Introduction to Quantum Nanotechnology: A Problem Focused Approach

Cover
Introduction to Quantum Nanotechnology: A Problem Focused Approach
Copyright
Dedication
Preface
Table of Contents
1: Introduction to Applied Quantum Mechanics: Why quantum behavior is impacting technology
2: Nano-Mechanical Oscillator and Basic Dynamics: Part I
	2.1 Introduction
	2.2 Classical Physics Approach: Finding x(t)
	2.3 The Quantum Approach: Finding ..(x, t)
	2.4 Is It Classical or Quantum?
	2.5 What is Knowable in a Quantum System?
	2.6 Coherent Superposition States and Coherent Dynamics
	2.7 The Particle and the Wave
	2.8 Summary
	Vocabulary (page) and Important Concepts
3: Free Particle, Wave Packet and Dynamics, Quantum Dots, Defects and Traps
	3.1 Introduction
	3.2 The Free Particle
	3.3 Localized State in Free Space: The Wave Packet
	3.4 Nano-Heterostructures: Quantum Dots and Deep Traps
	3.5 A Particle Trapped in a Shallow Defect
	3.6 A Particle Trapped in a Point Defect Represented by a Dirac Delta-Function Potential
	3.7 Physical Interpretation of the Dirac Delta-Function Potential
	3.8 Summary
	Vocabulary (page) and Important Concepts
4: Periodic Hamiltonians and the Emergence of Band Structure: The Bloch Theorem and the Dirac Kronig–Penney Model
	4.1 Introduction
	4.2 The Translation Operator
	4.3 Crystals and Periodic Potentials: The Bloch Theorem and the Dirac Kronig–Penney Model
	4.4 Summary
	Vocabulary (page) and Important Concepts
5: Scattering, Quantum Current, and Resonant Tunneling
	5.1 Introduction
	5.2 Scattering
	5.3 Tunneling Through a Repulsive Point Defect Represented by a Dirac Delta-Function Potential
	5.4 Resonant Tunneling
	5.5 Summary
	Vocabulary (page) and Important Concepts
6: Bound States in Three Dimensions: The Atom
	6.1 Introduction
	6.2 The Hydrogenic Atom
	6.3 Summary
	Vocabulary (page) and Important Concepts
7: New Design Rules for Quantum: The Postulates
	7.1 Introduction
	7.2 The Postulates of Quantum Mechanics
	7.3 The Heisenberg Uncertainty Principle: The Minimum Uncertainty State
	7.4 Interpreting the Expansion Coefficients: Relating Functional Form to Dirac Form
	7.5 Summary
	Vocabulary (page) and Important Concepts
8: Heisenberg Operator Approach: Nano-Mechanical Oscillator (Part 2) and the Quantum LC Circuit
	8.1 Introduction
	8.2 Heisenberg or Operator Approach to Solving the Time Independent Schrödinger Equation
	8.3 Matrix Representation of Operators and Eigenvectors in Quantum Mechanics
	8.4 The Quantum LC Circuit
	8.5 Summary
	Vocabulary (page) and Important Concepts
9: Quantum Dynamics: Resonance and a Quantum Flip-Flop
	9.1 Introduction
	9.2 Time Evolution Operator
	9.3 Heisenberg Picture of Dynamics
	9.4 Interaction Picture
	9.5 Quantum Flip-Flop: Coherent Control of a Two-Level System and Rabi Oscillations
	9.6 Summary
	Vocabulary (page) and Important Concepts
10: Angular Momentum and the Quantum Gyroscope: The Emergence of Spin
	10.1 Introduction
	10.2 The Heisenberg Approach
	10.3 Intrinsic Angular Momentum: Spin
	10.4 The Bloch Sphere and Spin
	10.5 Addition of Angular Momentum
	10.6 Angular Momentum and the Rotation Operator
	10.7 Summary
	Vocabulary (page) and Important Concepts
11: Approximation Techniques for Stationary and Dynamic Problems
	11.1 Introduction
	11.2 Time Independent Perturbation Theory
	11.3 Time Dependent Perturbation Theory: Fermi’s Golden Rule
	11.4 Summary
	Vocabulary (page) and Important Concepts
12: Bosons and Fermions: Indistinguishable Particles with Intrinsic Spin
	12.1 Introduction
	12.2 Eigenfunctions and Eigenvalues of the Exchange Operator
	12.3 The Exchange Symmetry Postulate: Bosons and Fermions
	12.4 The Heitler–London Model and the Heisenberg Exchange Hamiltonian
	12.5 Summary
	Vocabulary (page) and Important Concepts
13: Quantum Measurement and Entanglement: Wave Function Collapse
	13.1 Introduction
	13.2 Quantum Measurement
	13.3 Quantum Entanglement and the Impact of Measurement
	13.4 Quantum Teleportation
	13.5 Summary
	Vocabulary (page) and Important Concepts
14: Loss and Dissipation: The RLC Circuit
	14.1 Introduction
	14.2 Coupling to a Continuum of States: The Weisskopf–Wigner Approximation
	14.3 Decay in the Nano-Vibrator Problem
	14.4 RLC Circuit
	14.5 Summary
	Vocabulary (page) and Important Concepts
15: Quantum Radiation Field: Spontaneous Emission and Entangled Photons
	15.1 Introduction
	15.2 Finding the Hamiltonian for the Transverse Electromagnetic Field
	15.3 Quantizing the Field
	15.4 Spontaneous Emission
	15.5 Effects of the Quantum Vacuum on Linear Absorption and Dispersion
	15.6 Rabi Oscillations in the Quantum Vacuum: Jaynes–Cummings Hamiltonian
	15.7 Summary
	Vocabulary (page) and Important Concepts
16: Two-State Systems: The Atomic Operators
	16.1 Introduction
	16.2 Defining the Atomic Operators
	16.3 Physical Meaning of the Atomic Operators
	16.4 Atomic Operators in the Heisenberg Picture
	16.5 Exact Solution for the Atomic Operators for a Monochromatic Field
	16.6 Operator Equations of Motion Including the Vacuum Field
	16.7 Summary
	Vocabulary (page) and Important Concepts
17: Quantum Electromagnetics
	17.1 Introduction
	17.2 Number State Representation
	17.3 The Coherent State
	17.4 Quantum Beam Splitter: Quantum Interference
	17.5 Resonant Rayleigh Scattering: A Single Quantum Emitter
	17.6 Creating Quantum Entangled States Between a Photon and an Electron
	17.7 Engineering the Quantum Vacuum
	17.8 Summary
	Vocabulary (page) and Important Concepts
18: The Density Matrix: Bloch Equations
	18.1 Introduction
	18.2 The Density Matrix Operator
	18.3 The Density Matrix Equations Including Relaxation
	18.4 Solving the Reduced Density Matrix for a Two-Level System in the Presence of a Near Resonant Classical Electromagnetic Fiel
	18.5 Rate Equation Approximation
	18.5 Three-Level System: Emerging Importance in Quantum Technology
	18.7 Summary
	Vocabulary (page) and Important Concepts
Appendix A Review of Essential Math
	A.1 Differential Equations
	Examples of Solutions to Homogeneous Differential Equations
	Examples of Solutions to Inhomogeneous Differential Equations
	A.2 Partial Differential Equations (PDE)—Method of Separation of Variables
	A.3 Eigenvalue Problems
	A.4 Complex Numbers and Euler’s Theorem
	A.5 Dirac Delta-Function
	A.6 Gaussian Integral
	A.7 Linear Algebra: Matrices, Determinants, Permanents, and the Eigenvector Multiplication
	Determinants
	Permanents
	Adjoint, Hermiticity, and Unitarity
	Vectors: Inner and Outer Products and Dirac Notation
	The Identity Matrix and the Inverse Matrix
	Cramer’s Rule for Solving n Linear Inhomogeneous Algebraic Equations in n Unknowns
	The Eigenvector Problem
	Matrix Diagonalization
	Unitary Transformation
	Vocabulary (page) and Important Concepts
Appendix B Power Series for Important Functions
Appendix C Properties and Representations of the Dirac Delta-Function
Appendix D Vector Calculus and Vector Identities
Appendix E The Electromagnetic Hamiltonian and the Goeppert Mayer Transformation
Appendix F Maxwell’s Equations in Media, the Wave Equation, and Coupling of a Field to a Two-Level System
Appendix G Wigner–Eckart Theorem and Irreducible Tensors
Index