1. On the path to Bose-Einstein condensate (BEC) Basic concepts for achieving temperatures below 1 μK Author: Peter Ferjančič Mentors: Denis Arčon and Peter Jeglič

2. Introduction Bose-Einstein condensate – Atomic gasses cooled to VERY low temperatures (<μK) Predicted in 1925 by Bose and Einstein produced by Eric Cornell and Carl Wieman in 1995 – Nobel prize in 2001 T c ≈ 3.3 (ħ 2 n 2/3 )/ (m k b ) For alkali atoms at n=10 14 /cm 3 T c ≈ 0.1 μK 2

3. What is Bose-Einstein condensate 10 7 condensed gas atoms large fraction of the bosons occupy the lowest quantum state – atoms become indistinguishable Basically we have one single “super atom” Potential uses: – Simulation of solid state physics systems – Precision measurement – Quantum computing 3

4. Used techniques Slowing an atomic beam Optical molasses technique The magneto-optical trap Dipole / Magnetic trapping Evaporative cooling 4

5. Slowing an atomic beam Photon momentum: p=ħk Absorbed photon – fixed direction Emitted photon – random direction For λ=589 nm and Na atom, recoil velocity Δv=3 cm/s 5

6. Slowing an atomic beam Need to compensate for Doppler effect – Frequency shift ~1.7 GHz (Natural width ~10 MHz) – Zeeman cooling – Chirp cooling Laser cooling –Nobel 1997 6

7. Optical molasses techique 3 pairs of counter-propagating laser beams When moving towards beam, absorption increases → slowing force Force proportional to velocity Doppler cooling limit: ~3 cm/s 7

8. Magneto-optical trap (MOT) Atoms diffuse from molasses in seconds for 1 cm wide beam – we should stop them! Magnetic quadrupole – B=0 in the center, increases as we move away If photons move from center zeeman eff. causes resonance atoms are pushed back by laser beams → F(x) 8

9. MOT – how to cancel reppeling? Circularly polarized lasers: ΔM = +1 for right handed or ΔM = -1 for left handed Add polarized laser beams -> F(x) Change only in rate of photon absorption These are OPTICAL forces!!! 9

10. First stage cooling experiment First MOT then molasses Prediction: ~240 μK Result: an order of magnitude LOWER temperature But why? 10

11. Sisyphus cooling A sort of optical pumping mechanism 11

12. Dipole light force Refracted light excerts force on object (photon momentum: p=ħk) Particles are attracted to areas of high light intensity = Optical tweezers Wavelength is far from resonance! 12

13. Evaporative cooling Atoms with high enough energy escape the potential – taking above average energy with them Lowering borders speeds up the process 13

14. The experiment Laser slowing of an atomic beam 900 K-> ~5 K Magneto-optical trap ~300 mK Optical molasses ~240 μK Sisyphus cooling ~ 10-100 μK Evaporative cooling in dipole trap <100 nK Bose-Einstein condensate!!! (note: temperatures are informative and highly dependant on the experiment) 14

15. De jure 1 slowing beam 3 pairs of counter propagating beams 1 pair of coils 2 dipole force lasers 15

16. De facto 16

17. Conclusion & future What are other potential uses for BEC? – Bikes vs. Light races (c=25 km/h) – Light-> matter -> light transitions- 2007 – Single spin addressing – Excellent tool for quantum mechanics 2010 – first photon BEC Cold atoms today under 500 pK 17

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