1. Ultracold 3 He and 4 He atoms near quantum degeneracy: QED test and the size of the helion and  -particle Rob van Rooij, Joe Borbely, Juliette Simonet*, Maarten Hoogerland**, Kjeld Eikema, Roel Rozendaal and Wim Vassen * École Normale Supérieure, Laboratoire Kastler-Brossel, Paris, France ** University of Auckland, Auckland, New Zealand

2. Outline What is quantum electrodynamics (QED)? Why use helium spectroscopy to test QED? How we tested QED (and also nuclear few-body physics)

3. What is quantum electrodynamics (QED)? vacuum is never empty, but filled with virtual particles – appearing suddenly and then quickly disappearing electron self energy Dirac relativity, electron spin 100 GHz Lamb 10 GHz QED Modern era of QED began with the discovery of the Lamb shift in 1947 (Willis Lamb; hydrogen atom) Bohr Energy n=1 (13.6 eV = 10 6 GHz) 1 GHz proton spin Hyper-fine splitting 0.01 GHz proton size Nuclear effects Heisenberg uncertainty principle vacuum polarization Vacuum produces electron-positron pairs A theory that describes how light and matter interact contributions from empty space (the vacuum) Shift: Electrons interact with themselves

4. Why use helium spectroscopy to test QED? Next simplest atom (from a theoretical point of view) after atomic hydrogen 2-electron atom (get electron-electron interactions) 3-body system (electron, electron, nucleus) First excited state: 1s2s 2 3 S 1 ( n 2S+1 L J ) Ground state: 1s 2 1 1 S 0 n=1,2,3,… S = s 1 +s 2, s=±½ L = 0,1,2,… (S,P,D…) J = |L-S|,…,|L+S| E = h x 5 130 494.9(9) GHz Precision: 175 parts per billion (10 -9 ) 3 years later… E = h x 5 130 495.04(17) GHz Precision: 34 parts per billion (10 -9 )

5. Why use helium spectroscopy to test QED? Next simplest atom (from a theoretical point of view) after atomic hydrogen 2-electron atom (get electron-electron interactions) 3-body system (electron, electron, nucleus) E = h x 5 945 204 212(6) MHz Precision: 1 part per billion (10 -9 )

6. Why use helium spectroscopy to test QED? Next simplest atom (from a theoretical point of view) after atomic hydrogen 2-electron atom (get electron-electron interactions) 3-body system (electron, electron, nucleus) E = h x 192 510 702 145.6(1.8) kHz Precision: 8 parts per trillion (10 -12 ) Lifetimes (He*) 2 1 S 0 : 20 ms, FWHM = 8 Hz 2 3 S 1 : 8000 s QED effects strongest for low-lying S states

7. Why use helium spectroscopy to test QED? Next simplest atom (from a theoretical point of view) after atomic hydrogen 2-electron atom (get electron-electron interactions) 3-body system (electron, electron, nucleus) E = h x 192 510 702 145.6(1.8) kHz Precision: 8 parts per trillion (10 -12 ) Extremely weak transition long interaction time Modified from E. Eyler Science 333,164 (2011) Particle accelerators Sun (surface) Supernova Sun (centre) Room temperature Interstellar space

8. 1557 nm laser light 1083 nm laser light MCP Same laser but different frequency detunings for: collimation slowing cooling trapping detection How we tested QED: Experimental setup Energy 1s2s 1 S 0 1557 nm 1s2s 3 P 2 1s1s 1 S 0 1s2s 3 S 1 electron bombardment (20 eV) 1083 nm

9. 1s2s 1 S 0 1s2s 3 S 1 1557 nm 1s2s 3 P 2 1s2s 1 P 1 1s1s 1 S 0 2 3 S 1 can be trapped at 1557 nm (red detuned from 2 3 S 1 →2 3 P 2 : 1083 nm) 2 1 S 0 anti-trapped (blue detuned from 2 1 S 0 →2 1 P 1 : 2060 nm) How we tested QED: Optical trapping Energy

10. How we tested QED: Experimental tools Nobel prize in physics milestones: 2001: Eric A. Cornell, Wolfgang Ketterle, Carl E. Wieman achievement of Bose-Einstein condensation 2005: Roy J. Glauber, John L. Hall, Theodor W. Hänsch optical coherence / optical frequency comb

11. How we tested QED: Experimental tools Bose-Einstein condensate Long-interaction times W Ketterle 2001 Nobel lecture

12. Frequency comb locked to an atomic clock How we tested QED: Experimental tools Kjeld Eikema XUV: < 100 nm IR: > 800 nm Optical ruler 10 14 Hz10 7 Hz Optical frequenciesMicrowave frequencies beat note Frequency Comb Accurate timebase

13. Load atoms into the optical dipole trap Determine remaining atom number Apply spectroscopy beam Turn off the trap and record MCP signal 2 3 S 1 2 1 S 0 (trapped)(anti-trapped) How we tested QED: Experiment procedure

14. Recoil shift: ~20 kHz hv p AC Stark shift: ~ 1 kHz / 1 mW Mean field shift: < 1 kHz (collisional shift) How we tested QED: Systematics (Energy shift due to external laser light) Frequency comb: ~ 0.4 kHz (uncertainty in the time base) (Momentum transfer) M J =+1 M J =0 M J =-1 f R F Energy 0 B-field

15. How we tested QED: Results 4 He: 3 He: Agreement with QED theory BUT QED 1000 times less precise (challenge for theorists) Relative Precision 192 510 702 145.6 (1.8) kHz 192 504 914 426.4 (1.5) kHz 9 x 10 -12 8 x 10 -12 Our Result

16. GWF Drake: Can J Phys 86 45-54 (2008) Measure “identical” transitions in different isotopes: 3 He, 4 He QED terms independent of  /M cancel Radiative recoil ~ 10 kHz contribute to the uncertainty How we tested nuclear few-body theory Nuclear charge radius

17. Only relative charge radii can be deduced. To determine absolute charge radii the radius of the reference nucleus, 4 He, must be known with the best possible precision r c ( 4 He) = 1.681(4) fmelastic electron scattering from 4 He nucleus GWF Drake: Can. J. Phys. 83: 311–325 (2005) Measure “identical” transitions in different isotopes: 3 He, 4 He How we tested nuclear few-body theory Helium spectroscopy + QED: Nuclear theory + scattering: 1.961(4) fm 1.965(13) fm calculate the radius of the proton and the neutron the distribution in the nucleus

18. Summary First time: spectroscopy on ultracold trapped 4 He and 3 He observation of the 1557 nm 2 3 S 1 → 2 1 S 0 transition Challenge for absolute QED energy calculations to 8 x 10 -12 Determined the size of the 3 He nucleus to 4 x 10 -18 m

19. LaserLaB Amsterdam: Rob van Rooij, Joe Borbely, Juliette Simonet ‡, Maarten Hoogerland ¶, Kjeld Eikema, Roel Rozendaal ‡ ENS, Paris ¶ University of Auckland, New Zealand Maarten Joe Juliette WV Science 333, 196 (July 2011) The metrology team Rob

20. 1.The classical Hanbury Brown -Twiss effect: light as an electromagnetic wave 2. Quantum Optics interpretation of the HBT effect: light as a beam of photons 3. The HBT effect for atoms: 4 He bosons 4. What about fermions? The 3 He case. Hanbury Brown Twiss effect for ultracold bosons and fermions

21. Quantum Optics (Wikipedia): the study of the nature and effects of light as quantized photons Before 1960: light interference understood in electromagnetic wave picture, i.e. phase differences in amplitude of electric field 1956: Robert Hanbury Brown and Richard Twiss extended intensity interferometry to the optical domain Physics Nobel Prize 2005: Roy Glauber, Jan Hall, Ted Hänsch ~1963: birth of Quantum Optics

22. First-order coherence g (1) gives the contrast in amplitude interference experiments (Young’s double slit, Michelson interferometer, interfering Bose condensates) First order (phase) coherence: correlations in the amplitude of the field   = statistical average (= time average for stationary process)

23. Hanbury Brown and Twiss: Intensity correlations: HBT effect: (second-order) correlations between two photocurrents at two different points and times. Measuring intensity correlations gives information on phase coherence: g (2) deviates from 1 for  r < l c (correlation length) g (2) (0,0,0) = 2 Do photons bunch? How can they? Independent particles, no interactions ! g (2) rr   Nature, January 7, 1956

24. Hanbury Brown and Twiss Quantum Optics interpretation (Glauber): interference of probability amplitudes of indistinguishable processes: Correlation length = detector separation for which interference survives Sum over all pairs S 1 and S 2 in the source washes the interference out unless d is small enough d

25. For a laser: (Glauber’s coherent states) Intensity correlations: joint probability of detecting two photons at locations r and r’ For all chaotic sources (so no laser): Should also work for atoms ! (BEC is like a laser) Shot noise (independent particles) Correlations due to beat notes of random waves 1965, 1966: Armstrong, Arecchi

26. First experiment: Yasuda and Shimizu, Ne* MOT (1996), heroic experiment, T=100  K Amsterdam Orsay MCP (He* detector) 63 cm below trap Measurement of correlation of two particles emitted at S 1 and S 2 to be detected at D 1 and D 2 Position-sensitive MCP from Orsay to Amsterdam Science 310, 648 (2005) Science 310, 648 (2005)

27. VU experiment: Thermal 4 He atoms show bunching Fit: l =0.56 +/- 0.08 mm t: drop time Agrees very well with theory! T=0.5  K ( above BEC, s i >>  T )

28. What about fermionic atoms ? For fermions we need an antisymmetric wavefunction: d Does not really surprise us: Pauli principle! Interference takes place when particles arrive within the same phase space cell: Δx Δy Δz Δp x Δp y Δp z < h 3 Pure effect of quantum statistics: no classical interpretation possible !

29. Expected correlation function g (2) (0,0,  z) for bosons and fermions

30. 4 He 3 He T=0.5  K Fit: l =0.75 +/- 0.07 mm l =0.56 +/- 0.08 mm (difference due to masses 3 and 4) t: drop time Jeltes et al., Nature 445, 402 (2007) Comparison of the Hanbury Brown Twiss effect for bosons and fermions

31. The HBT team John Martijn Valentina Tom WV Laser Centre Amsterdam: Tom Jeltes, John McNamara, Wim Hogervorst Orsay: Valentina Krachmalnicoff, Martijn Schellekens, Aurelien Perrin, Hong Chang, Denis Boiron, Alain Aspect, Chris Westbrook Nature 445, 402 (2007) Ken Baldwin