Quantum Optics: Taming the Quantum

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