Phys 570V: Advanced Topics in Optics and Photonics Professor Tongcang Li

Lecture 20: cooling of

Course website: http://www.physics.purdue.edu/academic- programs/courses/course_detail.php?SEM=fall2015&c=phys570V Syllabus, Lecture notes, etc.

Purdue University Fall 2015 570V Room: Phys 331 Time: MW 2:30-3:45 PM 1 Take-home exam: due on Wed., 11/11/2015

Final presentations: 11/30-12/9 • 12-minute talk + 3 minute Q&A. • The content of the presentation can be about any recent (after 2000) development in optics and photonics. It can be about one particular paper, an overview of a research topic, or your own research if it is related to this course. • After each presentation, every student (including the speaker) will give a grade (0- 10) to it. The instructor will also grade it. The final grade of the presentation will be the average of the grades given by students (50%) and the instructor (50%).

• Presentation sequence: to draw lots on Nov. 11

2 Last lecture: Radiation Pressure

ℎ 퐸 Photon momentum: 푝 = = 휆 푐 푑푝 푑 퐸 푃 퐹 = = = for absorbed light 푑푡 푑푡 푐 푐 2푃 퐹 = for reflected light 푐

If we reflect 100W of light, 퐹~7 × 10−7 N

3 Last lecture: optical tweezers

Rayleigh approximation

4 Our vacuum optical tweezer at Purdue University

Nanodiamond (100 nm)

5 This lecture: of atoms

6 Laser cooling

2005 1981 2012 1989

D.J. Wineland, H. Dehmelt: Bull. Am. Phys. SOC. 20, 637 (1975) Neutral atoms Ions

Laser cooling/trapping

1997 , Claude Cohen-Tannoudji, William D. Phillips

Atomic Bose-Einstein condensation (BEC) Eric A. Cornell, Wolfgang Ketterle, Carl E. Wieman 2001 7 Laser cooling: basic idea

Absorption-emission

8 Doppler cooling

force

(Doppler limit)

9 10 11 Zeeman slower

Wikipedia 12 Optical Molasses

(Doppler temperature) (240 µK for Na atoms) 13 Sub-Doppler cooling

14 k 2 Recoil Velocity: vR   m mL

1 (k)2 Recoil Energy: E  mv2  R 2 R 2m

= 2.95cm/s For sodium atoms in 589nm laser: vR 1 E = 2    25.0 kHz = k  2.4 µK R 2 B

15 Magneto Optical Trap (MOT)

Nature Nanotechnology, 8, 317–318 (2013) 16 Magnetic trap   H    B

 (BmF gF )Bz 1 For sodium atoms in the state: Fm1,  1, g F F 2 V

Atoms can be trapped in a local minimum of magnetic field. x,y z

17 Evaporative cooling

Waferboard / Flickr

18 Bose-Einstein Condensate

19 Vacuum Chamber 1.1∙10-11 Torr 3∙10-9 Torr 800 m/s 30 m/s

6∙10-11 Torr

20 Creation of a Bose-Einstein condensate

800 m/s 30 m/s

24 cm/s

Na BEC 21 Signatures of BEC

• Bimodal distribution • Anisotropic expansion • Matter interference •

Cornell/Weiman

ketterle 22 Optics & Atom Laser

23 Atoms in an optical lattice

24 Creating a periodic potential

Magnetic BEC Waveguide

Mirror

532nm Laser Waist: 120 µm Max Power: 1 W Optical Lattice

Well Depth: 0 – 22 ER

YAG Tweezer (1064nm) Waist ≈ 180 µm Trap Depth ≈ 4 E R 25 Single particle in a periodic potential

2 V(z) V0 sin (kL z) V0

1. Classical: Trapped in a well if V0  Eatom 2. Quantum: Forms a band structure.

    ikRn  (r  Rn )  e (r)

26 Expansion in a periodic potential Dilute Thermal Atoms

V0  2.24ER  6.5K

11.8 ms 22.8 ms 33.7 ms

The expansion of thermal atoms (T=0.52 µK) is in excellent agreement with the single-particle model. 27 Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms

Nature 415, 39-44 (3 January 2002) 28 Next lecture: Optical refrigeration of solids

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