Quantum 20/20: Fundamentals, Entanglement, Gauge Fields, Condensates and Topology

Preface
Acknowledgements
1 Review of basic quantum physics
	1.1 Introduction
	1.2 The fundamental evidence
	1.3 De Broglie’s hypothesis
	1.4 The Bohr model of the atom
	1.5 Wave–particle duality
	1.6 The uncertainty principle
	1.7 Outline of quantum mechanics
	1.8 Schr¨odinger’s equation
	1.9 Eigenstates
	1.10 Observables and expectation values
	1.11 Collapse of the wavefunction
	1.12 Schr
	odinger’s cat
	1.13 No-cloning theorem
	1.14 Wavepackets
	1.15 State vectors
	1.16 Special relativity and electromagnetism
	1.17 Further reading
	Exercises
2 Solutions to Schrödinger’s equation
	2.1 Introduction
	2.2 The square potential well
	2.3 The harmonic oscillator potential
	2.4 The hydrogen atom
	2.5 Intrinsic angular momentum
	2.6 Fine structure
	2.7 Further reading
	Exercises
3 Quantum statistics
	3.1 Introduction
	3.2 Symmetries of fermion and boson states
	3.3 Multi-electron atoms
	3.4 White dwarfs, neutron stars and black holes
	3.5 The exchange force
	3.6 Fermi–Dirac and Bose–Einstein statistics
	3.7 Bose–Einstein condensation
	3.8 Condensates
	3.9 Further reading
	Exercises
4 Phonons
	4.1 Introduction
	4.2 Debye model of heat capacity
	4.3 Linear chains of atoms
	4.4 Anharmonic effects
	4.5 Phonons and photons
	4.6 Polaritons
	4.7 M¨ossbauer effect
	4.8 Further reading
	Exercises
5 Electrons in solids
	5.1 Introduction
	5.2 The free electron gas
	5.3 Plasma oscillations
	5.4 Electron screening
	5.5 Electrons in crystalline materials
	5.6 Bloch waves
	5.7 Tight and weak binding
	5.8 ARPES
	5.9 Outline of calculation of band structure
	5.10 Further reading
	Exercises
6 Semiconductors
	6.1 Introduction
	6.2 Electrons, holes and doping
	6.3 Diode operation
	6.4 MOSFETs and HEMTs
	6.5 Mesoscopic scale effects
	6.6 Quantum point contacts
	6.7 Coulomb blockade
	6.8 Quantum dots
	6.9 Quantum interference
	6.10 Universal conductance fluctuations
	6.11 Further reading
	Exercises
7 Transitions
	7.1 Introduction
	7.2 Fermi’s golden rule
	7.3 2p.1s decay in hydrogen atoms
	7.4 Selection rules
	7.5 Line widths and decay rates
	7.6 Cross-sections
	7.7 The Born approximation
	7.8 Nuclear
	decay
	7.9 Low-energy scattering
	7.10 Further reading
	Exercises
8 Field quantization
	8.1 Introduction
	8.2 Second quantization
	8.3 Absorption and emission processes
	8.4 Prerequisites for lasing
	8.5 First-order coherence
	8.6 Second-order coherence
	8.7 Laser light and thermal light
	8.8 Coherent (laser-like) states
	8.9 Thermal light
	8.10 Observations of photon correlations
	8.11 Correlation interferometry
	8.12 Fermions
	8.13 Further reading
	Exercises
9 Entanglement
	9.1 Introduction
	9.2 Non-locality of quantum mechanics
	9.3 Bell states
	9.4 Spontaneous parametric down conversion
	9.5 The HOM interferometer
	9.6 Teleportation
	9.7 Entanglement between remote atoms
	9.8 Interference
	9.9 Further reading
	Exercises
10 EPR and Bell’s theorem, and quantum algorithms
	10.1 Introduction
	10.2 Local realism and determinism
	10.3 Bell’s inequalities
	10.4 The AGR experiment
	10.5 Quantum Computing
	10.6 Basic tools
	10.7 Shor’s algorithm
	10.8 Challenges of quantum computing
	10.9 Quantum cryptography
	10.10 Further reading
	Exercises
11 Quantum measurement
	11.1 Introduction
	11.2 Uncertainty
	11.3 Analysis of quantum measurement
	11.4 Shot noise in interferometry
	11.5 Back action on interferometer mirrors
	11.6 The advanced LIGO interferometer
	11.7 The standard quantum limit
	11.8 Squeezing
	11.9 Squeezed light for LIGO
	11.10 Further reading
	Exercises
12 Cavity quantum physics
	12.1 The Jaynes–Cummings model
	12.2 Rabi flopping
	12.3 Microwaves and Rydberg atoms
	12.4 Ions in electromagnetic traps
	12.5 Quantum jumps, shelving and quantum amplification
	12.6 The 199Hg+ optical clock
	12.7 The electron’s anomalous magnetic moment
	12.8 Measurement of g–2
	12.9 The Purcell effect
	12.10 Further reading
	Exercises
13 Symmetry and topology
	13.1 Introduction
	13.2 Space-time symmetries
	13.3 Charge symmetry
	13.4 The Aharonov–Bohm effect
	13.5 Berry’s phase
	13.6 Phase and topology
	13.7 Further reading
	Exercises
14 Superfluid 4He
	14.1 Introduction
	14.2 Superfluid effects
	14.3 Condensate-linked properties
	14.4 Topological implications
	14.5 Spontaneous symmetry breaking
	14.6 Excitations
	14.7 Measurement of the condensate fraction
	14.8 Critical velocity
	14.9 Quantized circulation
	14.10 Vortices
	14.11 Further reading
	Exercises
15 Superconductivity
	15.1 Introduction
	15.2 London equations
	15.3 BCS theory
	15.4 Ginzburg and Landau approach
	15.5 Flux quantization
	15.6 Type-II superconductors
	15.7 Josephson effects
	15.8 The Josephson voltage standard
	15.9 SQUIDs
	15.10 Qubits
	15.11 Topology and Dehmelt’s question
	15.12 Further reading
	Exercises
16 Gaseous Bose–Einstein condensates
	16.1 Introduction
	16.2 Making the BEC
	16.3 Imaging
	16.4 Condensate properties
	16.5 Bragg spectroscopy of dispersion relations
	16.6 Vortices
	16.7 BEC to BCS crossover
	16.8 Further reading
	Exercises
17 Quantum Hall effects
	17.1 Introduction
	17.2 Conductance relations
	17.3 Landau levels
	17.4 Current flow
	17.5 The stability of IQHE
	17.6 Topological quantization
	17.7 The fractional quantum Hall effect
	17.8 Quantum spin Hall effect
	17.9 (HgCd)Te quantum well Hall bars
	17.10 Further reading
	Exercises
18 Particle physics I
	18.1 Prologue
	18.2 Introduction to the particles and forces
	18.3 What follows
	18.4 Natural units
	18.5 An early discovery
	18.6 Field equations
	18.7 e− + e+ → μ− + μ+
	18.8 Z0-boson production
	18.9 Higher order processes and renormalization
	18.10 Neutrinos
	18.11 The weak interaction
	18.12 Parity, CP and CPT
	18.13 Handedness of the weak interaction
	18.14 Neutrino oscillations
	18.15 Quark flavour oscillations
	18.16 Further reading
	Exercises
19 Particle physics II
	19.1 Introduction
	19.2 The strong interaction and QCD
	19.3 Proton structure
	19.4 Electroweak unification
	19.5 The discovery experiments
	19.6 Puzzles with the standard model
	19.7 Further reading
	Exercises
Appendix A: Vector calculus
Appendix B: Mode densities
	B.1 Harmonic wells
Appendix C: Density matrix
Appendix D: The Bloch sphere, spin-1/2, and qubits
Appendix E: Perturbation theory
Appendix F: RSA encryption
	F.1 RSA encryption
Appendix G: The Dirac equation
Appendix H: Higgs Lagrangian
Appendix I: Entangled beauty and CP violation
Appendix J: The Gross–Pitaevskii equation
	J.1 Excitations and Bogoliubov theory
Appendix K: Kubo’s Hall conductance formula
Index