Quantum Optics and Quantum Information

Unique in its rigorously combined treatment of quantum optics and quantum information, this textbook teaches the basic principles of light-matter interaction, the theoretical tools of quantum information, and how and which systems can be used for quantum information processing.
Adopting a didactical approach field-tested by the author in numerous lectures, the book introduces basic principles of quantum optics, ranging from cavity QED and the Jaynes-Cummings model to phase space functions, the detector theory and open quantum systems. While quantum information tools and formalisms are used to develop this theory, the quantum optics aspects serve as the foundation for a further discussion of physical implementations of quantum information processing devices. The foundations of quantum mechanics are discussed, such as decoherence, quasi-probability distributions, and entanglement, and the author additionally provides an introduction to the standard quantum information applications, such as quantum computation and quantum cryptography.
Problem sections at the end of each chapter help students to gain a deeper understanding of the subject matter, and a wide-ranging reference section covers quantum states often encountered in the literature.
The overall result is an integrated course on these two modern disciplines.

1. Introduction
1.1 From wave-functions to Dirac notation
1.2 Time evolution and unitary mappings
2. Two state systems and qubits
2.1 Pauli spin matrices
2.2 The Bloch sphere
2.3 Two qubit systems
2.4 The no cloning theorem
3. The density operator and density matrix
3.1 Quantum ensembles & the density operator
3.2 Purity of quantum states
3.3 The Bloch sphere and the density matrix
3.4 The reduced density operator
3.5 Correlation and entanglement
3.6 Distance between two states
4. Photons and quantum field states
4.1 Quantised cavity field, free field, and the harmonic oscillator.
4.2 Cavity vs. running wave quantization
4.3 Polarisation of photons
4.4 The number state
4.5 The thermal field
4.6 The coherent state
5. Atom and photon
5.1 Atoms and cavities
5.1.1 The Jaynes-Cummings cavity-atom model
5.1.2 A cavity system with a three-level atom: photons on demand
5.1.3 The Dicke model
5.2 Atoms and non-linear optical processes
5.2.1 Parametric down-conversion
5.2.2 Two-mode Squeezing
5.2.3 Single mode Squeezing
6. Quasi-probabilities, operators, and operator algebra
6.1 Operator theorems (I-IV)
6.2 Displacement operator
6.3 Coherent state as a basis
6.4 P-function & Q-function
6.5 Wigner function
6.6 The quantum phase operator
7. Detector theory and correlation functions
7.1 Detectors
7.2 Theory of a physical detector
7.3 The photon number distribution and photon counting
7.4 Correlation functions: G1, g1, and Young's slits
7.5 Correlation functions: g2 and the Hanbury-Brown-Twiss experiment
8. The Beam-splitter
8.1 Beam-splitter theory
8.2 The beam-splitter and phase choices
8.3 The beam-splitter and coherent states
8.4 The beam-splitter with two photons
8.5 The Hong-Ou-Mandel experiment
8.6 The Mach-Zehnder set-up
8.7 A quantum bomb detector
9. Quantum entanglement and some applications
9.1 Introduction to Quantum measurement
9.2 Quantum cryptography
9.2.1 BB84 protocol
9.2.2 B92 protocol
9.2.3 Ekert protocol
9.3 Quantum teleportation
9.4 Quantum dense coding
9.5 Quantum repeaters and Quantum memory
9.6 Entanglement distillation
9.7 Non-locality and the Einstein, Podolsky, and Rosen paradox
9.8 Bell's inequalities
9.9 Generalised measurement (POVM)
9.10 Example POVM problems
10. Decay of quantum systems
10.1 Introduction to decoherence
10.2 The bath model
10.3 Derivation of the master equation
10.4 Examples of master equations and decaying quantum systems
10.4.1 Decay of an atom
10.4.2 Decay of a number state
10.4.3 Decay of a coherent state
10.4.4 Decay of a "Schrödinger cat"
10.4.5 Master equation for dephasing
10.5 Unravelling a master equation
10.6 Measurement and the environment
10.7 Theory of effective modes
10.8 Measure of non-Markovianity
11. Cooling and trapping atoms with photons
11.1 Kinetic action of light on matter
11.2 Doppler cooling
11.3 Trapped atoms
11.4 Trapped ions
11.4.1 Paul trap and Penning trap
11.4.2 Lamb-Dicke limit
11.4.3 Cooling trapped ions
12. Measures of quantum information and entanglement
12.1 Quantum information and quantum entropy
12.2 Mutual information and the Araki-Lieb inequality
12.3 Concurrence
12.4 The tangle
12.5 Global entanglement
12.6 Quantum discord
13. Quantum gates
13.1 Quantum gates
13.2 Rotations and one-qubit gates
13.3 Two qubit gates
13.4 Three or more qubit gates
14. Quantum computing: algorithms
15. Physical systems for quantum computing
15.1 Ion traps
15.2 Linear optical Quantum computing
15.3 Cavity QED for Quantum computing
15.4 Circuit QED and superconducting qubits
15.5 Condensed matter: quantum dots
15.6 NMR Quantum computing
15.7 Cluster state Quantum computing
15.8 Continuous variable Quantum computing
16. Reference section
16.1 Introduction to the reference section
16.2 Additional theorems
16.3 Single mode states
16.3.1 Number state
16.3.2 Coherent state
16.3.3 Squeezed vacuum state
16.3.4 Squeezed coherent state
16.3.5 Thermal state
16.3.6 Displaced number state
16.3.7 Phase state
16.3.8 Even and odd coherent states
16.3.9 Yurke-Stoler cat state
16.3.10 Single mode binomial state
16.4 Multi-mode states
16.4.1 The Bell states
16.4.2 Werner state for 2 qubits
16.4.3 The X-state for 2 qubits
16.4.4 Two-mode squeezed state
16.4.5 Two-mode binomial state
16.4.6 GHZ state for 3 qubits
16.4.7 GHZ state for N qubits
16.4.8 The W-state for N qubits
16.5 Spin states and additional theorems for spins
16.5.1 Sz eigenstates and ladder operators
16.5.2 Spin coherent states
16.5.3 Spin squeezed states

Barry M. Garraway is a Reader in theoretical physics at Sussex University. After gaining a Physics degree at Oxford University, he moved to Manchester and did his PhD in the field of quantum optics in which he remains active. His postdoctoral work was in Helsinki with Prof. Stig Stenholm on quantum physics and molecular wave packet dynamics. After a stint at Imperial College, where he worked with Sir Peter Knight on quantum optics, Dr Garraway moved to Sussex University in 1997. At Sussex he now works on quantum optics, quantum information processing, and on trapping and cooling cold atoms and molecules. Currently he heads the Atomic, Molecular and Optical Physics research group at Sussex University.