Testing the Standard Model and Its Symmetries

Transcription

1 Fermi School Varenna, Italy Testing the Standard Model and Its Symmetries Gerald Leverett Professor of Physics, Harvard University 1-2. Electron Magnetic Moment - Most precisely measured property of an elementary particle - Most stringent test of the Standard Model and QED - One particle in a Penning trap Rev. Mod. Phys. 58, 233 (1986) 3. Antiprotons and Antihydrogen - Sensitive test of the symmetries of the Standard Model - Antiproton charge-to-mass ratio - Antiproton magnetic moment - No interesting tests with antihdrogen to date 4. Electron electric dipole moment - Precise test of most proposed extensions to the Standard Model Download papers:

2 1991 Last time I came to Varenna: School on Laser Cooling Started my lecture with I do not do laser cooling Gave a lecture on cooling particles: When laser cooling does not work 2013 This visit to Varenna: Trapped Ions The ions: positronium (e+e-) ion antihydrogen ion molecular ions electron, positron antiproton

3 Electron Magnetic Moment Magnetic moment and dimensional analysis Why measure a magnetic moment? History overview Results and implications Highlights of the measurement - illustrate one particle in a Penning trap - discuss crucial methods

4 I Am Used to Unusual Attempts to Help Explain Our Antimatter Experiments Serious Play: Hapgood Author: Tom Stoppard Fiction best seller Would you expect unusual publicity for a measurement of the electron s intrinsic magnetism?

5 Help from Jim Carrey and Conan O Brien Jim Carrey Conan O Brien Viewed more than 140,000 times on YouTube.com

6 Magnetic Moments, Motivation and Results

7 Orbital Magnetic Moment magnetic moment L g B angular momentum Bohr magneton e 2m e.g. What is g for identical charge and mass distributions? IA e ev L e e L ( 2 ) L 2 mv 2m 2m 2 v g 1 B v e, m

8 Electron Spin Magnetic Moment magnetic g S B 2 /2 moment angular momentum Bohr magneton e 2m / B g / 2 magnetic moment in Bohr magnetons for spin 1/2 / B g / 2 1/ 2 mechanical model with identical charge and mass distribution / B g / 2 1 spin for simple Dirac point particle / B g / simplest Dirac spin, plus QED (if electron g/2 is different electron has substructure)

9 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 for new physics needs aand test of QED

10 Three Programs to Measure Electron g U. Michigan U. Washington Harvard beam of electrons one electron one electron spins precess with respect to cyclotron motion quantum jump spectroscopy of quantum levels kev 4.2 K 100 mk cylindrical Penning trap inhibit spontaneous emission measure cavity shifts Crane, Rich, Dehmelt, Van Dyck self-excited oscillator

11 Historical Progress g 1 C1 C2 C3 C4... a

12 Most precisely measured property of an elementary particle Electron Magnetic Moment Measured to 3 x (improved measurement is underway)

13 0 73 (28) University of Washington Physics Building

14 The Standard Model Predicts the Electron Magnetic Moment in terms of the fine structure constant 1 e c 137

15 Standard Model of Particle Physics Prediction essentially exact

16 Lowest Orders are Calculated Analytically C2 = 1.2 (exact)

17 Lowest Orders are Calculated Analytically (eg. C4) 7 Feynman diagrams 1 Feynman diagram

18 Lowest Orders are Calculated Analytically (eg. C6) Too many terms to write down 48 Feynman diagrams 72 Feynman diagrams Numerical check:

19 C8 and C10 are Calculated Numerically 891 Feynman diagrams Estimate till last year: Complete calculation completed only very recently C (0.57) Feynman diagrams Uncertainties come from numerical integration error. Depends upon available comptuter time.

20 Basking in the Reflected Glow of Theorists g 1 C2 2 C4 2 C6 3 C8 4 C10... a 5 Remiddi Kinoshita (also Laporta) (also Nio) G.G 2004

21 Probing 10th Order and Hadronic Terms

22 (Greatest?) Triumph of the Standard Model Measured: Calculated : (Uncertainty from measured fine structure constant)

23 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.

24 Testing QED Test to increasingly high order in α free electron g (i.e. high precision with light particles and atoms) Bound electron g (more a measure of m/m now) Test when binding energy ~ electron mass high Z (also atomic structure is harder to calculate) Positronium is a bit unusual (e.g. annihilation changes exchange effects)

25 Comparing the Extremely Precise Tests of QED ppb = 10-9 QED theory free electron g tests QED to much higher order in α

26 What is the Fine Structure Constant? A better definition 1 e2 4 0 c Thanks to Enrico Fermi for making the rest of us feel better Enrico Fermi

27 Propagation of Errors

28 Fine Structure Constant 1 e c 137 Strength of the electromagnetic interaction (in the low energy limit) Important component of our system of fundamental constants Increased importance for new mass standard Energy scale for atoms Binding energy: E ~ 2 mc 2 Fine structure: E ~ 4 mc 2 Lamb shift: E ~ 5 mc 2 m 4 2 Hyperfine structure: E ~ mc M Feynman: every theorist should put 137 on their office wall

29 Assume Standard Model Prediction is Correct, Deduce Alpha from Electron g/2 essentially exact

30 Most Precise Determination of the Fine Structure Constant (g/2 + QED) exp`t Determinations of the fine structure constant theory before 2012

31 Widely Re-Reported Science Nature Physics Today New Scientist Cern Courier Fox News Moral: what is quoted is not necessarily what was said

32 Earlier Measurements Require Larger Uncertainty Scale ten times larger scale to see larger uncertainties many changes in one year

33 Next Most Accurate Way to Determine a use ( Cs example) Combination of measured Rydberg, mass ratios, and atom recoil 1 e2 4 0 hc 2 R h c me 2 2 R h M Cs M p c M Cs M p me Biraben, 2 4 R c f recoil M Cs M 12C ( f D1 ) 2 M 12C me e 4 me c 1 R (4 0 ) 2 2h3c 2 Pritchard, h 2 f recoil 2c M Cs ( f D1 ) 2 Haensch, Chu, Haensch, Tanner, Werthe, Quint, Blaum, Now this method is 3 times less precise We hope that it will also improve in the future test QED (Rb measurement is similar except get h/m[rb] a bit differently)

34 Test for Physics Beyond the Standard Model g 1 aqed ( ) asm :Hadronic Weak anew Physics B 2 measure to a very high precision calculate these to a very high precision look for a disagreement expected to be times larger for a muon compared to an electron m me 2 Measure electron moment test predictions of the standard model Measure muon moment look for physics beyond the Standard Model

35 Test for Physics Beyond the Standard Model g 1 aqed ( ) asm :Hadronic Weak anew Physics B 2 Does the electron have internal structure? m* total mass of particles bound together to form electron R m R m m 360 GeV / c 2 a m m* 1 TeV / c 2 a m* limited by the uncertainty in independent α value if our uncertainty was the only limit Not bad for an experiment done at 100 mk, but LEP does better R m m* 10.3 TeV / c 2 LEP contact interaction limit > electron masses of binding energy

36 Compare to Muon more massive version of the electron

37 Muon Magnetic Moment Measured In Storage Ring

38 Compare to Muon Magnetic Moment More people Much bigger budget 2500 times less precise >2.2 to 2.7 std. dev. disagreement with theory Moving from BNL to Fermilab Hint of break down of the Standard Model???????

39 Could We Check the 2.5 sdisagreement between Muon g Measurement and Calculation? g 1 aqed ( ) asm :Hadronic Weak anew Physics B 2 (mµ/me)2 ~ 40,000 muon more sensitive to new physics 2,500 how much more accurately we measure 2 2σ disagreement is now seen If we can reduce the electron g uncertainty by 8 times more should be able to have the precision to see the 2σ effect (or not) Also need: QED and SM calculations slightly improved Independent measurement of α improved by factor of 20 These are large numbers hard to imagine that this will happen quickly

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42 Now in Illinois, Close to Journey s End

43 Bound on Contributions of Small Particles to Dark Matter

44 Measuring the Electron Magnetic Moment to 3 Parts in 1013

45 Need Good Students and Stable Funding 20 years 8 theses Elise Novitski Joshua Dorr Shannon Fogwell Hogerheide David Hanneke Brian Odom, Brian D Urso, Steve Peil, Dafna Enzer, Kamal Abdullah Ching-hua Tseng Joseph Tan N$F

46 Need New Ideas Needed quantum homemade atom Van Dyck, Schwinberg, Dehemelt did a good job in 1987 Phys. Rev. Lett. 59, 26 (1987) (spent some years trying to improve but ) first measurement with these methods Takes time to develop new ideas and methods needed to measure with 2.8 parts in 1013 uncertainty 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 Trap without nuclear paramagnetism One-particle self-excited oscillator

47 One Particle in a Penning Trap no internal degrees of freedom available for detection Trap as container Trap as a homemade atom

48 Trap with charges One Electron Quantum Cyclotron f c 150 GHz n=4 n=3 n=2 n=1 n=0 2 h c 7.2 kelvin y B 6 Tesla Need low temperature cyclotron motion T << 7.2 K 0.1 µm µm

49 First Penning Trap Below 4 K 70 mk Need low temperature cyclotron motion T << 7.2 K

50 David Hanneke G.G.

51 Low Temperature Gives great vacuum: Pressure <<< 5 x Torr? brute force way to get a good vacuum? elegant way to get a good vacuum (i.e. cold fingerprints do not outgas) Eliminates black body photons

52 Electron Cyclotron Motion Comes Into Thermal Equilibrium T = 100 mk << 7.2 K ground state always Prob = spontaneous emission cold hot cavity n=4 n=3 n=2 n=1 n=0 absorb blackbody photons electron temperature describes its energy distribution on average

53 Electron in Cyclotron Ground State QND Measurement of Cyclotron Energy vs. Time 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 S. Peil and G., Phys. Rev. Lett. 83, 1287 (1999).

54 Observe Quantum Jumps QND measure cf cyclotron energy Stimulated absorptions stimulated by black body photons

55 Lowest Energy Cyclotron Eigenstates States (no magnetron motion) there is some magnetron motion n=0 2 n=1 n=2 0.1 µm n=3 n=4 n=5

56 For Fun: Coherent State Eigenfunction of the lowering operator: a 0 Fock states do not oscillate µm Coherent state with n 1 e n / 2 with 0 n n 0 nei in c' t e n, n! 0.1 µm

57 Electron has a Cyclotron Temperature At any instant in time the electron does not have a temperature it is either in one energy eigenstate or another Averaged over time, electron cyclotron motion has a temperature Boltzmann probability describes the probability of it occupying the various energy levels Pn e ( n 1/ 2) c kt For low enough temperature, temperature no longer matters electron stays in its ground state no fluctuations

58 Measure Electron s Cyclotron Temperature Temperature relates to time average of electron cyclotron energy measure the probability to find electron in each fock state x Fit to Boltzmann distribution: extract cyclotron temperature Pn e ( n 1/ 2) c kt

59 Electron Cyclotron Temp = Trap Temp Two methods used to measure electron cyclotron s temperature from <n> from measured rates Measured with temperature sensor

60 Average Values of n

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

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

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

64 Compare Relativistic Shift of Cyclotron Frequency for Free and Bound Electron Measurements For free electron: h c 9 10 c mc 2 For electron bound to an ion: fractional shift per quantum of excitation > times smaller Can excite to much larger cyclotron radii without causing a measureable frequency shift E.g. makes it possible to use Pritchard phase method that are not easy to use with a free electron (e.g. many years ago we had <10-10 precision with an antiproton)

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

66 All Motions in a Penning Trap are Really Quantum Mechanical (also true for a large accelerator) axial spin + cyclotron magnetron z When is QM needed?

67 Magnetron Motion Velocity filter: crossed E and B fields to make Lorentz force vanish at one perpendicular velocity 0 F qe v B Independent of q and m of the particle z In a trap: z + B v E

68 Cooling the Magnetron Motion To make it irrelevant Completely decoupled from its environment couple to one of the other motions to cool it z +

69 Cooling Magnetron Motion Couple to a cooled axial motion axial magnetron Sideband cooling (important technique) magnetron motion is cooled Quantum number reduces Kinetic energy reduces Total energy increases axial motion is heated axial motion cooled by another mechanism Quantum number increases Kinetic energy increases Total energy increases

70 Sideband Cooling PCooling k 1, l 1 a a k, l k l 2 (k 1)(l ) kl l PHeating k 1, l 1 ak a k, l l 2 (k )(l 1) kl k PCooling PHeating [kl l ] [kl k ] l k Cooling for l k (to limit l k ) Heating for l k

71 Sideband Cooling Lineshapes Sideband Cooling Rate Sideband Heating Rate drive frequency drive frequency Saturates with increasing drive strength No saturation with increasing drive strength

72 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)

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

74 Brown- Invariance Theorem c ( c ) 2 ( z ) 2 ( m ) 2 Leading Imperfections of a Reasonable Trap tilted B harmonic distortions to V Eg. ~ xy/d Does not protect from magnetic field gradients Does not protect from higher order (smaller) imperfections in the electrostatic potential e.g. ~ (z/d)4 (also does not protect from lightning strikes, holes drilled in trap, )

75 Brown- Invariance Theorem c ( c ) 2 ( z ) 2 ( m ) 2 c m (Corrections ) Approximation

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

77 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 2 c g 1 3 ( z ) 2 2 fc 2 2 c expansion for vc z m To deduce g measure only three eigenfrequencies of the imperfect trap

78 Detecting and Damping Axial Motion measure voltage V(t) Axial motion 200 MHz of trapped electron I2R damping self-excited oscillator feedback amplitude, φ

79 Detection of single electron axial motion The axial oscillator is coupled to a tuned-circuit amplifier Axial motion is driven to increase signal

80 Need Detector that Dissipates Little Power GaAS MESFET dissipates too much power (1 mw) Harvard-built hfet 10mW (less by 100) R. Beck, R. Westervelt, S. Peil, G. Now back to commercial devices

81 Better Detection Amplifier

82 Much Higher Axial Frequency 60 MHz 200 MHz

83 New Feedback Methods Feedback cooling of the axial motion PRL 90, (2003) Detector heats axial motion to 5 K Used feedback to cool this motion to 800 mk First one-particle self-excited oscillator PRL (2005) Feedback eliminates damping Oscillation amplitude is fixed by comparator or DSP Probing of cyclotron and spin motion is now done in the dark Axial detection is turned off Self-excited oscillator and detector turned on before cyclotron excitation decays

84 Feedback Cooling of an Oscillator Electronic Amplifier Feedback: Strutt and Van der Ziel (1942) Basic Ideas of Noiseless Feedback and Limitations: Kittel (1958) Dissipation : e (1 G ) Fluctuations: Te T (1 G ) Fluctuation-Dissipation Invariant: e / Te const faster damping rate higher temperature feedback gain Applications: Milatz, (1953) -- electrometer Dicke, (1964) -- torsion balance Forward, (1979) -- gravity gradiometer Ritter, (1988) -- laboratory rotor Cohadon, (1999) -- vibration mode of a mirror Realization of feedback cooling with one trapped electron (add detector noise to the analysis) D Urso, Odom,, PRL (2003)

85 Experimental Setup

86 feedback gain Measure oscillator temperature fluctuations Te T (1 G ) Measure oscillator damping rate dissipation e (1 G ) Observer the fluctuation-dissipation invariant e / Te const

87 Measure Temperature and Damping Rate higher temp and damping lower temp and damping Te T (1 G ) temperature Te damping rate e e (1 G ) temperature Te const e damping rate G undamped

88 Add Feedback Noise to the Analysis Need a Low Noise Amplifier g 2 Tg Te T 1 g 1 g T T [1 g ] noiseless Te 0 feedback gain (g) 1 amplifier Amplifier is single-gate, mistuned, current-starved HEMT Tg 40 mk V 2 g Vn 2 Tg T

89 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).

90 Self-excited Oscillator Setup

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

92 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)

93 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?

94 Detecting the Cyclotron Motion cyclotron frequency axial frequency nc = 150 GHz too high to detect directly nz = 200 MHz relatively easy to detect Couple the axial frequency nz to the cyclotron energy. B Small measurable shift in nz indicates a change in cyclotron energy. Bz B0 B 2z 2

95 Couple Axial Motion and Cyclotron Motion Add a magnetic bottle to uniform B 2 2 B B2 [( z / 2) zˆ z ] H m z z B2 z 2 2 n=3 n=2 n=1 n=0 B change in m changes effective wz spin flip is also a change in m

96 one-electron self-excited oscillator freq Ecyclotron QND Detection of One-Quantum Transitions 1 B B2 z 2 H m z 2 z 2 B2 z 2 2 n=0 n=1 n=0 cyclotron cyclotron cyclotron ground excited ground state state state n=1 hf c (n 12 ) n=0 time

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

98 Observe Tiny Shifts of the Frequency 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 B "Single-Particle Self-excited Oscillator" B. D'Urso, R. Van Handel, B. Odom and G. Phys. Rev. Lett. 94, (2005).

99 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

100 Inhibited Spontaneous Emission excite, measure time in excited state t= 16 s decay time (s) Y Axis 2 30 axial frequency shift (Hz) number of n=1 to n=0 decays Application of Cavity QED tim e (s) 300

101 Cavity-Inhibited Spontaneous Emission Free Space 1 75 ms Purcell Kleppner and Dehmelt B = 5.3 T Within Trap Cavity 1 16 sec Inhibited By 210! B = 5.3 T cavity modes c frequency Inhibition gives the averaging time needed to resolve a one-quantum transition

102 Big Challenge: Magnetic Field Stability Magnetic field cancels out n=2 n=1 n=0 n=3 n=2 n=1 n=0 ms = 1/2 ms = -1/2 a g s 1 2 c c But: problem when B drifts during the measurement Magnetic field take ~ month to stabilize

103 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)

104 Magnet Field from Dumpsters and Trucks

105 Good Magnetic Field Stability construction noise ~ 10-9 / (10 hours) regulate He pressure (solenoid) regulate N presssure (solenoid) regulate He pressure (fridge) regulate room temperature

106 B-field Stability Depends on Room Temperature Magnet with two broken shims No temperature regulation Magnet with working shims Shed temperature regulated 20 B-field shift (ppb) < 1 ppb noise and drift at night Friday, Saturday construction dewar temperature (C) dewar temperature (C) B-field shift (ppb) ~ 0.1 K temperature regulation of dewar time (hours) time (hours) 50 60

107 A tabletop experiment if you have a high ceiling

108 Magnetic Field is More Stable at Night Experiment is automated. Takes data while we sleep.

109 Carefully Choose Trap Materials 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

110 Eliminate Nuclear Paramagnetism 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 setback

111 2. Apply a microwave drive pulse of ~150 GH (i.e. measure in the dark ) Y Axis 2 1. Turn FET amplifier off axial frequency shift (Hz) Lower Detector Temperature Narrower Lines Turn FET amplifier on and check for axial frequency shift # of cyclotron excitations 4. Plot a histograms of excitations vs. frequency Good amp heat sinking, amp off during excitation Tz = 0.32 K frequency - c (ppb) tim e (s) 300

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

114 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=2 n=3 n=1 n=2 n=0 n=1 n=0 ms = 1/2 ms = -1/2 Precision: line s: L. Brown Sub-ppb line splitting (i.e. sub-ppb precision of a g-2 measurement) is now easy after years of work

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

116 Cavity modes and Magnetic Moment Error use synchronization of electrons to get cavity modes Operating between modes of cylindrical trap where shift from two cavity modes cancels approximately first measured cavity shift of g

117 Use the Electron to do Spectroscopy of the Cavity Measuring lifetime and g as a function of B Attempting cavity sideband cooling

118 Cavity Shifts Related: Does the cavity affect the spin frequency?

119 Careful Studies of the Lineshapes

120 Shifts and Uncertainties g (in ppt = ) cavity shifts not a problem lineshape broadening

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122 Emboldened by the Great Signal-to-Noise Make a one proton (antiproton) self-excited oscillator try to detect a proton (and antiproton) spin flips

123 Towards a One-Electron Qubit in a Scalable Geometry

124 Many Theory Papers on One-Electron Qubits Follow the Clean Observations of One-Electron Transitions

125 Can a One-Electron Qubit Be Realized in a Scalable Geometry? Cylindrical 3-d Penning traps are not easily scalable This last report was very pessimistic. No clean and narrow resonance lines were observed.

126 We Had Developed Many Trap Designs and We Thought that there Should be a Way Hyperbolic with Anharmonicity Compensation Van Dyck, Wineland, Ekstrom, and Dehmelt, APL 28, 446 (1976), PRA 27, 2227 (1983), PRA 29, 462 (1984) Orthogonalized design used for the most precise mass spectroscopy

127 Cylindrical Penning Trap, Haarsma, and Rolston Intl. J. of Mass Spec. and Ion Proc. 88, 319 (1989) Open Access Trap, Haarsma, and Rolston Intl. J. of Mass Spec. and Ion Proc. 88, 319 (1989)

128 Planar Penning Trap Covered Planar Trap 30 page theory paper. Key idea: treat distance to electron as a parameter

129 Identified Workable Trap Designs and Showed Why Previous Designs Should Not Work

130 Made a Large Trap to Test Center pad is 1 mm radius. Copper (0.2 mm) on alumina. back front Best possible symmetry Large aspect ratio on cuts top of laser cuts profile of laser cuts

131 One-electron axial linewidths One of the first cool downs in a completely new apparatus new traps new dilution fridge new superconducting solenoid student still learning Had some clear noise problems (now likely fixed) One or two electrons? Seems promising

132 Stowed away below the electron magnetic moment trap electron magnetic moment trap planar trap

133 Promising Hopefully we will have time to pursue soon

134 Summary How Does One Measure g to 7.6 Parts in 1013? first measurement with these new methods Use New Methods One-electron quantum cyclotron Resolve lowest cyclotron as well as spin states 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

135 New Measurement of Electron Magnetic Moment magnetic moment S g B spin Bohr magneton g / e 2m D. Hanneke, S. Fogwell and G. First improved measurements since times smaller uncertainty 1.7 standard deviation shift 2500 times smaller uncertainty than muon g

136 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 10 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