Fermi School – Varenna, Italy -- 2013 Gabrielse Testing the and Its Symmetries Gerald Gabrielse Leverett Professor of , 1-2. Magnetic Moment - Most precisely measured property of an elementary particle - Most stringent test of the Standard Model and QED - One particle in a Rev. Mod. Phys. 58, 233 (1986) 3. and - Sensitive test of the symmetries of the Standard Model - 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: http://gabrielse.physics.harvard.edu Gabrielse

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  electron, positron antihydrogen ion  antiproton molecular ions Gabrielse 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 I Am Used to Unusual Attempts to Help ExplainGabrielse Our Experiments

Serious Play: Hapgood Fiction best seller Author: Tom Stoppard

Would you expect unusual publicity for a measurement of the electron’s intrinsic magnetism? Gabrielse Help from Jim Carrey and Conan O’Brien

Jim Conan Carrey O’Brien

Viewed more than 140,000 times on YouTube.com Gabrielse Magnetic Moments, Motivation and Results Gabrielse Orbital Magnetic Moment  magnetic  L angular momentum  g B 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 IAL ()  2      2  2mv 2 m 2 m    v 

 g  1 B Gabrielse Electron Spin Magnetic Moment

 magnetic  g S angular momentum   B moment 2 / 2 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 / 2   1.001159 ... simplest Dirac spin, plus QED

(if electron g/2 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 for new physics needs aand test of QED Gabrielse Three Programs to Measure Electron g

U. Michigan U. Washington Harvard beam of one electron one electron cylindrical Penning trap 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 Historical Progress

2 3 4 g           1 CCC1   2    3   C4   ...  a 2         Most precisely measured property of an elementary particle Gabrielse Electron Magnetic Moment Measured to 3 x 10-13

2.8 1013

(improved measurement is underway) Gabrielse

0 73 (28)

University of Washington Physics Building Gabrielse The Standard Model Predicts the Electron Magnetic Moment

in terms of the 1e2 1 fine structure    4 c 137 constant 0  Gabrielse Standard Model of Particle Physics Prediction

essentially exact Gabrielse Lowest Orders are Calculated Analytically

C2 = 1.2 (exact) Gabrielse Lowest Orders are Calculated Analytically (eg. C4)

7 Feynman diagrams

1 Feynman diagram Gabrielse Lowest Orders are Calculated Analytically (eg. C6)

Too many terms to write down 48 Feynman diagrams

72 Feynman diagrams

Numerical check: Gabrielse C8 and C10 are Calculated Numerically

891 Feynman diagrams

Estimate till last year:

Complete calculation completed only very recently

C10  9.16 (0.57) 12696 Feynman diagrams

Uncertainties come from numerical integration error. Depends upon available comptuter time. Gabrielse Basking in the Reflected Glow of Theorists g   1  C2   2   2    C4     3    C6     4    C8     5    C10      Remiddi Kinoshita G.G ...  a (also Laporta) (also Nio) 2004 Gabrielse Probing 10th Order and Hadronic Terms Gabrielse (Greatest?) Triumph of the Standard Model

Measured: “Calculated”: (Uncertainty from measured fine structure constant) 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 Testing QED

• Test to increasingly high order in a  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) Gabrielse Comparing the Extremely Precise Tests of QED

ppb = 10-9

free electron g tests QED to much higher order in a QED theory Gabrielse 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 Gabrielse Propagation of Errors Gabrielse 1e2 1 Fine Structure Constant    40 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 ~ 2mc 2 Fine structure:  E ~ 4mc 2 Lambs hift:  E ~ 5 mc 2 m Hyperfinestructure:  E ~  4mc 2 M Feynman: every theorist should put 137 on their office wall Gabrielse Assume Standard Model Prediction is Correct, Deduce Alpha from Electron g/2

essentially exact Gabrielse Most Precise Determination of the Fine Structure Constant (g/2 + QED) exp`t theory before 2012

Determinations of the fine structure constant Gabrielse Widely Re-Reported

Science Nature Physics Today New Scientist Cern Courier … Fox News

Moral: what is quoted is not necessarily what was said Earlier Measurements Gabrielse Require Larger Uncertainty Scale

ten times larger scale to see larger uncertainties

many changes in one year Gabrielse Next Most Accurate Way to Determine a use( Cs example) Combination of measured Rydberg, mass ratios, and atom recoil

2 4 1e 1 e me c   R  2 3 2 Haensch, … 40hc (4  0 ) 2 h c 2R h  2   c m Pritchard, … e Chu, … 2R hMM h f  Csp   2c2 recoil c M M m M() f 2 Cs p e Cs D1 Haensch, … 2 frecoil M Cs M12 C Tanner, …   4R c 2 ()fD1 M 12 C m e Werthe, Quint, Blaum, … • Now this method is 3 times less precise • We hope that it will also improve in the future  test QED

Biraben, … Biraben, (Rb measurement is similar except get h/M[Rb] a bit differently) Gabrielse Test for Physics Beyond the Standard Model  g   1 aQED ()  aSM: Hadronic Weak  aNewPhysi c s B 2

measure calculate these look for a to a very high to a very high disagreement precision precision

expected to be 40000 times 2 m  larger for a muon    compared to an electron me 

Measure electron moment  test predictions of the standard model Measure muon moment  look for physics beyond the Standard Model Gabrielse Test for Physics Beyond the Standard Model  g   1 aQED ()  aSM: Hadronic Weak  aNewPhysi c s B 2 Does the electron have internal structure?

m*  total mass of particles bound together to form electron

m 2 limited by the uncertainty in R5  1019 m m*  360 GeV / c  a independent a value m R2  1019 m m*  1 TeV / c2 if our uncertainty  a was the only limit

Not bad for an experiment done at 100 mK, but LEP does better R2  1020 m m* 10.3 TeV / c2 LEP contact interaction limit > 20000 electron masses of binding energy Gabrielse Compare to Muon

more massive version of the electron Gabrielse Muon Magnetic Moment Measured In Storage Ring Gabrielse 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??????? Gabrielse Could We Check the 2.5 sDisagreement between Muon g Measurement and “Calculation”?  g   1 aQED ()  aSM: Hadronic Weak  aNewPhysi c s B 2 2 (mm /me) ~ 40,000  muon more sensitive to “new physics” ÷2,500  how much more accurately we measure ÷ 2  2s 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 2s effect (or not)

Also need: • QED and SM calculations slightly improved • Independent measurement of a improved by factor of 20

These are large numbers  hard to imagine that this will happen quickly Gabrielse Gabrielse Gabrielse Now in Illinois, Close to Journey’s End Gabrielse Bound on Contributions of Small Particles to Dark Matter Gabrielse Measuring the Electron Magnetic Moment to 3 Parts in 1013 Gabrielse Need Good Students and Stable Funding

Elise Novitski Joshua Dorr Shannon Fogwell Hogerheide David Hanneke Brian Odom, Brian D’Urso, 20 years Steve Peil, 8 theses Dafna Enzer, Kamal Abdullah Ching-hua Tseng Joseph Tan

N$F Gabrielse 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 …) 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

methods • • Cooling away of blackbody photons

these • Synchronized electrons identify cavity radiation modes • Trap without nuclear paramagnetism first measurement with measurement first • One-particle self-excited oscillator Gabrielse One Particle in a Penning Trap no internal degrees of freedom available for detection

Trap as container Trap as a homemade atom Gabrielse Trap with One Electron Quantum Cyclotron -charges------fc  150 GHz  2

n = 4 n = 3 n = 2 0.1 n = 1 m m hc  7.2 kelvin n = 0 y2

------Need low temperature B  6Tesla cyclotron motion T << 7.2 K 0.1 m m Gabrielse First Penning Trap Below 4 K  70 mK

Need low temperature cyclotron motion T << 7.2 K Gabrielse

David Hanneke G.G. Gabrielse Low Temperature

Gives great vacuum: Pressure <<< 5 x 10-17 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 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 Observe Quantum Jumps

QND measure cf cyclotron energy

Stimulated absorptions – stimulated by black body photons Gabrielse Lowest Energy Cyclotron Eigenstates States (no magnetron motion) there is some magnetron motion  2 n=0 n=1 n=2

0.1 m m n=3 n=4 n=5 Gabrielse For Fun: Coherent State Eigenfunction of the lowering operator: a   

  0   1 Fock states do not oscillate

0.1 m m

Coherent state with n 1

i n ne '   en / 2 einc t n ,  n0 n! with   0 0.1 m m Gabrielse 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

(n 1/ 2)    c kT Pn  e

For low enough temperature, temperature no longer matters  electron stays in its ground state  no fluctuations Gabrielse Measure Electron’s Cyclotron Temperature Temperature relates to time average of electron cyclotron energy  measure the probability to find electron in each fock state

0.23

0.11

0.03

9 x 10-39

(n 1/ 2)    c Fit to Boltzmann distribution: kT  extract cyclotron temperature Pn  e Gabrielse Electron Cyclotron Temp = Trap Temp

Two methods used to measure electron cyclotron’s temperature • from • from measured rates

Measured with temperature sensor Gabrielse Average Values of n Gabrielse Spin  Two Cyclotron Ladders of Energy Levels

n = 4  c n = 3 n = 4   c Cyclotron c n = 2 Spin n = 3  c frequency:  c n = 1 frequency: n = 2  c 1 eB  c n = 0 g   c n = 1   s   c 2 m c 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 Cyclotron c n = 2 Spin n = 3  c frequency:  c n = 1 frequency: n = 2  c  c n = 0 g 1 eB n = 1     c   s c 2 m c 2 n = 0

ms = -1/2 ms = 1/2

g    Measure a ratio of frequencies: s 1  s c B in free 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 d

n = 4  9  / 2 c n = 3 n = 4 c  7  / 2 Cyclotron c  7  / 2 n = 2 Spin n = 3 c  5  / 2 frequency: c  5  / 2 n = 1 frequency: n = 2 c  3  / 2 eB c  3  / 2 n = 0 g 2  c n = 1   / 2  s   c m c 2 n = 0

ms = -1/2 ms = 1/2

Not a huge relativistic shift,  h c 9 2 10 but important at our accuracy  c mc

Solution: Simply correct for d if we fully resolve the levels (superposition of cyclotron levels would be a big problem) Gabrielse Compare Relativistic Shift of Cyclotron Frequency for Free and Bound Electron Measurements fractional shift  h 9 For free electron: c 10 per quantum of  mc2 c excitation

For electron bound to an ion: > 400000000 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) 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 All Motions in a Penning Trap are Really Quantum Mechanical (also true for a large accelerator)

z magnetron

+ axial spin cyclotron

When is QM needed? Gabrielse Magnetron Motion Velocity filter: crossed E and B fields to make Lorentz force vanish at one perpendicular velocity    B 0 F qE  v  B v E Independent of q and m of the particlez

In a trap:

z

+ Gabrielse Cooling the Magnetron Motion

To make it irrelevant Completely decoupled from its environment  couple to one of the other motions to cool it

z

+ Gabrielse Cooling Magnetron Motion

Couple to a cooled axial motion

magnetron axial

Sideband cooling axial motion (important technique) cooled by another magnetron axial mechanism motion is motion is “cooled” heated

• Quantum number reduces • Quantum number increases • Kinetic energy reduces • Kinetic energy increases • Total energy increases • Total energy increases Gabrielse Sideband Cooling

2 † PCooling k1, l  1| a k a l | k , l (k 1)( l )  kl  l

2 † PHeating k1, l  1| a k a l | k , l (k )( l 1)  kl  k Cooling for l k PCooling  PHeating  [ kl l] [] kl k (tolimitl k )  l  k Heating f o r l k Gabrielse Sideband Cooling Lineshapes

Sideband Cooling Rate Sideband Heating Rate

drive frequency drive frequency

Saturates with increasing No saturation with drive strength increasing drive strength 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 Frequencies Shift Imperfect Trap • tilted B Perfect Electrostatic • harmonic B in Free Space Quadrupole Trap distortions to V eB   '    c m c c c  z  c ' z

m  z  m g g g   s  c   s2 c 2 s2 c g  Problem:  s not a measurable eigenfrequency in an 2  c imperfect Penning trap Solution: Brown-Gabrielse invariance theorem 2 2 2 c()()()  c   z   m Gabrielse Brown-Gabrielse Invariance Theorem

2 2 2 c()()()  c   z   m

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, …) Gabrielse Brown-Gabrielse Invariance Theorem

2 2 2 c()()()  c   z   m

c   m  ()Corrections

Approximation Gabrielse Basic Idea of the Fully-Quantum Measurement

n = 4  c n = 3 n = 4   c Cyclotron c n = 2 Spin n = 3  c frequency:  c n = 1 frequency: n = 2  c  c n = 0 g 1 eB n = 1     c   s c 2 m c 2 n = 0

ms = -1/2 ms = 1/2

g    Measure a ratio of frequencies: s 1  s c B in free 2  c  c space 103 • almost nothing can be measured better than a frequency • the magnetic field cancels out (self-magnetometer) Gabrielse Spectroscopy in an Imperfect Trap

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

g v()    v   s  c s c  c a 2 c  c  c 2 () z  a  g 2 c 1  2 2 3 () z 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)

I2R damping Axial motion 200 MHz of trapped electron self-excited oscillator feedback

amplitude, f Gabrielse Detection of single electron axial motion •The axial oscillator is coupled to a tuned-circuit amplifier

•Axial motion is driven to increase signal Gabrielse 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. Gabrielse

Now back to commercial devices Gabrielse Better Detection Amplifier Gabrielse Much Higher Axial Frequency

60 MHz  200 MHz Gabrielse 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 Feedback Cooling of an Oscillator Gabrielse Electronic Amplifier Feedback: Strutt and Van der Ziel (1942)

Basic Ideas of Noiseless Feedback and Limitations: Kittel (1958)

Dissipation :e   (1 GTTG ) Fluctuations: e  (1  ) faster damping rate  higher temperature Fluctuation-Dissipation Invariant: e /Te  const 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, Gabrielse, PRL (2003) Gabrielse Experimental Setup Gabrielse

feedback gain

Measure oscillator temperature  fluctuations TTGe (1  )

Measure oscillator damping rate  dissipation e  (1  G )

Observer the fluctuation-dissipation invariant e /Te  const Gabrielse Measure Temperature and Damping Rate higher temp and damping lower temp and damping

TTG(1  ) temperature e

Te damping rate e  (1  G ) e temperature T e  const damping rate e

G undamped Add Feedback Noise to the Analysis Gabrielse Need a Low Noise Amplifier

g 2 T  T T1  g  g T e   e 1 g T  T[1  g ] noiseless 0 feedback gain (g) 1 amplifier

Amplifier is single-gate, mistuned, current-starved HEMT Tg  40 mK

2 Vg  Tg  2 T Vn  Gabrielse 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. Gabrielse Phys. Rev. Lett. 94, 113002 (2005). Gabrielse Self-excited Oscillator Setup Gabrielse Use Digital Signal Processor  DSP

• Real time fourier transforms • Use to adjust gain so oscillation stays the same Cyclotron Quantum Jumps Gabrielse 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) Observe Tiny Shifts of the Frequency Gabrielse 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? Gabrielse Detecting the Cyclotron Motion

cyclotron too high to nC = 150 GHz frequency detect directly

axial relatively nZ = 200 MHz frequency easy to detect

Couple the axial frequency nZ to the cyclotron energy.

Small measurable shift in nZ indicates a change in cyclotron B energy. 2 Bz B 0  B 2 z Gabrielse Couple Axial Motion and Cyclotron Motion

Add a “magnetic bottle” to uniform B  2 2  B  B[( z  / 2) zˆ  z  ] 2 B 1 H  m 2 z2  B z2 2 z 2 change in m n=3 changes effective wz n=2 n=1 n=0

spin flip is also a change in m Gabrielse QND Detection of One-Quantum Transitions  1 B  B z2H  m 2 z 2   B z 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 electron -

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 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

"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 t= 16 s 15 12 20 9 6

10 Y Axis 2 3 0 0 number of n=1 to n=0 decays -3 axial frequency shift (Hz) 0 10 20 30 40 50 60 0 100 200 300 decay time (s) time (s) Gabrielse Cavity-Inhibited Spontaneous Emission Purcell Kleppner 1   Gabrielse and Dehmelt Free Space 75 ms B = 5.3 T

1 Within   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  c Gabrielse Big Challenge: Magnetic Field Stability

Magnetic field cancels out n = 2 n = 3 g   n = 2 n = 1 s 1  a n = 0 n = 1 2 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 Magnet Field from Dumpsters and Trucks Gabrielse Good Magnetic Field Stability construction ~ 10-9 / (10 hours) noise • regulate He pressure (solenoid) • regulate N presssure (solenoid) • regulate He pressure (fridge) • regulate “room temperature” Gabrielse B-field Stability – Depends on Room Temperature

•Magnet with two broken shims •Magnet with working shims •No temperature regulation •Shed temperature regulated 20 20 < 1 ppb noise and drift at night 10 10

0 0

-10 -10

B-field shift (ppb) Friday, Saturday construction B-field shift (ppb)

-20 -20

21.5 21.5

21.0 21.0 ~ 0.1 K temperature regulation of dewar

20.5 20.5

20.0 20.0

19.5 19.5 dewar temperature (C) dewar temperature (C) 19.0 19.0 0 20 40 60 0 10 20 30 40 50 60 time (hours) time (hours) Gabrielse A tabletop experiment … if you have a high ceiling Gabrielse Magnetic Field is More Stable at Night

Experiment is automated. Takes data while we sleep. Gabrielse

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  … 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 Lower Detector Temperature  Narrower Lines

15 12 1. Turn FET amplifier off 9 6 Y Axis 2 2. Apply a microwave drive pulse of ~150 GH 3 0 -3 axial frequency shift (Hz) (i.e. measure “in the dark”) 0 100 200 300 3. Turn FET amplifier on and check for axial frequency shift time (s) 4. Plot a histograms of excitations vs. frequency

Good amp heat sinking, amp off during excitation # of cyclotron excitations Tz = 0.32 K 0 100 200 300  frequency - c (ppb) Gabrielse Gabrielse Measurement Cycle

n = 3 n = 2 g   n = 1 s 1  a n = 2 n = 1 n = 0 2 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   n = 3 s 1  a n = 2 n = 1 n = 0 2 c  c n = 1 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 modes is shifted by interaction 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 Use the Electron to do Spectroscopy of the Cavity

• Measuring lifetime and g as a function of B

• Attempting cavity sideband cooling Gabrielse Cavity Shifts

 Related: Does the cavity affect the spin frequency? Gabrielse Careful Studies of the Lineshapes Gabrielse Shifts and Uncertainties g (in ppt = 10-12 )

cavity shifts not a problem lineshape broadening Gabrielse Gabrielse

Emboldened by the Great Signal-to-Noise

Make a one (antiproton) self-excited oscillator  try to detect a proton (and antiproton) spin flips Gabrielse Towards a One-Electron Qubit in a Scalable Geometry Gabrielse Many Theory Papers on One-Electron Qubits

Follow the Clean Observations of One-Electron Transitions Gabrielse 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. Gabrielse 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)

Gabrielse, PRA 27, 2227 (1983), PRA 29, 462 (1984)

Orthogonalized design used for the most precise mass spectroscopy Gabrielse Cylindrical Penning Trap Open Access Trap

Gabrielse, Haarsma, and Rolston Gabrielse, Haarsma, and Rolston Intl. J. of Mass Spec. and Ion Proc. 88, 319 (1989) Intl. J. of Mass Spec. and Ion Proc. 88, 319 (1989) Gabrielse

Planar Penning Trap Covered Planar Trap

30 page theory paper. Key idea: treat distance to electron as a parameter Identified Workable Trap Designs Gabrielse and Showed Why Previous Designs Should Not Work Gabrielse Made a Large Trap to Test Center pad is 1 mm radius. Copper (0.2 mm) on alumina.

front back Best possible symmetry

Large aspect ratio on cuts

top of profile of laser laser cuts cuts Gabrielse

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 Stowed away below the Gabrielse electron magnetic moment trap electron magnetic moment trap

planar trap Gabrielse

Promising

Hopefully we will have time to pursue soon Gabrielse Summary How Does One Measure g to 7.6 Parts in 1013?

 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

these new new methods these • Trap without nuclear paramagnetism first measurement with measurement first • One-particle self-excited oscillator Gabrielse New Measurement of Electron Magnetic Moment  magnetic  S spin  g  B moment  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 since 1987 • 15 times smaller uncertainty • 1.7 standard deviation shift • 2500 times smaller uncertainty than muon g 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 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