Physics 8.422 Spring 2015

Atomic and optical Physics









Prof. Martin Zwierlein




Kristin Beck


Boris Braverman




Michael Gutierrez


Colin Kennedy


Jennifer Schloss



Joanna Keseberg




Lectures:     Mondays, Wednesdays

(and some Fridays 3/6)

1:00-2:30, Room 4-163

                        First day of classes: Wed, 2/4

Office hours:         MWZ:  Wed 2:45-4pm, or by appointment (just send an e-mail)

                                    TAs:  announced on problem sets, and by appointment


Homework drop off:  In class, or in 26-237, Monday 1pm

Term papers due:  Thursday, 5/14/2013 (day of last class) Please email to MWZ



Main topics:

·  Quantum states and dynamics of photons

·  Photon-Atom interactions: semiclassical approximations, optical Bloch equations

·  Applications and limits of the optical Bloch equations: dressed atoms, light force, decoherence

·  Cold atoms, quantum states, and quantum dynamics; ion traps, magnetic traps, evaporative cooling, Bose-Einstein condensation, degenerate Fermi gases, interatomic interactions, Feshbach resonances, ultracold atoms in optical lattices


Web Site for 2013                   Web Site for 8.421

Atomic Physics Wiki with Typed Lecture Notes



updated HW1 due Feb 23, 1pm in class


HW2 due Mar 2, 1pm in dropbox folder


updated HW3 due Mar 11, 1pm in class or Dropbox


HW4, due Mar 16, 1pm in class or dropbox


HW5, due Mar 30, 1pm in class or dropbox


HW6, due Wednesday, April 8th


HW7, due Wednesday, April 15th


HW8, due Wednesday, April 22nd


HW9, due Wednesday, April 29th


HW10, due Wednesday, May 6th



MIT Stellar grade management                   Course requirements

Course info and calendar                  Recommended books


Course outline

1.  Introduction, atom-light Hamiltonian (L1-2)

2. Quantum light: states and dynamics (L3-6)

3. Photon-atom interactions (L7-8)

4.  Optical Bloch equations (L9-12)

5.  Light forces (L13-15)

6. Ion traps (L16-17)

7. Bose-Einstein Condensates and Ultracold Atoms (L18-25)


Class Notes and additional reading material:

1. L1 Introduction                                                                                   


A Brief History of Atomic Physics: See D. Kleppner, RMP 71, S78, 1999
Papers: Lamb Shift paper, Rabi’s Hydrogen Hyperfine paper

            Recent advances in AMO physics   

Topics of this course

8.421 vs. 8.422



2. L2 Photon-Atom Interactions I: Phenomenological Models

1.1 Lorentz Model

1.2 Einstein Model


3. L3 Photon-Atom Interactions II: Quantization of the E&M Field

2 Classical Electrodynamics

2.1 Maxwell’s and Lorentz equations

2.2 Vector potential

2.3 Electrodynamics in reciprocal space

2.4 Normal variables

2.5 Quantization of the E&M field

2.6 Total Hamiltonian and Momentum

2.7 State Space

2.8 The Dipole Interaction



The discussion follows the appendix in Atom –Photon Interactions.

Please read pp. 621 – 643   Download

Further reading:

A 500-page derivation and discussion of the basic equations of QED can be found in

Cohen-Tannoudji, Claude, Dupont-Roc, Jaques, and Grynberg, Gilbert, Photons & Atoms, Wiley-Interscience, 1997.

4. L4 Quantum States of Light I


Loudon, chapter 3; Weissbluth, 4.4-4.8

5. L5 Quantum States of Light II


Further reading:

Yamamoto and Rempe group papers (example of single photon g(2)(tau) meas.)

Yamamoto paper on Generation of number states


Wigner function: Term paper by Boris Braverman, lots of visual examples, including reconstruction via homodyne detection, plus lots of references

6. L6 Non-Classical Light


    Further reading:

Weissbluth, 4.9 .  Section on squeezed states

H.J. Kimble, Quantum fluctuations in quantum optics, in Les Houches 1990.  Extensive and advanced treatment of squeezed light.

R.W. Henry and S. C. Glotzer, A squeezed-state primer, Am. J. Phys. 56, 318 (1988).  Basic discussion using only elementary quantum mechanics.

M.C. Teich and B. E. A. Saleh Squeezed and AntiBunched Light, Physics Today, June 1990.   Popular article on non-classical light.

    Generation of squeezed states, classical squeezing

F. DiFilippo et al, Classical Amplitude Squeezing for Precision Measurements. PRL, 68, 2859 (1992).


A. Furusawa et al, Unconditional Quantum Teleportation. Science, 282, 706 (1998) .

     Beam splitter and homodyne detection                                                                       

B.L. Schumaker, “Noise in homodyne detection”, Optics Letters 9, 189 (1984)

     Experiments with squeezed light

Ling-An Wu, H.J. Kimble, J.L. Hall, H. Wu, “Generation of Squeezed States by Parametric Down Conversion”, PRL 57, 2520 (1986)

Min Xiao, Ling-An Wu, H.J. Kimble, “Precision Measurement beyond the Shot-Noise Limit”, PRL 59, 279 (1987)

E.S. Polzik, J. Carri, H.J. Kimble, “Spectroscopy with Squeezed Light”, PRL 68, 3020 (1992)

7. L7 Single Photons

8. L8 Single Photons II

9. Entangled states


C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, C. Monroe, “Experimental entanglement of four particles”, Nature 404, 256 (2000)


Excerpts from Nielsen and Chuang Quantum Computation and Quantum Information on Schmidt Decomposition


Gravitational wave detection:

C.M. Caves, “Quantum-mechanical noise in an interferometer”, Phys. Rev. D 23, 1693-1708 (1981)

Heisenberg limited interferometry

Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone, “Quantum-Enhanced Measurements: Beating the Standard Quantum Limit”, preprint quant-ph/0412078

Proposal for atom interferometry:

P. Bouyer, M. A. Kasevich, “Heisenberg-limited spectroscopy with degenerate Bose-Einstein gases”, PRA 56, R1083 (1997)

Creation of correlated states with Bose-Einstein condensates:

J.M. Vogels, J. K. Chin, and W. Ketterle, “Coherent Collisions between Bose-Einstein Condensates”, PRL 90, 030403 (2003).


Further reading on HW4: Note on g_2 for atoms and light

Reading:  some pages from Gordon Baym, Lectures on Quantum Mechanics

PRL on HBT experiment with cold atoms
2007 Nature paper

2014 Science paper on HBT with two atoms in a double-well


10. L10 Atom-Light Interactions

API see pp. 15-21 and Complement A_I

11. L11 Spontaneous Emission, Absorption, Scattering


Daniel Kleppner, Inhibited Spontaneous Emission, PRL 47, 233 (1981)


12. L12 Spontaneous Decay


Lecture notes on Wigner-Weisskopf treatment


Further reading:

API Complement CI, Discrete Level Coupled to a Broad Continuum, pp. 49-66

13. L13 Resonant Scattering – Simple Model


14. L14 Van der Waals and Casimir Forces I


Further reading:

Van der Waals interaction: API 118-126

four pages course notes from Dan Kleppner

Physics Today paper by L. Spruch (Nov. 1986, p. 37)

15. L15 Van der Waals and Casimir Forces II


Further reading:

Casimir, Polder, “The Influence of Retardation on the London-van der Waals Forces”, Phys. Rev. 73, 360 (1948)

Copies from Serge Haroche’s summer school notes

Jaffe paper on Casimir force and zero-point energy

16. L16 Non-Perturbative Calculation of Transition Amplitudes

API Chapter 3

Further reading:  J. Dalibard, J. Dupont-Roc and C. Cohen-Tannoudji, Vacuum fluctuations and radiation reaction: identification of their respective contributions, J. Physique 43, 1617-1638 (1982).


17. L17 Derivation of the Master Equation

API Chapter IV


18. L18 Optical Bloch Equations
API Chapter V


19. L19 Light Forces I

API Chapter V