Physics 8.422 Spring 2013


                             Atomic and optical Physics







Prof. Wolfgang Ketterle




Alexei Bylinskii



Lawrence Cheuk



Niklas Jepsen



Jee Woo Park




Molu Shi



Joanna Keseberg





Lectures:     Mondays, Wednesdays

(and some Fridays 3/1, 3/22, 4/12 –  room 4-237, 5/17 Room 37-212)

1:00-2:30, Room 37-212

                        First day of classes: Wed, 2/6

Office hours:         WK:  Thu 1:30-2:30, 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

Term papers due:  Fri, 5/17/2013 (day of last class) Please email to WK



Main topics:

·  Quantum states and dynamics of photons

·  Photon-Atom interactions: basics and semiclassical approximations

·  Photon-Atom interactions: open system dynamics, optical Bloch equations

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

·  Cold atoms, quantum states, and quantum dynamics: quantum algorithms and protocols, ion traps, magnetic traps, evaporative cooling, Bose-Einstein condensation


Web Site for 2011                   Web Site for 8.421

Atomic Physics Wiki with Typed Lecture Notes



HW 1   due Feb. 22


HW 2 due Mon March 4


HW 3 due Mon March 11


HW 4 due Mon March 18


HW5 due Mon April 1


HW 6 due Mon, April 8


HW 7 due Wed, April 17


HW 8 due Mon, April 22


HW 9 due on Fri, May 3


HW 10, due on Fri, May 10



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 (L3-8)

3. Photon-atom interactions (L9-10)

4.  Optical Bloch equations (L11-14)

5.  Light forces (L15-19)

6. Bose-Einstein Condensates and Ultracold Atoms (L20-24)

7. Ion traps and quantum information (L25-26)


Class Write-Ups:

L1 Introduction (Feb. 6)

L2 QED Hamiltonian (Feb. 11)

L3 Quantum description of light (Feb. 13, 19)

L4 Non-classical light, squeezing (Feb. 20, 25)    Clicker questions

L5 Single photons (Feb. 27, March 1)

L6 Entangled states (March 1, March 4, March 6)

L7 Metrology, shot noise and Heisenberg limit (March 6 and 18)

L8 g_2 for atoms and light (March 18, 20)

L9 Diagrams for light-atom interactions (March 20, 22)

L10 van der Waals and Casimir interactions (3/22, 4/1)

L11 Casimir force (4/1)

L12 Resonant interactions (4/1, 4/3))

L13 Derivation of optical Bloch equations (4/3, 4/8)

L14 Solutions of optical Bloch equations (4/10, 4/14)
        Nature paper on engineered dissipation

L15 Unraveling Open System Quantum Dynamics (4/22)

L16 Light forces part 1 (4/29)  part 2 (5/1)

L17 Dressed atom part 1 (5/1)
        part 2 (forces and sub Doppler and sub recoil cooling) 5/6, 5/8

L18 Techniques for ultralow temperatures (magnetic trapping, evap. cooling) 5/8, 5/13

L19 Bose gases, BEC, superfluid to Mott insulator transition 5/13, 5/15

L20 Fermi gases, BEC-BCS crossover 5/17

L21 Ion trapping and quantum gates 5/17


Additional reading material

L1 Introduction                                                                                       

Recent advances in AMO physics

Topics of this course

8.421 vs. 8.422


L2 The QED Hamiltonian                                                                      

Viewgraphs used in class:  Download



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.

I would recommend consulting this book whenever you want to know more about the “exact” formulation of the theory.  I am always amazed how easily you can open this book in the middle and still understand the explanations.

L3 Quantum description of light                                                                           


Loudon, chapter 3; Weissbluth, 4.4-4.8

Further reading:

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

L4 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                                                                       

3 pages lecture notes by W.K.

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)

L5 Single photons

L6 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

L7 Metrology, shot noise and Heisenberg limit

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).

L8 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

L9 Diagrams for light-atom interactions

API see pp. 15-21 and Complement A_I

L10/11 van der Waals and Casimir interactions

Van der Waals interaction            

see API, pp. 118-126

Reading:          four pages course notes from Dan Kleppner

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

Casimir interactions

            Lecture notes WK

            Copies from Serge Haroche’s summer school notes

Jaffe paper on Casimir force and zero-point energy

L12 Resonant scattering and radiative corrections

           Reading:  API, Chapter III

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).

L13/14 Derivation and solutions of Optical Bloch equations

Reading:  API 257 – 333, lecture notes

L15 Unraveling open quantum systems

Reading: lecture notes

Original 1992 paper on QMC wave function method Link

L16/17 Light forces, dressed atom

Reading: API 370 – 379

First realization of molasses Link

Advanced reading on friction force in a standing wave

pp. 34-35 in :
C. Cohen-Tannoudji, “Atomic Motion in Laser Light”, in “Fundamental Systems in Quantum Optics”, Les Houches, Session LIII, 1990, ed. by J. Dalibard, J.M. Raimond and J. Zinn Justin, pp. 1-164 (Elsevier Science Publisher B.V., 1992, Link

J.P. Gordon and A. Ashkin, PRA 21, 1606 (1980) Link

            Dressed atom and dipole forces

            Reading:  API Chapter VI – worth reading!

Important paper:

J. Dalibard and C. Cohen-Tannoudji, JOSA B 1985  Link

Spontaneous light force traps

Magneto-optical trap, Optical Earnshaw theorem

W.D. Phillips, Laser cooling and trapping of neutral atoms, in Laser Manipulation of Atoms and Ions, edited by E. Arimondo, W.D. Phillips, and F. Strumia, Proceedings of the International School of Physics “Enrico Fermi”, Course CXVIII (North-Holland, Amsterdam, 1992) Download

pp. 316 – 355 has a nice summary on dipole traps and raditation pressure traps

Original papers:

            Optical Earnshaw theorem (OET):  Ashkin and Gordon

            How to circumvent the OET:  Pritchard et al.

            Realization of the MOT:  Raab et al.


L18 Techniques for ultralow temperatures

Sub-Doppler and Sub-Recoil cooling

Magnetic trapping

Further reading: W. K., D.S. Durfee, D.M. Stamper-Kurn, Varenna Lecture Notes 1999, pp. 80-89

Evaporative cooling

Further reading:: W. Ketterle and N.J. van Druten, Adv. At. Mol. Opt. Phys. 37, 181-236 (1986).  Relevant pages:  pp. 181-193


L19 Bose gases, BEC, superfluid to Mott insulator transition

Variational derivation of Gross-Pitaevski equation:

J. Rogel-Salazar. Eur. J. Phys. 34 (2013) 247–257   Link

Bose-Einstein Condensation in Dilute Gases, C.J. Pethick and H. Smith, selected

On Bogoliubov transformation and collective excitation:   pp. 205-214
On nonlinear Schrödinger equation:  pp. 146-156
On hydrodynamics:  pp. 165-179

            Mean field theory of the superfluid to Mott insulator transition

D. van Oosten, P. van der Straten,  and H. T. C. Stoof, PRA 63, 053601
            (2001)  Link

L20 BEC-BCS crossover in fermions

Varenna notes on ultracold fermions  Link

L21 Trapped ions and quantum gates

See Wiki