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Gabrielse New Measurement of the Electron Magnetic Moment and the Fine Structure Constant Gerald Gabrielse Leverett Professor of Physics Harvard University Almost finished student: David Hanneke 2006 DAMOP Thesis Earlier contributions: Brian Odom, Prize Winner Brian D’Urso, Steve Peil, 2 20 years Dafna Enzer, 6.5 theses Kamal Abdullah Ching-hua Tseng Joseph Tan N$F 0.1 mm Gabrielse Recent Back-to-Back Papers New Measurement of the Electron Magnetic Moment B. Odom, D. Hanneke, B. D’Urson and G. Gabrielse, Phys. Rev. Lett. 97, 030801 (2006). New Determination of the Fine Structure Constant G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, B. Odom, Phys. Rev. Lett. 97, 030802 (2006). AIP Physics Story of the Year (Phys. News Update, 5 Dec. 2006) • Science 313, 448-449 (2006) • Nature 442, 516-517 (2006) • Physics Today, 15-17 (August, 2006) • Cern Courier (October 2006) • New Scientist 2568, 40-43 (2006) • Physics World (March 2007) Gabrielse Why Does it take Twenty Years and 6.5 Theses? Explanation 1: Van Dyck, Schwinberg, Dehemelt did a good job in 1987! Phys. Rev. Lett. 59, 26 (1987) Explanation 2a: We do experiments much too slowly Explanation 2b: Takes time to develop new ideas and methods needed to measure with 7.6 parts in 1013 uncertainty • One-electron quantum cyclotron first measurement with • Resolve lowest cyclotron states as well as spin these new methods • Quantum jump spectroscopy of spin and cyclotron motions • Cavity-controlled spontaneous emission • Radiation field controlled by cylindrical trap cavity • Cooling away of blackbody photons • Synchronized electrons identify cavity radiation modes • Trap without nuclear paramagnetism • One-particle self-excited oscillator Gabrielse The New Measurement of Electron g U. Michigan U. Washington Harvard beam of electrons one electron one electron spins precess observe spin quantum with respect to flip cyclotron 100 mK cyclotron motion motion thermal cyclotron resolve lowest self-excited motion quantum levels oscillator cavity-controlled inhibit spontan. radiation field emission Dehmelt, (cylindrical trap) Crane, Rich, … Van Dyck cavity shifts Gabrielse Magnetic Moments, Motivation and Results Gabrielse Magnetic Moments magnetic L angular momentum m g mB moment Bohr magneton e 2m e.g. What is g for identical charge and mass distributions? v e, m e ev L e e L m IA ( 2 ) L 2 2 mv 2m 2m v g 1 mB Gabrielse Magnetic Moments magnetic S angular momentum m g mB moment Bohr magneton e 2m g 1 identical charge and mass distribution g2 spin for Dirac point particle g 2.002 319 304 ... simplest Dirac spin, plus QED (if electron g is different electron has substructure) Gabrielse Why Measure the Electron Magnetic Moment? 1. Electron g - basic property of simplest of elementary particles 2. Determine fine structure constant – from measured g and QED (May be even more important when we change mass standards) 3. Test QED – requires independent a 4. Test CPT – compare g for electron and positron best lepton test 5. Look for new physics beyond the standard model • Is g given by Dirac + QED? If not electron substructure (new physics) • Muon g search needs electron g measurement Gabrielse New Measurement of Electron Magnetic Moment magnetic S spin m g mB moment Bohr magneton e 2m g / 2 1.001 159 652 180 85 0.000 000 000 000 76 7.6 1013 • First improved measurement since 1987 • Nearly six times smaller uncertainty • 1.7 standard deviation shift • Likely more accuracy coming • 1000 times smaller uncertainty than muon g B. Odom, D. Hanneke, B. D’Urso and G. Gabrielse, Phys. Rev. Lett. 97, 030801 (2006). Gabrielse 0 85 (76) (more digits coming) Gabrielse Dirac + QED Relates Measured g and Measured a a a a a 2 3 4 g 1 C1 C2 C3 C4 ... a 2 Dirac weak/strong point particle Sensitivity to other physics Measure QED Calculation (weak, strong, new) is low Kinoshita, Nio, Remiddi, Laporta, etc. 1. Use measured g and QED to extract fine structure constant 2. Wait for another accurate measurement of a Test QED Gabrielse Basking in the Reflected Glow of Theorists g a 1 C1 2 a 2 C2 a 3 C3 a 4 C4 a 5 C5 2004 Remiddi Kinoshita G.G . .. a Gabrielse a a a a 2 3 4 g 1 C1 C2 C3 C4 ... a 2 theoretical uncertainties experimental uncertainty Gabrielse New Determination of the Fine Structure Constant 1 e 2 • Strength of the electromagnetic interaction a • Important component of our system of 4 0 c fundamental constants • Increased importance for new mass standard a 1 137.035 999 710 0.000 000 096 7.0 1010 • First lower uncertainty since 1987 • Ten times more accurate than atom-recoil methods G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, B. Odom, Phys. Rev. Lett. 97}, 030802 (2006). Gabrielse Widely Re-Reported Science Nature Physics Today New Scientist Cern Courier … Fox News Moral: what is quoted is not necessarily what was said Gabrielse Next Most Accurate Way to Determine a (use Cs example) Combination of measured Rydberg, mass ratios, and atom recoil e2 1 1 e 4 me c a R Haensch, … 4 0 hc (4 0 ) 2 2h3c 2 2 R h a 2 Pritchard, … c me Chu, … 2 R h M Cs M p h 2 f recoil 2c c M Cs M p me M Cs ( f D1 ) 2 Haensch, … f recoil M Cs M 12C Tanner, … a 2 4 R c ( f D1 ) 2 M 12C me Werthe, Quint, … (also Van Dyck) Biraben, … • Now this method is 10 times less accurate • We hope that will improve in the future test QED (Rb measurement is similar except get h/M[Rb] a bit differently) Gabrielse Earlier Measurements Require Larger Uncertainty Scale ten times larger scale to see larger uncertainties Gabrielse Test of QED Most stringent test of QED: Comparing the measured electron g to the g calculated from QED using an independent a g 15 10 12 • The uncertainty does not comes from g and QED • All uncertainty comes from a[Rb] and a[Cs] • With a better independent a could do a ten times better test Gabrielse From Freeman Dyson – One Inventor of QED Dear Jerry, ... I love your way of doing experiments, and I am happy to congratulate you for this latest triumph. Thank you for sending the two papers. Your statement, that QED is tested far more stringently than its inventors could ever have envisioned, is correct. As one of the inventors, I remember that we thought of QED in 1949 as a temporary and jerry-built structure, with mathematical inconsistencies and renormalized infinities swept under the rug. We did not expect it to last more than ten years before some more solidly built theory would replace it. We expected and hoped that some new experiments would reveal discrepancies that would point the way to a better theory. And now, 57 years have gone by and that ramshackle structure still stands. The theorists … have kept pace with your experiments, pushing their calculations to higher accuracy than we ever imagined. And you still did not find the discrepancy that we hoped for. To me it remains perpetually amazing that Nature dances to the tune that we scribbled so carelessly 57 years ago. And it is amazing that you can measure her dance to one part per trillion and find her still following our beat. With congratulations and good wishes for more such beautiful experiments, yours ever, Freeman. Gabrielse Direct Test for Physics Beyond the Standard Model g 2 2aQED (a ) g SM :Hadronic Weak g New Physics Is g given by Dirac + QED? If not electron substructure Does the electron have internal structure? Brodsky, Drell, 1980 m limited by the uncertainty in m* 130 GeV / c 2 g/2 independent a values m m* 600 GeV / c 2 if our g uncertainty g/2 was the only limit Not bad for an experiment done at 100 mK, but LEP does better m* 10.3 TeV LEP contact interaction limit Gabrielse Muon Test for Physics Beyond the Standard Model Needs Measured Electron g less accurately measured expected to be bigger than we measure electron g than for electron by a factor of 1000 by ~40,000 g 2 2aQED (a ) g SM :Hadronic Weak g New Physics big contribution need a must be subtracted out need test the QED calculation of this large contribution Muon search for new physics needs the measurement of the electron g and a Gabrielse Could We Check the 3s Disagreement between Muon g Measurement and “Calculation”? g 2 2aQED (a ) g SM :Hadronic Weak g New Physics (mm/me)2 ~ 40,000 muon more sensitive to “new physics” ÷1,000 how much more accurately we measure ÷ 3 3s disagreement is now seen If we can reduce the electron g uncertainty by 13 times more should be able to have the precision to see the 3s effect (or not) Also need: • QED and SM calculations improved by factor of ~5 • Independent measurement of a improved by factor of 130 These are large numbers hard to imagine that this will happen quickly Gabrielse How Does One Measure the Electron g to 7.6 parts in 1013? Gabrielse How to Get an Uncertainty of 7.6 parts in 1013 • One-electron quantum cyclotron first measurement with • Resolve lowest cyclotron as well as spin states these new methods • Quantum jump spectroscopy of cyclotron and spin motions • Cavity-controlled spontaneous emission • Radiation field controlled by cylindrical trap cavity • Cooling away of blackbody photons • Synchronized electrons probe cavity radiation modes • Elimination of nuclear paramagnetism • One-particle self-excited oscillator Make a “Fully Quantum Atom” for the electron Challenge: An elementary particle has no internal states to probe or laser-cool Give introduction to some of the new and novel methods Gabrielse Basic Idea of the Measurement Quantum jump spectroscopy of lowest cyclotron and spin levels of an electron in a magnetic field Gabrielse One Electron in a Magnetic Field c 150 GHz 2 n=4 n=3 n=2 0.1 n=1 hc 7.2 kelvin mm n=0 2 Need low B 6 Tesla temperature cyclotron motion T << 7.2 K 0.1 mm Gabrielse First Penning Trap Below 4 K 70 mK Need low temperature cyclotron motion T << 7.2 K Gabrielse David Hanneke G.G. Gabrielse Electron Cyclotron Motion Comes Into Thermal Equilibrium T = 100 mK << 7.2 K ground state always Prob = 0.99999… cold electron hot cavity blackbody spontaneous emission photons Gabrielse Electron in Cyclotron Ground State QND Measurement of Cyclotron Energy vs. Time 0.23 0.11 0.03 9 x 10-39 average number On a short time scale of blackbody in one Fock state or another photons in the Averaged over hours cavity in a thermal state S. Peil and G. Gabrielse, Phys. Rev. Lett. 83, 1287 (1999). Gabrielse Spin Two Cyclotron Ladders of Energy Levels n=4 c n=3 n=4 c c Cyclotron n=2 Spin n=3 c c frequency: n=1 frequency: n=2 c c 1 eB n=0 g c n=1 c s c 2 m 2 n=0 ms = -1/2 ms = 1/2 Gabrielse Basic Idea of the Fully-Quantum Measurement n=4 c n=3 n=4 c c Cyclotron n=2 Spin n=3 c c frequency: n=1 frequency: n=2 c c 1 eB n=0 g c n=1 c s c 2 m 2 n=0 ms = -1/2 ms = 1/2 g s s c B in free Measure a ratio of frequencies: 1 2 c c space 103 • almost nothing can be measured better than a frequency • the magnetic field cancels out (self-magnetometer) Gabrielse Special Relativity Shift the Energy Levels n=4 c 9 / 2 n=3 n=4 c 7 / 2 c 7 / 2 Cyclotron n=2 Spin n=3 c 5 / 2 c 5 / 2 frequency: n=1 frequency: n=2 c 3 / 2 c 3 / 2 eB n=0 g 2 c n=1 c / 2 s c m 2 n=0 ms = -1/2 ms = 1/2 Not a huge relativistic shift, h c 109 but important at our accuracy c mc 2 Solution: Simply correct for if we fully resolve the levels (superposition of cyclotron levels would be a big problem) Gabrielse Cylindrical Penning Trap V 2z 2 x2 y 2 • Electrostatic quadrupole potential good near trap center • Control the radiation field inhibit spontaneous emission by 200x (Invented for this purpose: G.G. and F. C. MacKintosh; Int. J. Mass Spec. Ion Proc. 57, 1 (1984) Gabrielse One Electron in a Penning Trap • very small accelerator • designer atom cool 12 kHz 200 MHz detect need to Electrostatic 153 GHz measure quadrupole for g/2 Magnetic field potential Gabrielse Frequencies Shift Imperfect Trap • tilted B Perfect Electrostatic • harmonic B in Free Space Quadrupole Trap distortions to V eB c c ' c c m z c ' z m z m g g g s c s c s c 2 2 2 g s not a measurable eigenfrequency in an Problem: 2 c imperfect Penning trap Solution: Brown-Gabrielse invariance theorem c ( c )2 ( z )2 ( m )2 Gabrielse Spectroscopy in an Imperfect Trap • one electron in a Penning trap • lowest cyclotron and spin states g s vc ( s c ) vc a 2 c c c ( z ) 2 a g 2 c 1 2 3 ( z ) 2 fc 2 2 c expansion for vc z m To deduce g measure only three eigenfrequencies of the imperfect trap Gabrielse Detecting and Damping Axial Motion measure voltage V(t) I2 R damping Axial motion 200 MHz of trapped electron self-excited oscillator feedback amplitude, f Gabrielse Feedback Cooling of an Oscillator Electronic Amplifier Feedback: Strutt and Van der Ziel (1942) Basic Ideas of Noiseless Feedback and Its Limitations: Kittel (1958) Dissipation : e (1 g ) Fluctuations: Te T (1 g ) faster damping rate Fluctuation-Dissipation Invariant: e / Te const higher temperature Applications: Milatz, … (1953) -- electrometer Dicke, … (1964) -- torsion balance Forward, … (1979) -- gravity gradiometer Ritter, … (1988) -- laboratory rotor Cohadon, … (1999) -- vibration mode of a mirror Proposal to apply Kittel ideas to ion in an rf trap Dehmelt, Nagourney, … (1986) never realized Proposal to “stochastically” cool antiprotons in trap Beverini, … (1988) – stochastic cooling never realized Rolston, Gabrielse (1988) – same as feedback cooling (same limitations) Realization of feedback cooling with a trapped electron (also include noise) D’Urso, Odom, Gabrielse, PRL (2003) D’Urso, Van Handel, Odom, Hanneke, Gabrielse, PRL 94, 11302 (2005) Gabrielse one-electron self-excited oscillator QND Detection of One-Quantum Transitions 1 B B2 z 2 H mz 2 z 2 m B2 z 2 2 n=0 n=1 n=0 cyclotron cyclotron cyclotron ground excited ground state state state n=1 freq Ecyclotron hf c (n 1 ) 2 n=0 time QND Gabrielse Quantum Non-demolition Measurement B H = Hcyclotron + Haxial + Hcoupling [ Hcyclotron, Hcoupling ] = 0 QND condition QND: Subsequent time evolution of cyclotron motion is not altered by additional QND measurements Observe Tiny Shifts of the Frequency Gabrielse of a One-Electron Self-Excited Oscillator one quantum cyclotron excitation spin flip Unmistakable changes in the axial frequency signal one quantum changes in cyclotron excitation and spin "Single-Particle Self-excited Oscillator" B B. D'Urso, R. Van Handel, B. Odom and G. Gabrielse Phys. Rev. Lett. 94, 113002 (2005). Gabrielse Emboldened by the Great Signal-to-Noise Make a one proton (antiproton) self-excited oscillator try to detect a proton (and antiproton) spin flip • Hard: nuclear magneton is 500 times smaller • Experiment underway Harvard also Mainz and GSI (without SEO) (build upon bound electron g values) measure proton spin frequency we already accurately measure antiproton cyclotron frequencies get antiproton g value (Improve by factor of a million or more) Gabrielse Need Averaging Time to Observe a One-quantum Transition Cavity-Inhibited Spontaneous Emission Application of Cavity QED excite, number of n=1 to n=0 decays 30 measure time in excited state t = 16 s axial frequency shift (Hz) 15 12 20 9 6 10 3 0 0 -3 0 10 20 30 40 50 60 0 100 200 300 decay time (s) time (s) Gabrielse Cavity-Inhibited Spontaneous Emission 1 Free Space 75 ms B = 5.3 T Within 1 Inhibited Trap Cavity 16 sec By 210! B = 5.3 T cavity modes Purcell Kleppner c frequency Gabrielse and Dehmelt Gabrielse “In the Dark” Excitation Narrower Lines axial frequency shift (Hz) 15 1. Turn FET amplifier off 12 9 6 2. Apply a microwave drive pulse of ~150 GH 3 0 (i.e. measure “in the dark”) -3 0 100 200 300 time (s) 3. Turn FET amplifier on and check for axial frequency shift 4. Plot a histograms of excitations vs. frequency # of cyclotron excitations Good amp heat sinking, amp off during excitation Tz = 0.32 K 0 100 200 300 frequency - c (ppb) Gabrielse Big Challenge: Magnetic Field Stability Magnetic field cancels out n=2 n=3 g s a n=2 n=1 1 n=1 n=0 2 c c n=0 ms = 1/2 ms = -1/2 But: problem when B drifts during the measurement Magnetic field take ~ month to stabilize Gabrielse Self-Shielding Solenoid Helps a Lot Flux conservation Field conservation Reduces field fluctuations by about a factor > 150 “Self-shielding Superconducting Solenoid Systems”, G. Gabrielse and J. Tan, J. Appl. Phys. 63, 5143 (1988) Gabrielse Eliminate Nuclear Paramagnetism Deadly nuclear magnetism of copper and other “friendly” materials Had to build new trap out of silver ~ 1 year New vacuum enclosure out of titanium setback Gabrielse Gabrielse Gabrielse Quantum Jump Spectroscopy • one electron in a Penning trap • lowest cyclotron and spin states Gabrielse Measurement Cycle n=3 n=2 g s a n=1 1 n=2 2 c c n=1 n=0 n=0 ms = 1/2 simplified ms = -1/2 1. Prepare n=0, m=1/2 measure anomaly transition 3 hours 2. Prepare n=0, m=1/2 measure cyclotron transition 0.75 hour 3. Measure relative magnetic field Repeat during magnetically quiet times Gabrielse Measured Line Shapes for g-value Measurement It all comes together: • Low temperature, and high frequency make narrow line shapes • A highly stable field allows us to map these lines cyclotron anomaly n=3 n=2 n=2 n=1 n=1 n=0 n=0 ms = 1/2 ms = -1/2 Precision: Sub-ppb line splitting (i.e. sub-ppb precision of a g-2 measurement) is now “easy” after years of work Gabrielse Cavity Shifts of the Cyclotron Frequency n=2 g s a n=3 n=1 1 n=2 2 c c n=1 n=0 n=0 ms = 1/2 ms = -1/2 1 spontaneous emission 16 sec inhibited by 210 B = 5.3 T Within a Trap Cavity cavity cyclotron frequency is shifted by interaction modes with cavity modes c frequency Gabrielse Cavity modes and Magnetic Moment Error use synchronization of electrons to get cavity modes Operating between modes of cylindrical trap first measured where shift from two cavity modes cavity shift of g cancels approximately Gabrielse Summary of Uncertainties for g (in ppt = 10-12) Test of cavity shift Measurement understanding of g-value Gabrielse Gabrielse Attempting to Measure g for Proton and Antiproton • Improve proton g by more than 10 • Improve antiproton g by more than 106 • Compare g for antiproton and proton – test CPT Gabrielse Current Proton g Last Measured in 1972 CODATA 2002: gp=5.585 694 701(56) (10 ppb) m p ( H ge ( H g p mp g p ge me ( H ge g p ( H ) me proton-electron mass ratio, measured to < 1 ppb electron g-factor, bound / free corrections, (Mainz) measured to calculated to < 1 ppb < 0.001 ppb (Breit, Lamb, Lieb, Grotch, Faustov, Close, Osborn, Hegstrom, Persson, (Harvard) others) ge ( H 1 1 1 2 a 1 2 m 1 ( Za ( Za ( Za ( Za e 2 4 bound magnetic moment ratio, ge 3 12 4 2 m p measured to 10 ppb (MIT: P.F. Winkler, D. Kleppner, 1 17.7053 106 T. Myint, F.G. Walther, Phys. Rev. A 5, 83-114 (1972) ) gp (H 1 1 m 3 4a p 1 Za 2 Za 2 e gp 3 6 m 1 a p p 1 17.7328 106 Gabrielse History of Measurements of Proton g (from bound measurements of mp/me, with current values of ge, me/mp and theory) Gabrielse Antiproton g-factor Antiproton g-factor is known to less than a part per thousand g p 5.601(18 We hope to do roughly one million times better. Gabrielse Apparatus Working Only With Electrons (so far) iron detect spin flip make spin flip 6 mm inner diameter Nick Guise Gabrielse Summary and Conclusion Gabrielse Summary How Does One Measure g to 7.6 Parts in 1013? Use New Methods • One-electron quantum cyclotron first measurement with • Resolve lowest cyclotron as well as spin states these new methods • Quantum jump spectroscopy of lowest quantum states • Cavity-controlled spontaneous emission • Radiation field controlled by cylindrical trap cavity • Cooling away of blackbody photons • Synchronized electrons probe cavity radiation modes • Trap without nuclear paramagnetism • One-particle self-excited oscillator Gabrielse New Measurement of Electron Magnetic Moment magnetic S spin m g mB moment Bohr magneton e 2m g / 2 1.001 159 652 180 85 0.000 000 000 000 76 7.6 1013 • First improved measurement since 1987 • Nearly six times smaller uncertainty • 1.7 standard deviation shift • Likely more accuracy coming • 1000 times smaller uncertainty than muon g B. Odom, D. Hanneke, B. D’Urso and G. Gabrielse, Phys. Rev. Lett. 97, 030801 (2006). Gabrielse New Determination of the Fine Structure Constant 1 e 2 • Strength of the electromagnetic interaction a • Important component of our system of 4 0 c fundamental constants • Increased importance for new mass standard a 1 137.035 999 710 0.000 000 096 7.0 1010 • First lower uncertainty since 1987 • Ten times more accurate than atom-recoil methods G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, B. Odom, Phys. Rev. Lett. 97}, 030802 (2006). Gabrielse We Intend to do Better Stay Tuned – The new methods have just been made to work all together • With time we can utilize them better • Some new ideas are being tried (e.g. cavity-sideband cooling) • Lowering uncertainty by factor of 13 check muon result (hard) Spin-off Experiments • Use self-excited antiproton oscillator to measure the antiproton magnetic moment million-fold improvement? • Compare positron and electron g-values to make best test of CPT for leptons • Measure the proton-to-electron mass ration directly Gabrielse Further Reading New Measurement of the Electron Magnetic Moment B. Odom, D. Hanneke, B. D’Urson and G. Gabrielse, Phys. Rev. Lett. 97, 030801 (2006). New Determination of the Fine Structure Constant G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, B. Odom, Phys. Rev. Lett. 97, 030802 (2006). AIP Physics Story of the Year (Phys. News Update, 5 Dec. 2006) • Science 313, 448-449 (2006) • Nature 442, 516-517 (2006) • Physics Today, 15-17 (August, 2006) • Cern Courier (October 2006) • New Scientist 2568, 40-43 (2006) • Physics World (March 2007)

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