The Dark Sector
12.2.1 Coupling to Photons
12.2.2 Atom-Interferometric Searches
12.2.3 Cavity Optomechanical Searches
References
Index
