Helium Spectroscopy 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

He Energy Levels First excited state: eV All bound states are (1s)(n l) 2 3 S 1 ( n 2S+1 L J )

He Energy Levels First excited state: eV All bound states are (1s)(n l) 2 3 S 1 ( n 2S+1 L J ) What can we learn from helium spectroscopy?

2. determine the fine-structure constant,  1. test 2-electron QED theory Derived from measurements of the isotope shift. Important for nucelar structure 1970s: ML Lewis and PH Serafino ; M Douglas and NM Kroll O(  6 mc 2 ) Modern era of QED began with the discovery of the Lamb shift in 1947 (electron self energy and vacuum polarization) 1990s - present: GWF Drake ; K Pachucki O(  7 mc 2 ), O(  8 mc 2 ) 1964: C Schwartz developed a scheme for an O(  6 mc 2 ) calculation Coupling strength of electromagnetic interactions between charged elementary particles proportional to the strength of the electromagnetic force 3. nuclear charge radius Argonne National Laboratory, Argonne, Illinois, USA What can we learn from helium spectroscopy?

1 1 S 0 –to – 2 1 P 1 Test 2-electron QED theory 58 nm transition in helium Lamb shift measurements in helium provide a stringent test of QED effects Isotope shift measurement: 3 He and 4 He

2 3 S 1 –to – 2 3 P 0,1,2 Hydrogen n=2 2P 3/2 2S 1/2 2P 1/2 1.0 GHz Natural width 100 MHz  =1.6 ns (to 1S)  Helium 2 3 P J 23P023P GHz Natural width 1.6 MHz 23P123P1 23P223P2 (60X narrower than H) (3X larger than H) (to 2 3 S)  180X better candidate than H!  =98 ns I. large energy intervals (2.3 GHz and 29.6 GHz) II. long lifetime (  = 98 ns) Why use the 2 3 P J states of helium to determine  ? GHz9.9 GHz

2 3 S 1 –to – 2 3 P 0,1,2 How does one determine  from helium fine structure? Comparison between theory and experiment for the 29.6 GHz interval is used to determine  The smaller 2.3 GHz interval tests 2-electron QED. Nonrelativistic Schrödinger equation, Kinetic energy of the 2 electrons Potential energy from the nucleus and between the 2 electrons transformation into center-of-mass frame of the nucleus. (Mass polarization term)

2 3 S 1 –to – 2 3 P 0,1,2 The fine-structure energies are expressed as a power series expansion of  since  2 ~ one can use perturbation theory How does one determine  from helium fine structure? Comparison between theory and experiment for the 29.6 GHz interval is used to determine  The smaller 2.3 GHz interval tests 2-electron QED. ” Each coefficient, C, is itself a power series expansion of the form (  /M ~ ) 30 GHz50 MHz1 MHz50 kHz <15 kHz

2 3 S 1 –to – 2 3 P 0,1,2 Relating experiment and theory (K. Pachucki: Phys Rev A ) experiment theory How does one determine  from helium fine structure? Comparison between theory and experiment for the 29.6 GHz interval is used to determine  The smaller 2.3 GHz interval tests 2-electron QED.

It is vital to measure  using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics. i)different degrees of reliance on QED expansions of the measured quantities ii)experiments performed using dissimilar techniques are not affected by the same systematic errors Determinations of  AC Josephson  dc vaoltage, V, applied across a superconducting junction leads to an alternating current of frequency f

It is vital to measure  using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics. i)different degrees of reliance on QED expansions of the measured quantities ii)experiments performed using dissimilar techniques are not affected by the same systematic errors Determinations of  AC Josephson  muonium hfs  + (antiparticle to  - ) Ground state HFS

It is vital to measure  using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics. i)different degrees of reliance on QED expansions of the measured quantities ii)experiments performed using dissimilar techniques are not affected by the same systematic errors Determinations of  quantum Hall effect AC Josephson  muonium hfs A strong, perpendicular magnetic field is applied to a two-dimensional electron gas at a low temperature, the resistance of the gas is quantized with n

It is vital to measure  using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics. i)different degrees of reliance on QED expansions of the measured quantities ii)experiments performed using dissimilar techniques are not affected by the same systematic errors Determinations of  Cs recoil Rb recoil quantum Hall effect AC Josephson  muonium hfs hv p

It is vital to measure  using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics. i)different degrees of reliance on QED expansions of the measured quantities ii)experiments performed using dissimilar techniques are not affected by the same systematic errors Determinations of  Cs recoil Rb recoil quantum Hall effect AC Josephson  muonium hfs g e (electron magnetic moment) (0.37ppb) one-electron orbit in a Penning trap (amp. & freq. not to scale) measure trap frequencies yields g s

It is vital to measure  using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics. i)different degrees of reliance on QED expansions of the measured quantities ii)experiments performed using dissimilar techniques are not affected by the same systematic errors Determinations of  Cs recoil Rb recoil quantum Hall effect AC Josephson  muonium hfs 20 ppb – dominated by theory g e (electron magnetic moment) (0.37ppb) helium spectroscopy X 5 ppb

Nuclear Charge Radius Drake: Can J Phys (2008) Measure “identical” transitions in different isotopes: 3 He, 4 He, 6 He, 8 He ” QED terms independent of  /M cancel Radiative recoil ~ 10 kHz contribute to the uncertainty 2 3 S 1 –to– 2 3 P J 2 3 S 1 –to– 3 3 P J 2 3 S 1 –to– 2 1 S S 0 –to– 2 1 P 1

Nuclear Charge Radius Measure “identical” transitions in different isotopes: 3 He, 4 He, 6 He, 8 He 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) = ± fmelastic electron scattering from 4 He nucleus Drake: Can. J. Phys. 83: 311–325 (2005)

2 3 S 1 –to– 2 1 S 0

eV 1s2s 1 S 0 1s2s 3 S nm 1s2s 3 P 2 1s2s 1 P 1 1s1s 1 S 0 Lifetimes (He*) 2 1 S 0 : 20 ms, 2  = 8 Hz 2 3 S 1 : 8000 s 2 3 S 1 → 2 3 P 2 laser cooling / trapping 2 3 S 1 → 2 1 S 0 (M1): 1557 nm QED effects strongest for low-lying S states 2 3 S 1 can be trapped at 1557 nm (red detuned from 2 3 S→2 3 P: 1083 nm) 2 1 S 0 anti-trapped (blue detuned from 2 1 S→2 1 P: 2060 nm) Isotope shift

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

Frequency comb Mode-locked erbium doped fiber laser (Menlo Systems) Referenced to a GPS-controlled Rubidium clock f laser = nf rep + f ceo + f beat f rep ~ 250 MHz f ceo ~ 20 MHz f beat ~ 60 MHz

Load a 4 He BEC or 3 He DFG from magnetic trap into optical dipole trap Measurement sequence Time of Flight (ms) MCP Signal (a.u.) Determine remaining atom number Apply spectroscopy beam Turn off the trap and record MCP signal FWHM: 90 kHz Beat frequency (MHz) Remaining atoms (%)

Systematics Recoil shift: ~20 kHz 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 hv p AC Stark shift: Measure for various powers Extrapolate to zero power Mean field: < exp. uncertainty Zeeman shift

AC Stark shift 4 He Accounted for: –Recoil shift (20.6 kHz) –Mean field shift –Zeeman shift (41) MHz Relative uncertainty: 3 x Preliminary result

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

AC Stark shift 3 He Accounted for: –Recoil shift (27.3 kHz) –Mean field shift –Zeeman shift (14) MHz Relative uncertainty: 8 x Preliminary result

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 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 1557 nm 2 3 S → 2 1 S transition Observed quantum statistical effects in the dipole trap