Physics 8.422

Atomic and optical Physics

		Room	Tel.	e-mail
Lecturers:	Prof. Wolfgang Ketterle	26-243	253-6815	ketterle@mit.edu
	Prof. Isaac Chuang	E15-424	253-1692	ichuang@mit.edu
Assistants:	Micah S Boyd	26-269	452-2501	micahb@mit.edu
	Jit Kee Chin	26-259	253-5926	jitkee@mit.edu
	Daniel E Miller	26-259	253-5926	coldatom@mit.edu
	Thomas A Pasquini	26-253	253-4178	pasquini@mit.edu
	Erik W Streed	26-267	324-0500	streed@mit.edu
Secretary:	Ellenor Barish	26-237	253-6830	ellenor@mit.edu

Lectures: Wednesday, Friday, 9:30-11:00, Room 26-302

First day of classes: Wed, 2/2

Office hours: by appointment (just send an e-mail ….)

Course outline 1999 Recommended books Course requirements

Reminder: Term papers are due on Wednesday, May 11

Assignments: Assignment 1 due Friday Feb 11

Assignment 2 due Friday Feb 25

Assignment 3 due Friday March 4

Assignment 4 due Friday March 11

Assignment 5 due Friday March 18

Assignment 6 due Friday April 1

Assignment 7 due Friday April 8

Assignment 8 due Friday April 15

Assignment 9 due Friday April 22

Assignment 10 due Wed, May 4

Covered Topics and Handouts:

1. Introduction [L1: 2/2/05]

Recent advances in AMO physics

Topics of this course

8.421 vs. 8.422

Requirements

2. Classical molasses and beam slowing

Handouts:

1. 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) pp. 289-304 (the second part on atom traps will be covered later in this course). Download

2. S. Chu, L. Hollberg, J.E. Bjorkholm, A. Cable, and A. Ashkin, Three-Dimensional Viscous Confinement and Cooling of Atoms by Resonance Radiation Pressure, Phys. Rev. Lett. 55, 48 (1985). Download

3. One-page note on chirped slowing. Download

Further reading:

1. W.D. Phillips, J.V. Prodan, and H.J. Metcalf, Laser cooling and electromagnetic trapping of neutral atoms, J. Opt. Soc. Am. B 2, 1761 (1985).

2. P.D. Lett, W.D. Phillips, S.L. Rolston, C.E. Tanner, R.N. Watts, and C.I. Westbrook, Optical Molasses, J. Opt. Soc. Am. B 6, 2084 (1989).

3. W. Ertmer, R. Blatt, J.L. Hall, and M. Zhu, Laser Manipulation of Atomic Beam Velocities: Demonstration of Stopped Atoms and Velocity Reversal, Phys. Rev. Lett. 54, 996 (1985).

4. W. Ketterle, A. Martin, M.A. Joffe, and D.E. Pritchard, Slowing and cooling atoms in isotropic laser light, Phys. Rev. Lett. 69, 2483 (1992).

5. T.E. Barrett, S.W. Dapore-Schwartz, M.D. Ray, and G.P. Lafyatis, Slowing Atoms with (sigma-minus) Polarized Light, Phys. Rev. Lett. 67, 3483 (1991).

2.1. The spontaneous light force

2.2. 1D optical molasses

2.3. The Doppler cooling limit

2.4. Beam slowing [L2: 2/4/05]

2.5. Energy vs. momentum picture

2.6. 3D molasses and higher intensity

2.7. Momentum and spatial diffusion

3. The QED Hamiltonian [L3: 2/6/05]

Viewgraphs used in class: Download

Reading:

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.

4. Properties of light [L4: 2/11/05]

Handouts:

Loudon, chapter 3; Weissbluth, 4.4-4.8

Further reading:

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

4.1. The quantized radiation field

4.1.1. Thermal states (chaotic light)

4.1.2. Coherent states; Q(alpha) representation

4.1.3. Fluctuations, noise, and second order coherence

4.1.4. Single photon states & the Hanbury-Brown Twiss experiment

4.2. Squeezed states of light [L5: 2/16/05]

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.

4.2.1. The displacement and squeeze operators

4.2.2. Generation of squeezed states, classical squeezing

Handout: 1 page, lecture notes by Dave Pritchard

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

4.2.3. Homodyne detection

4.2.4. Teleportation

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

4.2.5. Beam splitter and homodyne detection [L6: 2/18/05]

3 pages lecture notes by W.K.

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

4.2.6. 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)

[L7: 2/23/05]

4.3. Interferometry and Entanglement

4.3.1. Gravitational wave detection:

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

4.3.2. 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: 2/25/05]

4.3.3. Entanglement

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

[L9: 3/2/05]

5. Basic aspects of the interaction between light and atoms

5.1. Transition amplitudes and diagrams

Reading: API, pp. 15-22 and complement A

[L10: 3/4/05]

Extra topic: Hanbury-Brown and Twiss experiment and the g2 function

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

PRL on HBT experiment with cold atoms

5.2. Some interaction processes between photons and atoms

Reading: API, Chapter II

5.2.1. Emission

5.2.2. Absorption

5.2.3. Scattering

5.3. Resonant scattering and radiative corrections

Reading: API, Chapter III

[L11: 3/9/05]

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).

5.4. Interaction by photon exchange and collisions

5.4.1. 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)

[L12: 3/11/05]

5.4.2. Casimir interactions

Reading: course notes (WK)

Haroche summer school notes

5.4.3. Langevin model for inelastic collisions

Handouts: four pages course notes on inelastic and elastic

collisions (WK)

[L13: 3/16/05]

5.4.4. Elastic collisions between cold atoms

Handouts:: Some pages of review paper by Metcalf, van der Straten

(Physics Reports 244, 203 (1994)).

5.4.5. s-wave scattering

6. Master Equation

Handout: Lecture notes (Prof. Chuang)

Langevin approach, vacuum as a reservoir

Reading: API, Chapter IV

Further reading: Weissbluth, pp. 287-297

[L14: 3/18/05]

7. Optical Bloch Equations]

Reading: API, Chapter V

7.1. Derivation

7.2. Rotating-wave approximation

[L15: 3/30/05]

7.3. Adiabatic elimination of coherences

7.4. Steady-state solution

7.5. Spectrum of emitted light

[L16: 4/1/05]

7.6. Mean radiation forces

Reading: API pp. 370 - 379

7.6.1. Radiation pressure force

7.6.2. Reactive force

7.7. Moving atoms, friction force

Further reading:

C. Cohen-Tannoudji, Les Houches 1990, pp. 34-35

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

[L17: 4/4/05]

7.8. Diffusion in a standing wave (not covered in class)

Optional reading:

C. Cohen-Tannoudji, Les Houches 1990, pp. 46-53

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

7.9. Experiments on the stimulated light force

Further reading:

Aspect et al. 1987: Cooling Atoms with Stimulated Emission

Salomon et al. 1987: Channeling Atoms

Jessen et al. 1992: Localization of Atoms

Raithel et al. 1998: Motion of Wave Packets in Optical Lattices

Chu et al. 1996: First optical trap

Miller et al. 1993 : Far-off-resonance trap

8. The dressed atom approach

Reading: API Chapter VI – worth reading!

8.1. Derivation of the energy levels of the dressed atom

[L18: 4/8/05]

8.2. Resonance fluorescence in the dressed atom picture

8.3. Dipole forces within the dressed atom picture

Lecture notes

Important paper:

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am .B 2, 1707 (1985)

8.3.1. Mean dipole force for an atom at rest

8.3.2. Mean dipole force for a slowly moving atom

8.3.3. Energy balance in a small displacement

[L19: 4/13/05]

8.3.4. Momentum diffusion due to dipole force fluctuations

8.3.5. Atoms moving in a standing wave

8.3.6. Cooling in a standing wave

9. Spontaneous light force traps

Magneto-optical trap, Optical Earnshaw theorem

Reading: pp. 316-335 of the paper which was already used in lecture 1

(Nice summary on both dipole traps and radiation pressure traps)

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

Original papers:

Optical Earnshaw theorem (OET): Ashkin and Gordon

How to circumvent the OET: Pritchard et al.

Realization of the MOT: Raab et al.

[L20: 4/15/05]

10. Quantum Monte Carlo wavefunction method

Reading:

J. Dalibard, Y. Castin, K. Molmer, Phys. Rev. Lett. 68, 580 (1992)

10.1. Basic concepts

10.2. MCWF procedure

[L21: 4/20/05]

10.3. Proof of equivalence to the Optical Bloch equations

11. Models of Decoherence

11.1. Decoherence - definition and perspective

11.2. Three models of phase damping

11.2.1. Random phase noise

11.2.2. Elastic collisions

11.2.3. Random phase flips

11.3. Jaynes-Cummings collapses and revivals

Lecture Notes

[L22: 4/22/05]

12. Ion traps

12.1. Hamiltonians and Cooling

12.1.1. The ion trap physical system

12.1.2. The Hamiltonian

12.1.3. Sideband cooling - process and limits

12.1.4. Experimental observations of sideband cooling

Further reading:

Blatt, Les Houches Lecture Notes on ion trapping

Diedrich et al., sideband cooling

Eschner et al., review paper on laser cooling of ions

[L23: 4/27/05]

12.2. Quantum Control of Single Ions

12.2.1. The challenge of quantum state preparation

12.2.2. Review of unusual states

12.2.3. Motional state control in ion traps

12.2.4. Motional Fock, Coherent, and Schroedinger cat states

12.2.5. Recipe for arbitrary motional states

Further reading:

Leibfried et al., Quantum dynamics of single trapped ions

[L24: 4/29/05]

12.3. Quantum Computation with Trapped Ions

12.3.1. Quantum Gates and Circuits

12.3.2. The Cirac-Zoller CNOT

12.3.3. Geometric Phase Gate

Further reading: Three original papers on quantum gates

Monroe et al. 1995

Schmidt-Kaler et al. 2003

Leibfried et al. 2003

[L25: 5/4/05]

13. Magnetic traps and evaporative cooling

13.1. Stability, Majorana flops, magnetic levitation

13.2. Wing’s theorem

13.3. Magnetic trap configurations

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

[L26: 5/6/05]

13.4. Evaporative cooling

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

14. Bose-Einstein condensation

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

14.1. Homogeneous interacting Bose gas, Bogoliubov solution

14.2. Elementary excitations

Reading: pp. 205-214

[L27: 5/11/05]

14.3. Inhomogeneous Bose gas, nonlinear Schrödinger equation

14.4. The Thomas-Fermi approximation

Reading: pp. 146-156

14.5. Hydrodynamic flow of a superfluid

Reading: pp. 165-179