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

eV Singlet (S=0) Parahelium Triplet (S=1) Orthohelium 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 +

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

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 eV Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p

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 s -1 Γ = 2π x 8 Hz QED effects strongest for low- lying S states eV Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

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 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) eV Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

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 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 eV Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

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 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 eV Orbital angular momentum 1s 1s2s 1 S 0 2p 1s2s 3 S 1 (He*) 2p 1557nm

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

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

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 Time of Flight (ms) MCP Signal (a.u.) TOF on Micro-channel Plate (MCP)

Experimental setup Crossed optical dipole trap at 1557 nm Bose-Einstein condensate of 4 He* Degenerate Fermi gas of 3 He* 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

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

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 Time of Flight (ms) MCP Signal (a.u.)

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 Beat frequency (MHz) Remaining atoms (%) Time of Flight (ms) MCP Signal (a.u.)

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

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

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

AC Stark shift 4 He Accounted for: –Recoil shift (20.1 kHz) –Mean field –Zeeman shift (41) MHz Relative uncertainty: 3 x Preliminary result

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

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

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 Power (mW) 0.2 Fit Temperature (uK)

AC Stark shift 3 He Accounted for: –Recoil shift (26.7 kHz) –Mean field –Zeeman shift (14) MHz Relative uncertainty: 8 x Preliminary result

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

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

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

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