New Measurement of the Electron Magnetic Moment and the Fine Structure Constant

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New Measurement of the Electron Magnetic Moment and the Fine Structure Constant Gerald Leverett Professor of Physics Harvard University Almost finished student: David

1 New Measurement of the Electron Magnetic Moment and the Fine Structure Constant Gerald Leverett Professor of Physics Harvard University Almost finished student: David Hanneke Earlier contributions: Brian Odom, Brian D Urso, 20 years 6.5 theses Steve Peil, Dafna Enzer, Kamal Abdullah Ching-hua Tseng Joseph Tan (poster session) 2 ψ N$F 0.1 µm

2 Why Does it take Twenty Years and 6.5 Theses? Explanation 1: We do experiments much too slowly Explanation 2: Takes time to develop new methods for measurement with 7.6 parts in uncertainty One-electron quantum cyclotron Resolve lowest cyclotron and spin states Quantum jump spectroscopy 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

3 New g and α 2 ψ Gerald Leverett Professor of Physics Harvard University Magnetic moments, motivation and results Before this measurement situation unchanged since 1987 Quantum Cyclotron and Many New Methods electron g i.e. Why it took ~20 years to measure g to 7.7 parts in µm Determining the Fine Structure Constant Spin-off measurements N. Guise (poster) million-fold improved antiproton magnetic moment Also Quint, et al. best lepton CPT test (comparing g for electron and positron) direct measurement of the proton-to-electron mass ratio N$F

4 Magnetic Moments, Motivation and Results

5 magnetic moment Magnetic Moments µ = gµ B L e Bohr magneton 2 m angular momentum e.g. What is g for identical charge and mass distributions? e 2 ( ) ev ρ µ = IA = πρ L e L e L 2πρ = 2 mvρ = 2m = 2m v g = 1 µ B ρ v em,

6 magnetic moment Magnetic Moments µ = gµ B J e Bohr magneton 2 m angular momentum g = 1 cyclotron motion, identical charge and mass distribution g = 2 spin for simplest Dirac particle g = simplest Dirac spin, plus QED (if electron g is different the electron must have substructure)

7 Previous Status: Electron Magnetic and Muon Moments UW, 1987 Electron ( UW ) : g / 2 = ± ppt Positron ( UW ) : g / 2 = ± ppt + Muon µ ( E821) : g / 2 = ± ppt Muon µ ( E821) : g / 2 = ± ppt Electron magnetic moment test QED (with another measured fine structure constant) measure fine structure constant (with QED theory) best lepton CPT test by comparing electron and positron Muon magnetic moment look for unexpected new physics in expected forms Electron more accurate by 200 Muon more sensitive to unexpected new physics

8 Previous Status: Electron and Muon Moments UW, 1987 E821, 2004 Electron ( UW ) : g / 2 = ± ppt Positron ( UW ) : g / 2 = ± ppt + Muon µ ( E821) : g / 2 = ± ppt Muon µ ( E821) : g / 2 = ± ppt Electron magnetic moment test QED (with another measured fine structure constant) measure fine structure constant (with QED theory) best lepton CPT test by comparing electron and positron Muon magnetic moment look for unexpected new physics in expected forms Electron more accurate by 200 ( 1000) Muon more sensitive to unexpected new physics

9 New Measurement of Electron Magnetic Moment magnetic moment µ = gµ B S spin e Bohr magneton 2 m g / 2 = ± 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 Urson and G., Phys. Rev. Lett. (in press).

10 Why Measure the Electron Magnetic Moment? 1. The electron g-value is a basic property of the simplest of elementary particles 2. Use measured g and QED to extract fine structure constant (Will be even more important when we change mass standards) 3. Wait for another accurate measurement of α test QED 4. Best lepton CPT test compare g for electron and positron 5. Look for new physics Is g given by Dirac + QED? If not electron substructure Enable the muon g search for new physics - provide α - test of QED Needed so the large QED term can be subtracted to see if there is new physics heavy particles, etc.

11 QED Relates Measured g and Measured α g α α α α = 1 + C C C C π + π + π + π +.. δ a weak/strong Measure QED Calculation Kinoshita, Nio, Remiddi, Laporta, etc. Sensitivity to other physics (weak, strong, new) is low 1. Use measured g and QED to extract fine structure constant 2. Wait for another accurate measurement of α Test QED

Kinoshita Remiddi After dinner at the apartment in St. Genis in 20

12 Kinoshita Remiddi After dinner at the apartment in St. Genis in C C C C g a α π α π α π δ α π = Basking in the reflected glow of theorists

13 New Determination of the Fine Structure Constant α = 1 4πε 0 2 e c 1 α = Strength of the electromagnetic interaction Important component of our system of fundamental constants Increased importance for new mass standard ± First lower uncertainty since 1987 Ten times more accurate than atom-recoil methods G., D. Hanneke, T. Kinoshita, M. Nio, B. Odom, Phys. Rev. Lett. (in press)

14 2 1 e 1 R 0 hc πε 0 4 emc e α 4 πε (4 ) 2h c 2 α = α 2R c h m e 2R M M h h f = = c M M m M f Cs p 2 recoil 2c 2 Cs p e Cs ( D1) f M M = 4Rc f M m 2 recoil Cs 12C 2 ( D1) 12C e Next Most Accurate Way to Determine α (use Cs example) Combination of measured Rydberg, mass ratios, and atom recoil 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)

15 Famous Earlier Measurements No Longer Fit on the Same Scale ten times larger scale

16 Test of QED Most stringent test of QED: Comparing the measured electron g to the g calculated from QED using an independent α δ g < None of the uncertainty comes from g and QED All uncertainty comes from α[rb] and α[cs] With a better independent α could do a ten times better test

17 Dear Jerry, From Freeman Dyson One Inventor of QED... 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.

18 Test for Electron Substructure (from any difference between experiment and theory g) m m* > = 130 GeV / c δ g /2 m m* > = 600 GeV / c δ g /2 2 2 limited by the independent α values if our g uncertainty was the only limit Brodsky and Drell, 1980 Not bad for an experiment done at 100 mk, but LEP does better m* > 10.3 TeV LEP contact interaction limit

19 The New Measurement

20 The 1987 measurement is already very accurate 4.3 ppt = How Does One Measure g More Accurately? New Methods One-electron quantum cyclotron Resolve lowest cyclotron and spin states Quantum jump spectroscopy 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 Give introduction to some new and novel methods

21 Quantum Cyclotron one electron quantum average quantum number < 1, etc. quantum υ c 150 GHz B 6 Tesla n = 4 n = 3 n = 2 n = 1 n = 0 ω c = 7.2 kelvin To realize a quantum cyclotron: need cyclotron temperature << 7.2 kelvin 100 mk apparatus need sensitivity to detect a one quantum excitation

22 First Penning Trap Below 4 K 70 mk Cyclotron motion comes into thermal equilibrium with its container K 7.2 K = ω / k c

23 Particle Thermometer 70 mk, lowest storage energy for any charged elementary particles

24 Lowest Energy Cyclotron Eigenstates States ψ 2 (ignore magnetron motion in a trap) n=0 n=1 n=2 0.1 µm n=3 n=4 n=5

25 For Fun: Coherent State Eigenfunction of the lowering operator: a α = αα Fock states do not oscillate ψ = 0 n=0 n = 1 ψ = µm Coherent state with n = 1 ψ ne iβ ' n /2 n= inωct e e n n 0 = = n!, 0.1 µm

26 We Use Only the Lowest Cyclotron States n = 4 n = 3 n = 2 n = 1 n = 0 υ B c 6 Tesla 150 GHz

27 Spin Two Cyclotron Ladders of Energy Levels Cyclotron frequency: eb ν c = m n = 4 n = 3 n = 2 n = 1 n = 0 ν c ν c ν c ν c ν c ν c ν c ν c m s = -1/2 m s = 1/2 n = 4 n = 3 n = 2 n = 1 n = 0 Spin frequency: g ν s = ν c 2

28 Basic Idea of the Fully-Quantum Measurement Cyclotron frequency: eb ν c = m n = 4 n = 3 n = 2 n = 1 n = 0 ν c ν c ν c ν c Measure a ratio of frequencies: ν c ν c ν c ν c m s = -1/2 m s = 1/2 g 2 n = 4 n = 3 n = 2 n = 1 n = 0 ν s ν s ν c = = 1+ ν ν c c 10 3 almost nothing can be measured better than a frequency the magnetic field cancels out (self-magnetometer) Spin frequency: g ν s = ν c 2 B in free space

29 Modifications to the Basic Idea Special relativity shifts the levels We add an electrostatic quadrupole potential V ~ 2z 2 x 2 -y 2 to weakly confine the electron for measurement shifts frequencies The electrostatic quadrupole potential is imperfect additional frequency shifts

30 Modification 1: Special Relativity Shift δ Cyclotron frequency: eb ν c = m n = 4 n = 3 n = 2 n = 1 n = 0 ν c ν c ν c ν c 7 δ /2 5 δ /2 3 δ /2 δ /2 ν c 9 δ /2 c 7 δ /2 ν c 5 δ /2 3 δ /2 ν ν c n = 4 n = 3 n = 2 n = 1 n = 0 Spin frequency: g ν s = ν c 2 m s = -1/2 m s = 1/2 Not a huge relativistic shift, but important at our accuracy δ ν c hν c = 10 2 mc 9 Solution: Simply correct for δ if we fully resolve the levels (superposition of cyclotron levels would be a big problem)

Modification 2: Add Electrostatic Quadrupole Cylindrical Penning Trap V 2z x y 2 2 2 Electrostatic

31 Modification 2: Add Electrostatic Quadrupole Cylindrical Penning Trap V 2z x y Electrostatic quadrupole potential good near trap center Control the radiation field inhibit spontaneous emission by 200x

32 B in Free Space ν = ν c s = eb m g ν c 2 Problem: g 2 ν s = ν c Frequencies Shift Perfect Electrostatic Quadrupole Trap ν ' ν ν ν c z m s < ν c ν c ν c' ν z ν z ν m = g ν c 2 Imperfect Trap tilted B harmonic distortions to V ν s = g ν c 2 not a measurable eigenfrequency in an imperfect Penning trap Solution: Brown- invariance theorem ν = ( ν ) + ( ν ) + ( ν ) c c z m

33 Spectroscopy in an Imperfect Trap one electron in a Penning trap lowest cyclotron and spin states g 2 g 2 ν s vc + ( νs νc) vc + νa = = = ν ν ν 1+ c c c f c 2 ( ν z ) ν a 2ν c 3δ ( ν z ) ν c 2 expansion for vc ν z νm δ To deduce g measure only three eigenfrequencies of the imperfect trap

34 Detecting One Quantum Cyclotron Transitions

Detecting the Cyclotron Motion cyclotron frequency ν C = 150 GHz too high to detect directly axial frequency ν Z = 200 MHz relatively easy to detect

35 Detecting the Cyclotron Motion cyclotron frequency ν C = 150 GHz too high to detect directly axial frequency ν Z = 200 MHz relatively easy to detect Couple the axial frequency ν Z to the cyclotron energy. nickel rings B Small measurable shift in ν Z indicates a change in cyclotron energy. B = B + B z z 0 2 2

36 Couple Axial Motion and Cyclotron Motion Add a magnetic bottle to uniform B n=3 n=2 n=1 n=0 B = B [( z / 2) z zρ ] H = ρ ˆ mω 2 z z µ Bz B change in µ changes effective ω z spin flip is also a change in µ

37 QND Quantum Non-demolition Measurement B H = H cyclotron + H axial + H coupling [ H cyclotron, H coupling ] = 0 QND condition QND: Subsequent time evolution of cyclotron motion is not altered by additional QND measurements

38 An Electron in a Penning Trap very small accelerator designer atom cool 12 khz 200 MHz detect Electrostatic quadrupole potential 153 GHz Magnetic field need to measure for g/2

39 Cylindrical Penning Trap Electrostatic quadrupole potential good enough near trap center

40 Detection of single electron axial motion The axial oscillator is coupled to a tuned-circuit amplifier Signal Out Axial motion is driven to increase signal amplitude (a. u.) frequency ν z (Hz)

41 Better Detection Amplifier

42 Detecting a High Axial Frequency 60 MHz 200 MHz

43 First One-Particle Self-Excited Oscillator Feedback eliminates damping Oscillation amplitude must be kept fixed Method 1: comparator Method 2: DSP (digital signal processor) "Single-Particle Self-excited Oscillator" B. D'Urso, R. Van Handel, B. Odom and G. Phys. Rev. Lett. 94, (2005).

44 Use Digital Signal Processor DSP Real time fourier transforms Use to adjust gain so oscillation stays the same

45 Cyclotron Quantum Jumps to Observe Axial Self-Excited Oscillator Use positive feedback to eliminate the damping Use comparator to make constant drive amplitude Measure very large axial oscillations (again using cyclotron quantum jump spectroscopy)

46 Observe Tiny Shifts of the Frequency of the Self-Excited Oscillator one quantum cyclotron excitation spin flip Tiny, but unmistakable, changes in the axial frequency signal one quantum changes in cyclotron excitation and spin B How?

47 Quantum Jump Spectroscopy one electron in a Penning trap lowest cyclotron and spin states

49 One-Electron in a Microwave Cavity n=3 n=2 n=1 B n=0 one-electron cyclotron oscillator within a cavity QND measurement of the cyclotron energy cyclotron energy time

50 0.23 Cool to Eliminate Blackbody Photons one electron Fock states of a cyclotron oscillators due to blackbody photons x average number of blackbody photons in the cavity On a short time scale in one Fock state or another Averaged over hours in a thermal state

51 Control Inhibition of Spontaneous Emission within a Cavity In free space, cyclotron lifetime = 0.1 s In our cylindrical trap 16 s lifetime How long to make a quantum jump down number of n=1 to n=0 decays τ = 16 s axial frequency shift (Hz) decay time (s) time (s)

52 Spontaneous Emission is Inhibited Free Space γ = 1 75 ms B = 5.3 T Within Trap Cavity B = 5.3 T cavity modes γ = 1 16 sec Inhibited By 210! ν c frequency

53 Some Challenges

54 Big Challenge: Magnetic Field Stability n = 3 n = 2 n = 1 n = 0 m s = -1/2 m s = 1/2 n = 2 n = 1 n = 0 Experimenter s definition of the g value g ω ω = s = 1+ a ω ω 2 c c relatively insensitive to B But: problem when B drifts during the measurement large magnetic field (5 Tesla) from solenoid nuclear magnetism of trap apparatus

55 Magnetic Field Takes Months to Settle after a Change Two months is a long time to wait for the magnetic field to settle.

56 Self-Shielding Solenoid Helps a Lot Flux conservation Field conservation Reduces field fluctuations by about a factor > 150 Self-shielding Superconducting Solenoid Systems, G. and J. Tan, J. Appl. Phys. 63, 5143 (1988)

57 A tabletop experiment if you have a high ceiling

58 Eliminate Nuclear Paramagnetism One Year Setback Deadly nuclear magnetism of copper and other friendly materials Had to build new trap out of silver New vacuum enclosure out of titanium ~ 1 year

59 Silver trap improvement magnetic field shift (ppb) expanded 200 x copper trap silver trap ppb / K ppb / K -1 copper trap silver trap temperature (Kelvin) temperature -1 (Kelvin -1 ) The new silver trap decreases T-dependence of the field by ~ 400 With the silver trap, sub-ppb field stability is easily achieved

60 New Silver Trap

61 In the Dark Excitation Narrower Lines 1. Turn FET amplifier off 2. Apply a microwave drive pulse of ~150 GH (i.e. measure in the dark ) 3. Turn FET amplifier on and check for axial frequency shift 4. Plot a histograms of excitations vs. frequency axial frequency shift (Hz) time (s) # of cyclotron excitations Good amp heat sinking, amp off during excitation T z = 0.32 K frequency - υ c (ppb)

63 Quantum Jump Spectroscopy Lower temperature so there are no blackbody photons in the cavity Introduce microwave photons into the trap cavity near resonance with the cyclotron frequency cyclotron energy count the quantum jumps/time for a particular drive frequency time quantum jump rate look for resonance drive frequency

64 Measurement Cycle g ω ω = s = 1+ a ω ω 2 c c simplified n = 3 n = 2 n = 1 n = 0 m s = -1/2 m s = 1/2 n = 2 n = 1 n = 0 3 hours 0.75 hour 1. Prepare n=0, m=1/2 measure anomaly transition 2. Prepare n=0, m=1/2 measure cyclotron transition 3. Measure relative magnetic field Repeat during magnetically quiet times

65 It all comes together: Low temperature, and high frequency make narrow line shapes A highly stable field allows us to map these lines Measured Line Shapes for g-value Measurement cyclotron anomaly n = 3 n = 2 n = 1 n = 0 m s = -1/2 m s = 1/2 n = 2 n = 1 n = 0 Precision: Sub-ppb line splitting (i.e. sub-ppb precision of a g-2 measurement) is now easy after years of work

66 Cavity Shifts Uncertainty completely limited now by how well we understand the cavity shifts

67 Cavity Shifts of the Cyclotron Frequency g ω ω = s = 1 a ω ω 2 c c n = 3 n = 2 n = 1 n = 0 m s = -1/2 m s = 1/2 n = 2 n = 1 n = 0 B = 5.3 T γ = 1 16 sec Within a Trap Cavity spontaneous emission inhibited by 210 cavity modes ν c frequency cyclotron frequency is shifted by interaction with cavity modes

68 Cylindrical Penning Trap Good approximation to a cylindrical microwave cavity Good knowledge of the field within Challenge is to make a sufficiently good electrostatic quadrupole Holes and slits to make a trap Must still measure resonant EM modes of the cavity have done this

69 Cavity modes and Magnetic Moment Error Operating between modes of cylindrical trap where shift from two cavity modes cancels approximately first measured cavity shift of g

70 Summary of Uncertainties for g (in ppt = ) Test of cavity shift understanding Measurement of g-value

72 Spinoff Measurements Planned 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

73 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)

74 Summary and Conclusion

75 Summary How Does One Measure g to 7.6 Parts in 10 13? New Methods One-electron quantum cyclotron Resolve lowest cyclotron and spin states Quantum jump spectroscopy 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

76 New Measurement of Electron Magnetic Moment magnetic moment µ = gµ B S spin e Bohr magneton 2 m g / 2 = ± 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 Urson and G., Phys. Rev. Lett. (in press).

77 New Determination of the Fine Structure Constant α = 1 4πε 0 2 e c 1 α = Strength of the electromagnetic interaction Important component of our system of fundamental constants Increased importance for new mass standard ± First lower uncertainty since 1987 Ten times more accurate than atom-recoil methods G., D. Hanneke, T. Kinoshita, M. Nio, B. Odom, Phys. Rev. Lett. (in press)

78 Stay Tuned. We Have Some More Ideas for Doing Better 2 ψ 0.1 µm

Cavity Control in a Single-Electron Quantum Cyclotron

Cavity Control in a Single-Electron Quantum Cyclotron An Improved Measurement of the Electron Magnetic Moment David Hanneke Michelson Postdoctoral Prize Lectures 13 May 2010 The Quantum Cyclotron Single