Quantum Optics An Introduction

by Fox, Mark

• ISBN13: 9780198566731
• ISBN10: 0198566735
• eBook ISBN(s): 9780191524257
• Format: Paperback
• Copyright: 2006-06-22
• Publisher: Oxford University Press

Summary

Most previous texts on quantum optics have been written primarily for the graduate student market at PhD level and above. Quantum optics: an introduction aims to introduce a wide range of topics at a lower level suitable for advanced undergraduate and Masters level students in physics. Thetext is divided into four main parts, covering modern topics in both pure and applied quantum optics: I. Introduction and background material. II. Photons. III. Atom-photon interactions. IV. Quantum information processing. The emphasis of the subject development is on intuitive physicalunderstanding rather than mathematical arguments, although many derivations are included where appropriate. The text includes numerous illustrations, with a particular emphasis on the experimental observations of quantum optical phenomena. Each chapter includes worked examples, together with 10-15exercises with solutions. Six appendices are included to supplement the main subject material.

Author Biography

Dr A M Fox is Reader in Physics, Dept of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK.

Table of Contents

List of symbols	xv
List of abbreviations	xviii
I. Introduction and background	1	(72)
Introduction	3	(5)
What is quantum optics?	3	(1)
A brief history of quantum optics	4	(2)
How to use this book	6	(2)
Classical optics	8	(18)
Maxwell's equations and electromagnetic waves	8	(5)
Electromagnetic fields	8	(2)
Maxwell's equations	10	(1)
Electromagnetic waves	10	(2)
Polarization	12	(1)
Diffraction and interference	13	(3)
Diffraction	13	(2)
Interference	15	(1)
Coherence	16	(3)
Nonlinear optics	19	(7)
The nonlinear susceptibility	19	(1)
Second-order nonlinear phenomena	20	(3)
Phase matching	23	(3)
Quantum mechanics	26	(22)
Formalism of quantum mechanics	26	(9)
The Schrodinger equation	26	(2)
Properties of wave functions	28	(2)
Measurements and expectation values	30	(1)
Commutators and the uncertainty principle	31	(1)
Angular momentum	32	(2)
Dirac notation	34	(1)
Quantized states in atoms	35	(6)
The gross structure	35	(4)
Fine and hyperfine structure	39	(2)
The Zeeman effect	41	(1)
The harmonic oscillator	41	(2)
The Stern--Gerlach experiment	43	(2)
The band theory of solids	45	(3)
Radiative transitions in atoms	48	(25)
Einstein coefficients	48	(3)
Radiative transition rates	51	(3)
Selection rules	54	(2)
The width and shape of spectral lines	56	(2)
The spectral lineshape function	56	(1)
Lifetime broadening	56	(1)
Collisional (pressure) broadening	57	(1)
Doppler broadening	58	(1)
Line broadening in solids	58	(1)
Optical properties of semiconductors	59	(2)
Lasers	61	(12)
Laser oscillation	61	(3)
Laser modes	64	(3)
Laser properties	67	(6)
II. Photons	73	(92)
Photon statistics	75	(30)
Introduction	75	(1)
Photon-counting statistics	76	(2)
Coherent light: Poissonian photon statistics	78	(4)
Classification of light by photon statistics	82	(1)
Super-Poissonian light	83	(4)
Thermal light	83	(3)
Chaotic (partially coherent) light	86	(1)
Sub-Poissonian light	87	(1)
Degradation of photon statistics by losses	88	(1)
Theory of photodetection	89	(5)
Semi-classical theory of photodetection	90	(3)
Quantum theory of photodetection	93	(1)
Shot noise in photodiodes	94	(5)
Observation of sub-Poissonian photon statistics	99	(6)
Sub-Poissonian counting statisties	99	(2)
Sub-shot-noise photocurrent	101	(4)
Photon antibunching	105	(21)
Introduction: the intensity interferometer	105	(3)
Hanbury Brown--Twiss experiments and classical intensity fluctuations	108	(3)
The second-order correlation function g(2)(τ)	111	(2)
Hanbury Brown--Twiss experiments with photons	113	(2)
Photon bunching and antibunching	115	(2)
Coherent light	116	(1)
Bunched light	116	(1)
Antibunched light	117	(1)
Experimental demonstrations of photon, antibunching	117	(3)
Single-photon sources	120	(6)
Coherent states and squeezed light	126	(25)
Light waves as classical harmonic oscillators	126	(3)
Phasor diagrams and field quadratures	129	(2)
Light as a quantum harmonic oscillator	131	(1)
The vacuum field	132	(2)
Coherent states	134	(1)
Shot noise and number--phase uncertainty	135	(3)
Squeezed states	138	(1)
Detection of squeezed light	139	(3)
Detection of quadrature-squeezed vacuum states	139	(3)
Detection of amplitude-squeezed light	142	(1)
Generation of squeezed states	142	(4)
Squeezed vacuum states	142	(2)
Amplitude-squeezed light	144	(2)
Quantum noise in amplifiers	146	(5)
Photon number states	151	(14)
Operator solution of the harmonic oscillator	151	(3)
The number state representation	154	(2)
Photon number states	156	(1)
Coherent states	157	(3)
Quantum theory of Hanbury Brown--Twiss experiments	160	(5)
III. Atom--photon interactions	165	(76)
Resonant light--atom interactions	167	(27)
Introduction	167	(1)
Preliminary concepts	168	(4)
The two-level atom approximation	168	(1)
Coherent superposition states	169	(2)
The density matrix	171	(1)
The time-dependent Schrodinger equation	172	(2)
The weak-field limit: Einstein's B coefficient	174	(3)
The strong-field limit: Rabi oscillations	177	(10)
Basic concepts	177	(3)
Damping	180	(2)
Experimental observations of Rabi oscillations	182	(5)
The Bloch sphere	187	(7)
Atoms in cavities	194	(22)
Optical cavities	194	(3)
Atom-cavity coupling	197	(3)
Weak coupling	200	(6)
Preliminary considerations	200	(1)
Free-space spontaneous emission	201	(1)
Spontaneous emission in a single-mode cavity: the Purcell effect	202	(2)
Experimental demonstrations of the Purcell effect	204	(2)
Strong coupling	206	(5)
Cavity quantum electrodynamics	206	(3)
Experimental observations of strong coupling	209	(2)
Applications of cavity effects	211	(5)
Cold atoms	216	(25)
Introduction	216	(2)
Laser cooling	218	(12)
Basic principles of Doppler cooling	218	(3)
Optical molasses	221	(3)
Sub-Doppler cooling	224	(2)
Magneto-optic atom traps	226	(1)
Experimental techniques for laser cooling	227	(2)
Cooling and trapping of ions	229	(1)
Bose--Einstein condensation	230	(6)
Bose--Einstein condensation as a phase transition	230	(2)
Microscopic description of Bose--Einstein condensation	232	(1)
Experimental techniques for Bose Einstein condensation	233	(3)
Atom lasers	236	(5)
IV. Quantum information processing	241	(111)
Quantum cryptography	243	(21)
Classical cryptography	243	(2)
Basic principles of quantum cryptography	245	(4)
Quantum key distribution according to the BB84 protocol	249	(4)
System errors and identity verification	253	(2)
Error correction	253	(1)
Identity verification	254	(1)
Single-photon sources	255	(1)
Practical demonstrations of quantum cryptography	256	(8)
Free-space quantum cryptography	257	(1)
Quantum cryptography in optical fibres	258	(6)
Quantum computing	264	(32)
Introduction	264	(3)
Quantum bits (qubits)	267	(3)
The concept of qubits	267	(2)
Bloch vector representation of single qubits	269	(1)
Column vector representation of qubits	270	(1)
Quantum logic gates and circuits	270	(9)
Preliminary concepts	270	(2)
Single-qubit gates	272	(2)
Two-qubit gates	274	(1)
Practical implementations of qubit operations	275	(4)
Decoherence and error correction	279	(2)
Applications of quantum computers	281	(7)
Deutsch's algorithm	281	(2)
Grover's algorithm	283	(3)
Shor's algorithm	286	(1)
Simulation of quantum systems	287	(1)
Quantum repeaters	287	(1)
Experimental implementations of quantum computation	288	(4)
Outlook	292	(4)
Entangled states and quantum teleportation	296	(56)
Entangled states	296	(2)
Generation of entangled photon pairs	298	(3)
Single-photon interference experiments	301	(3)
Bell's theorem	304	(6)
Introduction	304	(1)
Bell's inequality	305	(3)
Experimental confirmation of Bell's theorem	308	(2)
Principles of teleportation	310	(3)
Experimental demonstration of teleportation	313	(3)
Discussion	316	(5)
Appendices
A. Poisson statistics	321	(3)
B. Parametric amplification	324	(6)
B.1 Wave propagation in a nonlinear medium	324	(2)
B.2 Degenerate parametric amplification	326	(4)
C. The density of states	330	(3)
D. Low-dimensional semiconductor structures	333	(6)
D.1 Quantum confinement	333	(2)
D.2 Quantum wells	335	(2)
D.3 Quantum dots	337	(2)
E. Nuclear magnetic resonance	339	(7)
E.1 Basic principles	339	(2)
E.2 The rotating frame transformation	341	(3)
E.3 The Bloch equations	344	(2)
F. Bose--Einstein condensation	346	(6)
F.1 Classical and quantum statistics	346	(2)
F.2 Statistical mechanics of Bose--Einstein condensation	348	(2)
F.3 Bose--Einstein condensed systems	350	(2)
Solutions and hints to the exercises	352	(8)
Bibliography	360	(9)
Index	369