1. Light scattering and atom amplification in a Bose- Einstein condensate March 25, 2004 Yoshio Torii Institute of Physics, University of Tokyo, Komaba Workshop on Chemistry of Cold Molecules

2. The overview The review of BEC in atomic gases Atom-optics elements for BECs Superradiant light scattering in a BEC (Matter wave amplification in a BEC) Quest for Continuous atom lasers

3. What is Bose-Einstin condensation? Macroscopic occupation of atoms in the lowest quantum state of motion

4. The criterion of BEC Phase space density (the number of atoms in the lowest quantum state) Thermal de Briglie wave length (the average size of wavepackets) Predicted by Einstein in 1925 BEC is formed when the wavepackets overlap with each other !

5. atoms behave as “billiard balls” Wave nature begins to manifest Wavepackets begin to overlap One giant matter wave Bose-Einstein condensation T ～ 300K T～1KT～1K T ～ 100nK T ～ 100μK Laser cooling Evaporative cooling BEC 波動論的説明

6. 1924,25Bose-Einstein statistics (Bose) prediction of Bose-Einstein condensation (Einstein) 1938 Superfluidity in liquid helium explained as BEC （ London ） 1957 BCS theory for Superconductivity （ Bardeen, Cooper, Schrieffer ） 1960Invention of laser （ Maiman ） 1975The idea of laser cooling （ Hänsch,Schawlow ） 1980 ～ Deceleration of atomic beam （ Phillips ）～ mK 1985Laser cooling of atoms in 3-D （ Chu ） ～ 240μK 1988 Polarization Gradient cooling ～ 3μK （ Phillips, Cohen-Tannoudji ） 1995Realization of BEC in Rb, Na （ Cornel, Wieman, Ketterle ）～ 100nk Nobel Prize in 1997 Nobel Prize in 2001 The history of Bose-Einstein condensation

7. The BEC apparatus at Tokyo Univ.

8. The principle of laser cooling →cooling! Laser light: Scattered light: Example 1 : Doppler cooling Example 2: Cavity cooling H. W. Chan, et. al., PRL 90, 063003, 2003

9. Magneto-optical Trap (MOT)

10. MOT of Rb atoms in a glass cell 4cm

11. What is evaporative cooling? http://www.colorado.edu/physics/2000/applets/bec.html Nice applet at Colorado University Website

12. Zeeman shift of Rb87

13. Cloverleaf coils for magnetic trap

14. Evaporative cooling an a cigar- shaped magnetic trap 5 MHz 5mm 1MHz 5 MHz 10 MHz 20 MHz

15. BEC phase transition

16. The properties of BEC 1ms16.5ms11ms5.5ms22ms 27.5ms 33ms 1mm Images of a BEC released from the magnetic trap 1. narrow velocity spread below the recoil velocity （ 6mm/s for Rb87 ） 2. Well localized in space （ 10μm ～ 100μm ） 3. Spatial density of ～ 10 14 atoms/cm 3 4. Coherent

17. Atom-optics elements for BECs The Basic idea : Bragg scattering matter wave (BEC) Optical standing wave Bragg diffracted matter wave light wave Modulation of refractive index in the matter Acoust-Optics Modulator Bragg diffracted light wave

18. Bragg scattering of BEC [M. Kozuma et. al.Phys. Rev. Lett. 82, 871 (1999)]

19. Absorption Images of Bragg diffracted BEC (20 ms TOF) Half beamsplitter Perfect mirror Y. T, et. al., PRA 61, R041602 (2000)

20. Mach-Zehnder interferometer for light waves and matter waves Light wave matter wave (BEC)

21. Mach-Zehnder interferometer for BECs Y. T, et. al., PRA 61, R041602 (2000)

22. S. Inouye, et. al., Science 285, 571 (1999) Superradiant Rayleigh scattering in a Bose-Einstein condensate 35  s 75  s 100  s Na BEC Off-resonant pump light

23. Superradiant Rayleigh scattering in a Rb BEC Week pump light Rb BEC D. Schneble, Y.T., M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, Science 300, 475 (2003) Strong pump light Rb BEC

24. The origin of superradiance The rate of light scattering is enhanced by the number of already scattered photons Pump light Spontaneous emission BEC … goes on

25. Laser Light Amplification by Stimulated Emission of Radiation N photons already in the cavity Emission rate from an excited atoms Stimulated emission Spontaneous emission

26. (10 fold amplification) Matter wave amplification Pump pulse only Nothing happened Bragg pulse only 6.5% of atoms were Bragg diffracted Bragg pulse, then pump pulse 66% of atoms were coupled out M. Kozuma, et. al., Science 286, 2309 (1999) BEC Pump beam

27. How to check the coherence of the amplified wave

28. Interferometer for the amplified matter wave M. Kozuma, et. al., Science 286, 2309 (1999) reference Matter wave amplified Matter wave seeded Matter wave Bragg pulse  Bragg pulse  Bragg pulse pump pulse

29. The gallery of atom lasers MIT ‘97Munich ‘99Yale ‘98 NIST ‘99 Rf sweep Rf knife gravityBragg pulses

30. Continuous atom laser A device which converts thermal atoms into a coherent matter wave “continuously” Thermal atoms Coherent matter wave E. Mandonnet, et. al., Eur. Phys. J. D 10, 9 (2000) Rf evaporation 2-D Magnetic guide

31. Our strategy for CW atom laser Goal: MOT loading rate more than 10 10 atoms/s Zeeman slower

32. The whole apparatus 2m

33. Zeeman coils 1m Trimming coils

34. Velocity distribution of a Zeeman-slowed Rb atomic bean ・ Flux of the thermal atoms ～１０ １２ atoms/s ・ Flux of the slowed atoms ～２ × １０ １１ atoms/s （ 20% of the thermal atoms ） ・ final velocity ～ 20 m/s

35. Loading a MOT from slowed atoms 4cm 2×10 10 atoms/s

36. The world of Bose-Einstein condensation Superconductor 01 Condensed-matter physics Quantum Optics Superfluid Atomic BEC (atom laser) Optical laser Chemistry with Molecular BECs