1. Spectroscopy of a forbidden transition in a 4 He BEC and a 3 He degenerate Fermi gas Rob van Rooij, Juliette Simonet*, Maarten Hoogerland**, Roel Rozendaal, Joe Borbely, Kjeld Eikema, and Wim Vassen Institute for Lasers, Life and Biophotonics, VU University, Amsterdam * École Normale Supérieure, Laboratoire Kastler-Brossel, Paris, France ** University of Auckland, Auckland, New Zealand

2. 0 5 10 15 20 eV Singlet (S=0) Parahelium Triplet (S=1) Orthohelium 012012 Orbital angular momentum 1s 2s 3s 3p 2p 3d 2s 3s 3p 2p 3d First excited state: 19.8 eV Always one 1s electron No electric-dipole- allowed transitions between singlet and triplet states He Level Scheme He +

3. He Level Scheme Lifetimes 2 1 S 0 : 20 ms 2 3 S 1 : 8000 s(He*) 0 20 22 eV 012012 Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p

4. He Level Scheme Lifetimes 2 1 S 0 : 20 ms 2 3 S 1 : 8000 s(He*) 2 3 S 1 → laser cooling and trapping 0 20 22 eV 012012 Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p

5. He Level Scheme Lifetimes 2 1 S 0 : 20 ms 2 3 S 1 : 8000 s(He*) 2 3 S 1 → laser cooling and trapping 2 3 S 1 → 2 1 S 0 (M1): 1557 nm A 21 = 9.1 x 10 -7 s -1 Γ = 2π x 8 Hz QED effects strongest for low- lying S states 0 20 22 eV 012012 Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

6. He Level Scheme Lifetimes 2 1 S 0 : 20 ms 2 3 S 1 : 8000 s(He*) 2 3 S 1 → laser cooling and trapping 2 3 S 1 → 2 1 S 0 (M1): 1557 nm A 21 = 9.1 x 10 -7 s -1 Γ = 2π x 8 Hz QED effects strongest for low- lying S states 2 3 S 1 can be trapped at 1557nm (2 3 S→2 3 P : 1083 nm) 0 20 22 eV 012012 Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

7. He Level Scheme Lifetimes 2 1 S 0 : 20 ms 2 3 S 1 : 8000 s(He*) 2 3 S 1 → laser cooling and trapping 2 3 S 1 → 2 1 S 0 (M1): 1557 nm A 21 = 9.1 x 10 -7 s -1 Γ = 2π x 8 Hz QED effects strongest for low- lying S states 2 3 S 1 can be trapped at 1557nm (2 3 S→2 3 P : 1083 nm) 2 1 S 0 anti-trapped 0 20 22 eV 012012 Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

8. He Level Scheme Lifetimes 2 1 S 0 : 20 ms 2 3 S 1 : 8000 s(He*) 2 3 S 1 → laser cooling and trapping 2 3 S 1 → 2 1 S 0 (M1): 1557 nm A 21 = 9.1 x 10 -7 s -1 Γ = 2π x 8 Hz QED effects strongest for low- lying S states 2 3 S 1 can be trapped at 1557nm (2 3 S→2 3 P : 1083 nm) 2 1 S 0 anti-trapped Similar for fermionic isotope 3 He Isotope shift 0 20 22 eV 012012 Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

9. Experimental setup Crossed optical dipole trap at 1557 nm Bose-Einstein condensate of 4 He* Degenerate Fermi gas of 3 He* Dipole trap laser: 40 MHz detuned from atomic transition

10. Experimental setup Crossed optical dipole trap at 1557 nm Bose-Einstein condensate of 4 He* Degenerate Fermi gas of 3 He* Absorption imaging Dipole trap laser: 40 MHz detuned from atomic transition

11. Experimental setup Crossed optical dipole trap at 1557 nm Bose-Einstein condensate of 4 He* Degenerate Fermi gas of 3 He* Absorption imaging Dipole trap laser: 40 MHz detuned from atomic transition 160170180190200210 Time of Flight (ms) MCP Signal (a.u.) TOF on Micro-channel Plate (MCP)

12. Experimental setup Crossed optical dipole trap at 1557 nm Bose-Einstein condensate of 4 He* Degenerate Fermi gas of 3 He* 160170180190200210 Time of Flight (ms) MCP Signal (a.u.) TOF on Micro-channel Plate (MCP) Absorption imaging Dipole trap laser: 40 MHz detuned from atomic transition Mode-locked erbium doped fiber laser (Menlo Systems) Referenced to a GPS-controlled Rubidium clock

13. Load a 4 He BEC or 3 He DFG from magnetic trap into optical dipole trap Apply spectroscopy beam Measurement sequence

14. Load a 4 He BEC or 3 He DFG from magnetic trap into optical dipole trap Apply spectroscopy beam Turn off the trap and record MCP signal Determine remaining atom number Measurement sequence 160170180190200210 Time of Flight (ms) MCP Signal (a.u.)

15. Load a 4 He BEC or 3 He DFG from magnetic trap into optical dipole trap Apply spectroscopy beam Turn off the trap and record MCP signal Determine remaining atom number Increment laser frequency via Measurement sequence FWHM: 90 kHz 6060.160.2 60.3 60.4 Beat frequency (MHz) 120 100 80 60 40 20 0 Remaining atoms (%) 160170180190200210 Time of Flight (ms) MCP Signal (a.u.)

16. Systematics Recoil shift, 20 kHz Mean field, < exp. uncertainty

17. Systematics Recoil shift, 20 kHz Mean field, < exp. uncertainty Zeeman shift 2 3 S 1 M J =+1 M J = 0 M J =-1 M J =+1 M J =0 M J =-1 f R F Energy 0 B-field

18. Systematics Recoil shift, 20 kHz Mean field, < exp. uncertainty Zeeman shift AC Stark shift: Measure for various powers Extrapolate to zero power 2 3 S 1 M J =+1 M J = 0 M J =-1 M J =+1 M J =0 M J =-1 f R F Energy 0 B-field

19. AC Stark shift 4 He Accounted for: –Recoil shift (20.1 kHz) –Mean field –Zeeman shift 192 510 702.150 4 (41) MHz Relative uncertainty: 3 x 10 -11 Preliminary result

20. Quantum statistical effect 4 He* BEC occupy ground state fluctuating atom number

21. Quantum statistical effect 4 He* BEC occupy ground state fluctuating atom number 3 He*, low power atoms fill up the trap constant atom number

22. Quantum statistical effect 4 He* BEC occupy ground state fluctuating atom number 3 He*, low power atoms fill up the trap constant atom number 3 He*, P > 300 mW Trap depth large enough to accommodate full thermal distribution Measured AC-Stark shift curve non-linear 100 200300400500600 Power (mW) 0.2 Fit Temperature (uK) 0.6 0.4

23. AC Stark shift 3 He Accounted for: –Recoil shift (26.7 kHz) –Mean field –Zeeman shift 192 504 914.431 7 (14) MHz Relative uncertainty: 8 x 10 -12 Preliminary result

24. Results Drake Pachucki Indirect expt. Our result f – 192510700 (MHz) Helium 4 transition frequency

25. Results Drake Pachucki Indirect expt. Our result f – 192510700 (MHz) Helium 4 transition frequency f – 192502660 (MHz) Drake Pachucki Our result Indirect expt. Helium 3 transition frequency

26. Results Drake Pachucki Indirect expt. Our result f – 192510700 (MHz) Helium 4 transition frequency f – 192502660 (MHz) Drake Pachucki Our result Indirect expt. Helium 3 transition frequency f – 8034 (MHz) Drake Pachucki Our result Isotope shift In isotope shift calculations many terms cancel, reducing the theoretical uncertainty Theoretical uncertainty dominated by nuclear charge radii determined from electron- nucleus scattering experiments

27. Summary First time: spectroscopy on ultracold trapped 4 He* and 3 He* direct measurement between triplet and singlet states in He observation of the 1557nm 2 3 S → 2 1 S transition Observed quantum statistical effects in the dipole trap