Download Physics 610: Quantum Optics

Fall 2009
Physics 610
Lloyd M. Davis
Quantum Optics
[email protected]
931-393-7335
Class Time: Tuesdays and Thursdays, 8:15—9:30 a.m. Central Time E-113 at UTSI and at 9:15 a.m. – 10:30 a.m.
Eastern Time by link to UTK Interactive classroom, South College room 107
Course Content and Texts:
Quantum Optics is a rapidly developing field that has now become quite extensive (see “Map of Quantum Optics”
given below). In this course we will not follow any one text but will use material from a number of texts, which are
listed below, as well as some papers from the literature. However, we will begin the course by following text book
No. 1—Optical Coherence and Quantum Optics, by Mandel and Wolf, which you are recommended to purchase.
In October 1995, Leonard Mandel (now deceased) and Emil Wolf from the University of Rochester published a
treatise that encompasses a very broad range of topics, both in the classical and quantum theories of light. Topics on
the classical theory of light propagation and on the coherence of light, the research specialty of Wolf, are treated in
detail in the first 9 chapters. In this course, we will touch only briefly on classical coherence theory (in lecture 13).
Most of the lectures will cover material on the fully-quantum mechanical description of the radiation field and its
interaction with matter, as treated in the later chapters. We begin at chapter 10, in which Maxwell’s equations are
quantized, and we then proceed to consider various properties, measurements, and physical states of the quantized
radiation field, including states that have no classical counterpart. A current area of interest in quantum optics, and in
fundamental quantum theory, relates to “entangled two-photon states”, and Bell’s inequality. Mandel was an expert in
this area, and his chapter 10 on the quantization of Maxwell’s equations seems to be slanted towards giving a very
thorough foundation for covering such topics. In this course we will not follow section by section through Mandel and
Wolf’s text, but instead we will attempt to present a broader perspective by skipping some of the more specialized
sections and embedding material from other texts and articles from the literature. In particular, some of the lecture
notes and some problems will be drawn from Loudon’s texts “The Quantum Theory of Light”, now in its third edition,
and from other texts listed below. Also, some use will be made of Eberly and Allen’s short treatise on the two-level
atom, and of other now-classic texts. Some classes will include problems that will be performed as worked examples.
There will also be problems set for homework each class. These set problems are due to be scanned and e-mailed to
me before the next class, unless otherwise specified. Model answers will be provided, usually at the next class. Many
references from the texts and the literature will be given for background reading. A course outline is given below. This
is tentative and may be changed to incorporate some material from the recent text on Quantum Optics by Garrison and
Chiao (No. 3, below).
Grades:
Homework assignments:
Midterm test 1:
Midterm test 2:
Final exam:
50 %
15 %
15 %
20 %
Recommended Prerequisite courses/background:
Quantum Mechanics, Maths Methods, Electrodynamics, Classical Optics, Classical Mechanics
Texts:
1. MW=Mandel and Wolf (1995) “Optical Coherence and Quantum Optics” (*Recommended to purchase)
http://www.amazon.com/Optical-Coherence-Quantum-Optics-Leonard/dp/0521417112/ref=sr_1_1?ie=UTF8&s=books&qid=1241028296&sr=1-1
2. FX=Fox (2006) “Quantum Optics: An Introduction” (Undergraduate level; Recommended for summer reading)
http://www.amazon.com/Quantum-Optics-Introduction-Oxford-Physics/dp/0198566735/ref=sr_1_2?ie=UTF8&s=books&qid=1241032576&sr=1-2
3. GC=Garrison and Chiao (2008) “Quantum Optics”
http://www.amazon.com/Quantum-Optics-Oxford-Graduate-Texts/dp/0198508867/ref=sr_1_1?ie=UTF8&s=books&qid=1241031018&sr=1-1
4. WM=Walls and Milburn (a:1994, b:2008) “Quantum Optics”
http://www.amazon.com/Quantum-Optics-D-F-Walls/dp/3540285733/ref=sr_1_1?ie=UTF8&s=books&qid=1241031075&sr=1-1
5. SZ=Scully and Zubairy (1997) “Quantum Optics”
http://www.amazon.com/Quantum-Optics-Marlan-O-Scully/dp/0521435951/ref=sr_1_1?ie=UTF8&s=books&qid=1241030904&sr=1-1
6. MS=Meystre and Sargent (1990,2007) “Elements of Quantum Optics”
http://www.amazon.com/Elements-Quantum-Optics-Pierre-Meystre/dp/3540742093/ref=sr_1_1?ie=UTF8&s=books&qid=1241032140&sr=1-1#
7. BR=Bachor and Ralph (2004) “A Guide to Experiments in Quantum Optics”
http://www.amazon.com/Guide-Experiments-Quantum-Optics/dp/3527403930/ref=sr_1_1?ie=UTF8&s=books&qid=1241032689&sr=1-1
8. NC=Nielsen and Chuang (2000) “Quantum Computation and Quantum Information”
http://www.amazon.com/Quantum-Computation-Information-Michael-Nielsen/dp/0521635039/ref=sr_1_1?ie=UTF8&s=books&qid=1241035387&sr=1-1
9. L3=Loudon, 3rd edn (2000) “The Quantum Theory of Light”
http://www.amazon.com/Quantum-Theory-Oxford-Science-Publications/dp/0198501765/ref=sr_1_1?ie=UTF8&s=books&qid=1241035436&sr=1-1
10.
11.
12.
13.
14.
L2=Loudon, 2nd edn (1983) “The Quantum Theory of Light”
L1=Loudon, 1st edn (1973) “The Quantum Theory of Light”
EA=Eberly and Allen (1975) “Optical Resonance and Two-Level Atoms”
KS=Klauder & Sudarshan (1968) “Fundamentals of Quantum Optics”
GK=Gerry and Knight (2005) “Introductory Quantum Optics”
http://www.amazon.com/Introductory-Quantum-Optics-Christopher-Gerry/dp/052152735X/ref=sr_1_5?ie=UTF8&s=books&qid=1241035672&sr=1-5#
Quantum Optics
Lecture
Date
Fall 2009
Tentative Course Outline (5-8-09)
Topics
States of the Quantized Radiation Field
1
8-20
MW 10.1-3
Quantization of Maxwell’s equations
2
8-25
MW 10.4-6
Fock states, linear and angular momentum
3
8-27
MW 10.7
Phase in quantum optics
4
9-1
MW 11.1-4
Coherent states
5
9-3
MW 11.5, 21.0-7;L3 4.7
Quantum dynamics; Squeezed states
6
9-8
L3 4.6; MW 13.1-3
Mixed States; Chaotic State
7
9-10
MW 11.6-9; WMa 4.2
Coherent state representation
Take-home midterm test 1 (Lectures 1-6) (Due: 9-15 )
Coherence
8
9-15
WMa 3.1-5; MW 12.1-3; L2 6.1-2 Young’s experiment; First order coherence
9
9-17
MW 12.4; L2 6.3-5;
Higher order coherence
10
9-22
Hanburry-Brown Twiss; Cross-spectral density
11
9-24
Photon counting
12
9-29
Stationarity, homogeneity, isotropy; Photon localization
13
10-1
Propagation of coherence; Spectrum change with propagation
Interaction of light with matter
14
10-6
Semiclassical theory
15
10-8
Atom-radiation interaction; Minimal coupling Hamiltonian
16
10-13 Atomic second quantization; Perturbative transition rates; Heisenberg representation
Take-home midterm test 2 (Lectures 7-14) (Due: 10-20)
10-15 Fall break
17
10-20 Interaction picture calculations; Superfluoresence; Derivation of optical Bloch equations
18
10-22 Damping mechanisms; Power broadening; Linewidths
19
10-27 Motion on the Bloch sphere; Pulse propagation; Maxwell-Bloch equations; Solitons;20 10-29
21
11-3
Photon echoes; Super fluorescence; Superradiance; Optical bistability
22
11-5
Resonance fluorescence
23
11-10 Quantum theory of damping
Entanglement
24
11-12
25
11-17
26
11-19
27
11-24
28
12-1
12-8
Einstein-Podolsky-Rosen paradox; Bell’s inequality; Transactional interpretation
Beam splitters; Interferometers; Hong-Ou-Mandel & Franson experiments
Entanglement
Quantum Cryptography and Teleportation
Quantum Computing
Final Exam