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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


 g2     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 1013

                   • 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 1010


                                               • 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                  hc  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
                                                  103
        • 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
                                                          109
               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      mz 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 106
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 106
                                                  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 1013

                   • 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 1010


                                               • 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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