sign in sign up
<<
Home , Electron magnetic moment, Gerald Gabrielse

One- Quantum : Gabrielse A New Measurement of the Electron and the Constant Gerald Gabrielse Leverett Professor of , with Shannon Fogwell and Josh Dorr 2006 DAMOP Thesis Earlier contributions: David Hanneke Prize Winner Brian Odom, 2 Brian D’Urso, ψ Steve Peil, 20 years Dafna Enzer, 7 theses Kamal Abdullah Ching-hua Tseng Joseph Tan N$F 0.1 µm Gabrielse Three Programs to Measure Electron g

U. Michigan U. Washington Harvard beam of one electron one electron cylindrical spins precess quantum jump with respect to spectroscopy of inhibit cyclotron motion quantum levels spontaneous emission keV 4.2 K 100 mK measure cavity shifts

self-excited Dehmelt, oscillator Crane, Rich, … Van Dyck Gabrielse References

2006: B. Odom, D. Hanneke, B. D’Urso, G. Gabrielse PRL 97 , 030801 (2006).

2008: D. Hanneke, S. Fogwell and G. Gabrielse PRL 100, 120801 (2008).

Two recent review chapters in book Lepton Moments , edited by Roberts and Marciano, (World Scientific, Singapore, 2009) G. Gabrielse, “Measuring the Electron Magnetic Moment” G. Gabrielse, “Determining the Fine Structure Constant” Gabrielse New Measurement of Electron Magnetic Moment magnetic S µµ = g B moment ℏ ℏ e 2m g / 2= 1.001159 652 180 73 ±0.000 000 000 000 28 2.8 × 10 −13

D. Hanneke, S. Fogwell and G. Gabrielse

• First improved measurements (2006, 2008) since 1987 • 15 times smaller uncertainty • 1.7 standard deviation shift • 2500 times smaller uncertainty than muon g Gabrielse New Determination of the Fine Structure Constant 1 e2 • Strength of the electromagnetic interaction α = • Important component of our system of ℏ fundamental constants 4πε0 c • Increased importance for new mass standard α −1 =137.035 999 084 (12) (37) (33) ±0.000000051 3.7 × 10 −10

• First lower uncertainty since 1987 (2006, 2008) • 20 times more accurate than -recoil methods D. Hanneke, S. Fogwell and G. Gabrielse Gabrielse Key: Resolving One-Quantum Transitions for One Trapped Electron

one-quantum spin flip cyclotron transition

electron magnetic moment in Bohr magnetons Gabrielse Twenty Years and 7 PhD Theses?

Takes time to develop new ideas and methods needed to determine g/2 to 2.8 parts in 10 13 uncertainty – one PhD at a time

• One-electron quantum cyclotron • Resolve lowest cyclotron states as well as spin • 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

these new new new methods methods thesethese • Trap without nuclear first measurement withwith measurement measurement firstfirst • One-particle self-excited oscillator Gabrielse Orbital Magnetic Moment magnetic L µ= g moment B ℏ ℏ Bohr magneton e 2m e.g. What is g for identical charge and mass distributions?

v e, m e evLρ e eLℏ πρ µ ==IA(2 ) = == L ρ 2πρ  2mvρ 2 m 2 m ℏ   v 

g = 1 µB Gabrielse magnetic S angular momentum µ= g moment B ℏ ℏ Bohr magneton e 2m

g = 1 identical charge and mass distribution

g = 2 spin for simplest 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 ααα 4. Test CPT – compare g for electron and positron best lepton test 5. Look for new physics beyond the • Is g given by Dirac + QED? If not electron substructure (new physics) • Muon g search for new physics needs α and test of QED Gabrielse Gabrielse Trap with One Electron in a ------charges fc ≈ 150 GHz ψ 2

n = 4 n = 3 n = 2 0.1 n = 1 µm hυc = 7.2 kelvin n = 0 ψ 2

------Need low temperature B ≈ 6 Tesla cyclotron motion T << 7.2 K 0.1 µm Gabrielse Electron Cyclotron Motion Comes Into Thermal Equilibrium T = 100 mK << 7.2 K ground state always Prob = 0.99999…

n = 4 n = 3 n = 2 spontaneous n = 1 absorb blackbody emission n = 0 photons cold hot electron “temperature” – describes its energy distribution cavity on average 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

David Hanneke G.G. Gabrielse First Penning Trap Below 4 K 70 mK

Need low temperature cyclotron motion T << 7.2 K Gabrielse Gabrielse Spin Two Cyclotron Ladders of Energy Levels

n = 4 ν c n = 3 n = 4 ν ν c Cyclotron c n = 2 Spin n = 3 ν c frequency: ν c n = 1 frequency: n = 2 ν c 1 eB ν c n = 0 g ν = n = 1 c ν ν s = ν c 2π m c 2 n = 0

ms = -1/2 ms = 1/2 Gabrielse Basic Idea of the Fully-Quantum Measurement

n = 4 ν c n = 3 n = 4 ν ν c Cyclotron c n = 2 Spin n = 3 ν c frequency: ν c n = 1 frequency: n = 2 ν c ν c n = 0 g 1 eB n = 1 ν = ν ν c = ν s c 2π m c 2 n = 0

ms = -1/2 ms = 1/2

g ν ν −ν Measure a ratio of frequencies: =s =1 + s c B in free 2 ν c ν c space ≈10 −3 • almost nothing can be measured better than a frequency • the magnetic field cancels out (self-magnetometer) Gabrielse Shift the Energy Levels δδδ

n = 4 δν − 9 / 2 c n = 3 n = 4 δν c − 7 / 2 Cyclotron δν c − 7 / 2 n = 2 Spin n = 3 δν c − 5 / 2 frequency: δν c − 5 / 2 n = 1 frequency: n = 2 δν c − 3 / 2 eB δν c − 3 / 2 n = 0 g 2πν = c n = 1 ν δ − / 2 ν s = ν c m c 2 n = 0

ms = -1/2 ms = 1/2

Not a huge relativistic shift, δ hν c −9 =2 ≈ 10 but important at our accuracy ν c mc

Solution: Simply correct for δ if we fully resolve the levels (superposition of cyclotron levels would be a big problem) Gabrielse Cylindrical Penning Trap V~ 2 z2− x 2 − 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 for g/2 quadrupole Magnetic field potential Gabrielse Frequencies Shift Imperfect Trap • tilted B Perfect Electrostatic • harmonic B in Free Space Quadrupole Trap distortions to V eB ν = ν ' < ν c m c c c ν ν νz= c ' z

ν m= z ν m g g g νν = νν s= c νν = s2 c 2 s2 c g ν Problem: = s not a measurable eigenfrequency in an 2 ν c imperfect Penning trap Solution: Brown-Gabrielse invariance theorem 2 2 2 ν ν ν ν c=() c + () z + () m An Aside Arising from the Last of These Conferences Gabrielse

M

More detail: G. Gabrielse, Int. J. of Mass Spec. 279 , 107 (2009)

Measured sideband frequency – function of B tilt and harmonic distortion

ω θ+ θ φ(,,) ε +ω φ ε − (,,) ≈ ωc only an approx.

How bad is this common approximation? ∼ dimensional analysis : ∆ω ωc θ ω ε c+ c ~1%

92 1 2  using invariance theorem: ∆ ωε θ ω c ≈  −  − (and a bit of symmetry) 4 2  much, much smaller Gabrielse Spectroscopy in an Imperfect Trap

• one electron in a Penning trap • lowest cyclotron and spin states

g ν ν ν ν v+( − ) v + =s = c sc = ca ν2 ν ν c c c 2 (ν z ) ν a − g 2ν c ≈1 + 2 2 3δ (ν z ) fc + + 2 2 ν c ≫ ≫ ≫ expansion for vc δ ν z m

To deduce g measure only three eigenfrequencies of the imperfect trap Feedback Cooling of an Oscillator Gabrielse Electronic Amplifier Feedback: Strutt and Van der Ziel (1942) Basic Ideas of Noiseless Feedback and Its Limitations: Kittel (1958)

Dissipation :Γ=Γ−e (1g ) Fluctuations: TTge =− (1 ) faster damping rate

Fluctuation-Dissipation Invariant: Γe / 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 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 QND Detection of One-Quantum Transitions 1 ∆BBz =2 →H = mω 2 z 2 − µ Bz 2 2 2 z 2

-excited oscillator -excited n=0 n=1 n=0 cyclotron cyclotron cyclotron ground excited ground state state state electron self self electronelectron

one- n=1 1 freq= Ecyclotron = hf c ( n + 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 Gabrielse One-Electron Self-Excited Oscillator measure voltage

V(t)

I2R damping axial motion 200 MHz of trapped electron crucial to limit the osc. amplitude

feedback amplitude , φ 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 Quantum Jump Spectroscopy

• one electron in a Penning trap • lowest cyclotron and spin states

“In the dark” excitation turn off all detection and cooling drives during excitation Gabrielse Inhibited Spontaneous Emission Application of Cavity QED

excite, measure time in excited state 30 τττ = 16 s 15 12 20 9 6 10 3 0 0 number of n=1 to n=0 decays decays n=1 n=1 totoofof n=0 n=0 number number -3 axial frequency shift (Hz) (Hz) frequency frequency shiftshift axialaxial 0 10 20 30 40 50 60 0 100 200 300 decay time (s) time (s) Gabrielse Cavity-Inhibited Spontaneous Emission Purcell Kleppner 1 γ = Gabrielse and Dehmelt Free Space 75 ms B = 5.3 T

1 Within γ = Inhibited Trap Cavity 16 sec By 210! B = 5.3 T

cavity modes Inhibition gives the averaging time needed to resolve a frequency one-quantum transition ν c Gabrielse Big Challenge: Magnetic Field Stability

Magnetic field cancels out n = 2 n = 3 g ω ω n = 2 n = 1 =s =1 + a n = 0 n = 1 2 ωω c c n = 0 ms = 1/2 m = -1/2 But: problem when B s 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 Measurement Cycle

n = 3 n = 2 g ω ω n = 1 =s =1 + a n = 2 n = 1 n = 0 2 ωω c c n = 0 m = 1/2 simplified s 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

line s: L. Brown 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 ω ω n = 3 =s =1 − a n = 2 n = 1 n = 0 2 ωω c c n = 1 n = 0 ms = 1/2 ms = -1/2

1 γ = spontaneous emission 16 sec inhibited by 210 B = 5.3 T Within a Trap Cavity

cyclotron frequency cavity is shifted by interaction modes with cavity modes ν 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 2008 Measurement reduced cavity shift correction uncertainty

• Measuring lifetime and g as a function of B

• Attempting cavity sideband cooling Gabrielse Gabrielse New: Careful Study of the Cavity Shifts Gabrielse Electron as Magnetometer Lineshapes Gabrielse Shifts and Uncertainties g (in ppt = 10 -12 )

cavity shifts not a problem lineshape broadening Gabrielse New Measurement of Electron Magnetic Moment magnetic S spin µµ = g B moment ℏ ℏ Bohr magneton e 2m g / 2= 1.001159 652 180 73 ±0.000 000 000 000 28 2.8 × 10 −13

D. Hanneke, S. Fogwell and G. Gabrielse

• First improved measurements (2006, 2008) since 1987 • 15 times smaller uncertainty • 1.7 standard deviation shift • 2500 times smaller uncertainty than muon g Gabrielse Gabrielse Dirac + QED Relates Measured g and Measured ααα 2 fine structure 1 e magnetic S α = µ = g B constant ℏ moment ℏ 4πε0 c

g α α α 2  3 α  4 =+1 C + C  + C  +C   + ... δ a 2 1 π 2 π 3 π 4 π 

Dirac QED Calculation hadronic, weak point standard model particle Kinoshita, Nio, tiny Measure Remiddi, Laporta, etc.

1. Use measured g and QED to extract fine structure constant 2. Wait for another accurate measurement of α Test QED Basking in the Reflected Glow of Theorists Gabrielse g α  =1 + C   2 1 π  α  2 + C   2 π  α  3 + C   3 π  α  4 + C   4 π  α  5 + C   2004 5 π  RemiddiKinoshita G.G +. .. δ a “Simple” Analytic Expressions from QED Gabrielse (where calculations are completed)

7 Feynman diagrams

72 Feynman diagrams

871 Feynman diagrams

12672 Feynman diagrams

polylog: Gabrielse g α α α 2  3 α  4 =+1 C + C  + C  +C   + ... δ a 2 1 π 2 π 3 π 4 π 

experimental uncertainty Gabrielse New Determination of the Fine Structure Constant 1 e2 • Strength of the electromagnetic interaction α = • Important component of our system of ℏ fundamental constants 4πε0 c • Increased importance for new mass standard α −1 =137.035 999 084 (12) (37) (33) ±0.000000051 3.7 × 10 −10

• First lower uncertainty since 1987 (2006, 2008) • 20 times more accurate than atom-recoil methods D. Hanneke, S. Fogwell and G. Gabrielse Gabrielse Fine Structure Constant Uncertainties Gabrielse Next Most Accurate Way to Determine α (α ( use Cs example) Combination of measured Rydberg, mass ratios, and atom recoil

2 4 1e 1 e me c α ≡ ←R∞ ≡ 2 3 2 Haensch, … επε 4πε 0 hc (4)20 h c

2 2R∞ h α = Pritchard, … c m e Chu, … 2R hMM h f =∞ Cs p ← = 2c2 recoil cMMm M( f ) 2 Cs p e Cs D 1 Haensch, … 2 frecoil M Cs M 12 C Tanner, … α = 4R∞ c 2 (fD1 ) M 12 C m e Werthe, Quint, … (also Van Dyck) • Now this method is >10 times less accurate • We hope that will improve in the future test QED

Biraben, … Biraben, (Rb measurement is similar except get h/M[Rb] a bit differently) Gabrielse Several Measurements Needed for the Atom-Recoil Determinations of the Fine Structure Constant Gabrielse Earlier Measurements (On Much Larger Uncertainty Scale) Gabrielse Test of QED

Most stringent test of QED: Comparing the measured electron g to the g calculated from QED using an independent α

−12 α δ g=| gexp eriment − g theory ()| <× 1510

• The uncertainty does not comes from g and QED, + SM • All uncertainty comes from α[Rb] and α[Cs] • With a better independent α 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 In Progress

Better measurement of the electron magnetic moment and the fine structure constant

Better comparison of the positron and electron magnetic moments

Spinoffs

Observe a spin flip with one-proton self-excited oscillator (close, see new PRL)

Attempt to make a one-electron qubit (see new PRA) Goldman talk this afternoon Gabrielse

Close to observing a proton spin flip (we hope).

(Mainz talk by Ulmer is coming.) Gabrielse New Dilution Refrigerator and Suspension

support plates

dilution refrigerator 4.2 K superconducting solenoid

100 mK trap old new

100 mK trap and suspended electron moves with the 4.2 K superconducting solenoid Gabrielse New Superconducting Solenoid Gabrielse Solenoid in Place

Larger • to allow positron access • to let electron move with the solenoid

One superconducting lead was broken inside. We had to repair Gabrielse New Silver Trap

old new

Room for positron entry path Improved cavity mode spectrum (to allow cavity sideband cooling) Gabrielse Conclusion

Took many years to develop the quantum methods to measure the electron magnetic moment

Most precise measurement of the electron magnetic moment Most precise determination of the fine structure constant Most stringent test of QED (higher order and precision)

Soon: Most precise test of CPT invariance with leptons More precise electron magnetic moment More precise determination of the fine structure constant

Spinoffs: proton magnetic moment one-electron qubit