Determining α from Helium Fine Structure

Transcription

1 Determining α from Helium Fine Structure How to Measure Helium Energy Levels REALLY Well Lepton Moments 2006 June 18, 2006 Daniel Farkas and Gerald Gabrielse Harvard University Physics Dept Funding provided by the National Science Foundation

2 Outline Determining α from fine structure why helium? Current Status of He fine structure Experimental Approach improvements Brief Survey of Systematics Outlook and Conclusions how well can we measure the intervals? how accurately could we determine α?

3 α from Fine Structure: Why Helium? Small ratio of linewidth to splitting σ ~ Δf f = 1.6 MHz MHz = times better than Hydrogen!

4 Measured Determining α ν 01 2 = α ( α, α,,k) MHz + Δν α QED 2 3 P P 1 Determined Larger interval used Assumes QED is correct Calculated 2 3 P 2 ν 12 Testing QED ( α, α,,k) 2 = α MHz + Δν α QED 2 3 P P 1 Measured CODATA Calculated 2 3 P 2 Theoretical prediction for smaller interval G.W.F. Drake, CJP 80, 1195 (2002). K. Pachucki, arxiv:physics/ (2006)

5 Present Status of Helium Fine Structure year Pachucki '06 ν 02 -ν 01 Harvard '05 Drake '03 LENS '05 York '00 UNT ' P P P 2 Two Two theoretical values values disagree! year Significant disagreement between theory theory and and experiment! frequency khz ν 02 -ν 12 Pachucki '06 Harvard '05 Drake '03 LENS '05 UNT '95+'00 York ' frequency khz Experimental agreement < 1 khz khz 2 3 P P P 2 year Pachucki '06 Drake '03 LENS '05 ν 01 +ν 12 Harvard '05 York '00+' P P UNT ' P frequency khz

6 Warning! Theory and Expt Disagree! Experimental Values of α Helium Spectroscopy (12 ppb; -7σ) (12 ppb; -12σ) Muonium Hyperfine Structure (58 ppb; +0.3σ) protron g' (31 ppb; -2.7σ) Neutron de Broglie λ (34 ppb; +0.5σ) 700 Hz error in ν ppb in α Can we do better? Cs h/m (8.0 ppb; +0.8σ) UW electron g-2 (3.8 ppb; -0.6σ) Rb h/m (6.7 ppb; -0.4σ) 2002 CODATA (3.3 ppb) Quantum Hall Effect (18 ppb; +0.8σ) Harvard electron g-2 (0.7 ppb; +1.3σ) (α ) x 10 5

7 Objectives Goals improve measurements the 2 3 P fine structure splitting measure the 2 3 S-2 3 P optical transition frequencies Test QED Determine α Study properties of helium Develop techniques for laser spectroscopy

8 Experimental Setup Doppler-free saturated absorption spectroscopy External cavity diode laser at 1083 nm Scan laser offsetlocked from a second stabilized diode laser Vertical magnetic field resolves sublevels

9 Frequency Reference Stability Allan Deviation (a) (b) (c) Iodine Reference Helium Reference GPS receiver Hydrogen Maser (d) 600 Hz 40X improvement! 15 Hz uncertainty at 1083 nm (Hz) Frequency-doubled Nd:YAG NPRO Hyperfine transitions in 127 I 2 at 532 nm Modulation Transfer Spectroscopy (MTS) τ (sec)

10 Optical Frequency Combs RF/microwave spacing Thousands of optical frequencies f = n f + n rep δ RF/microwave offset integer ~ 10 5 KEY IDEA: Thousands of optical frequency f n are determined by two microwave frequencies Comb can extend over IR and visible regions - thousands of teeth!

11 Using the Optical Frequency Comb Transfers stability of iodine reference to 1083 nm Narrow 2 khz NPRO linewidth transferred to all wavelengths Counting f rep accurately determines optical transition frequency D. Farkas and G. Gabrielse, Proceedings of the 2005 IEEE IFCS, 937 (2005).

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14 Experimental Lineshapes 2 3 S-2 3 P S-2 3 P S-2 3 P lock-in signal size (mv) Data Best Fit lock-in signal size (mv) Data Best Fit lock-in signal size (mv) Data Best Fit residuals (mv) residuals (mv) residuals (mv) m=0 transition 7 parameters m=±1 transitions m=0 transition forbidden Splitting gives B field 11 parameters m=±1 transitions m=0 transition 2 crossovers 18 parameters

15 Experimental Resolution frequency from MHz S-2 3 P 0 frequency from MHz ν 01 =2 3 P P time (hours) time (hours) σ < 75 Hz in a few hours! Linesplitting up to 20000!

16 Systematics Overview Systematic Typical Size Error (Hz) B field measurement & inhomogeneity 0 25 Zeeman 1 MHz 10 AC Stark 1 khz 75 RF Discharge Shifts 200 Hz 100 Linear Pressure 1 khz 250 Light-Pressure 5-10 khz <100 Beam Misalignment ~20 khz 1 Wavefront Curvature 0 Velocity-Changing Collisions 0 Polarization 0 Self-focusing <20 khz???

17 Systematics: Linear Pressure Shifts frequency khz pressure (mtorr) frequency khz ν 01 =2 3 P P S-2 3 P 0 σ y0 = 230 Hz σ y0 = 470 Hz slope = (15) MHz/Torr pressure (mtorr) optical frequencies intervals D. Vrinceanu, S. Kotochigova, and H.R. Sadeghpour, PRA 69, (2004).

18 Systematics: Light-Pressure Shifts Atomic recoil modifies velocity distribution N ( v) = N 0 ( v) + N 0 ( v 0 4Sk ( v v0 ) Γ ) ε rτ 2 2 [ k ( v v ) + Γ recoil energy interaction time ] 2 Small (ε r τ<< 1) asymmetric kink is superimposed on symmetric Lorentzian ( 1 Ω 1 1 L Ω) = + ε 2 rτ 2 2 2( Ω + 1) ( Ω + 1) 2 ( Ω ε τ ) 2 r + 1 optical frequencies ν 01, ν 02 intervals Corrected by comparing m=±1 and m=0 peaks of the 2 3 P 2 lineshape ν 12 interval 0

19 Systematics: Self-focusing Intensity-dependent index of refraction causes focusing of pump/probe beams Small asymmetric signal component ~ D(Ω) Asymmetric component shifts Lorentzian frequency signal (a.u.) Solutions: residuals (a.u.) frequency MHz Without D(Ω) residuals (a.u.) With D(Ω) 20 khz shift! frequency MHz frequency MHz (1) Include D(Ω) in fits (2) Extrapolate to zero pressure laser power RF discharge power optical frequencies intervals

20 Systematics: Beam Misalignment frequency khz Center Frequency Radial flow of atoms Transverse velocity distribution is NOT a Maxwell-Boltzmann Residual Doppler shifts+broadening uncertainty = ±20 khz optical frequencies vertical misalignment (mrad) intervals 0

21 Future Outlook ~0.25 khz khz self-focusing T. Zelevinsky, D. Farkas, and G. Gabrielse, PRL 95, (2005). Interval Accuracy (2005) Projected Accuracy Improvement ν khz 0.30 khz (130 ppb) 1.7 X ν khz 0.30 khz (10 ppb) 2.3 X α to 5 ppb! ν khz 0.30 khz (9.4 ppb) 3.2 X

22 Conclusions Theory Two groups have calculated terms up to α 5 Disagreement of ~3 khz Experiment Agreement to <1 khz Disagreement with theory between 8-20 khz! Source of disagreement: terms of α 6? Harvard experiment fine structure intervals to 300 Hz 2-3X improvement over 2005 results determines α to 5 ppb 2S-2P optical measurements to 20 khz