One-Electron Quantum Cyclotron: A New Measurement of the Electron Magnetic Moment and the Fine Structure Constant

Transcription

1 One-Eletron Quantum Cylotron: A New Measurement of the Eletron Magneti Moment and the Fine Struture Constant Gerald Leverett Professor of Physis, Harvard University with Shannon Fogwell and Josh Dorr Earlier ontributions: David Hanneke Brian Odom, Brian D Urso, 0 years 7 theses Steve Peil, Dafna Enzer, Kamal Abdullah Ching-hua Tseng Joseph Tan N$F 006 DAMOP Thesis Prize Winner ψ 0.1 µm

2 Three Programs to Measure Eletron g U. Mihigan U. Washington Harvard beam of eletrons spins preess with respet to ylotron motion kev one eletron 4. K one eletron quantum jump spetrosopy of quantum levels 100 mk ylindrial Penning trap inhibit spontaneous emission measure avity shifts Crane, Rih, Dehmelt, Van Dyk self-exited osillator

3 Referenes 006: B. Odom, D. Hanneke, B. D Urso, G. PRL 97, (006). 008: D. Hanneke, S. Fogwell and G. PRL 100, (008). Two reent review hapters in book Lepton Moments, edited by Two reent review hapters in book Lepton Moments, edited by Roberts and Mariano, (World Sientifi, Singapore, 009) G., Measuring the Eletron Magneti Moment G., Determining the Fine Struture Constant

4 New Measurement of Eletron Magneti Moment magneti moment µ = g µ B S ħ g / = spin eħ Bohr magneton m ± D. Hanneke, S. Fogwell and G. First improved measurements (006, 008) sine times smaller unertainty 1.7 standard deviation shift 500 times smaller unertainty than muon g

5 New Determination of the Fine Struture Constant α = 1 4πε 0 e ħ 1 α Strength of the eletromagneti interation Important omponent of our system of fundamental onstants Inreased importane for new mass standard = (1) (37) (33) ± First lower unertainty sine 1987 (006, 008) 0 times more aurate than atom-reoil methods D. Hanneke, S. Fogwell and G.

6 Key: Resolving One-Quantum Transitions for One Trapped Eletron one-quantum ylotron transition spin flip eletron magneti moment in Bohr magnetons

7 Twenty Years and 7 PhD Theses? Takes time to develop new ideas and methods needed to determine g/ to.8 parts in unertainty one PhD at a time first measurement with these new metho ods One-eletron quantum ylotron Resolve lowest ylotron states as well as spin Quantum jump spetrosopy of spin and ylotron motions Cavity-ontrolled spontaneous emission Radiation field ontrolled by ylindrial trap avity Cooling away of blakbody photons Synhronized eletrons identify avity radiation modes Trap without nulear paramagnetism One-partile self-exited osillator

8 magneti moment Orbital Magneti Moment µ = gµ B L ħ eħ Bohr magneton m angular momentum e.g. What is g for idential harge and mass distributions? e ( ) ev ρ µ = IA = πρ L e L e L πρ = mvρ = m = ħ mħ v g = 1 µ B ρ v e, m

9 magneti moment Spin Magneti Moment µ = gµ B S ħ eħ Bohr magneton m angular momentum g = 1 idential harge and mass distribution g = spin for simplest Dira point partile g = simplest Dira spin, plus QED (if eletron g is different eletron has substruture)

10 Why Measure the Eletron Magneti Moment? 1. Eletron g - basi property of simplest of elementary partiles. Determine fine struture onstant from measured g and QED (May be even more important when we hange mass standards) 3. Test QED requires independent α 4. Test CPT ompare g for eletron and positron best lepton test 5. Look for new physis beyond the standard model Is g given by Dira + QED? If not eletron substruture (new physis) Muon g searh for new physis needs α and test of QED

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12 Trap with harges One Eletron in a Magneti Field f 150 GHz ψ n = 4 n = 3 n = n = 1 n = 0 hυ = 7. kelvin ψ 0.1 µm B 6 Tesla Need low temperature ylotron motion T << 7. K 0.1 µm

13 Eletron Cylotron Motion Comes Into Thermal Equilibrium T = 100 mk << 7. K ground state always Prob = old hot avity spontaneous emission n = 4 n = 3 n = n = 1 n = 0 absorb blakbody photons eletron temperature desribes its energy distribution on average

14 Eletron in Cylotron Ground State QND Measurement of Cylotron Energy vs. Time x average number of blakbody photons in the avity On a short time sale in one Fok state or another Averaged over hours in a thermal state S. Peil and G., Phys. Rev. Lett. 83, 187 (1999).

15 David Hanneke G.G.

16 First Penning Trap Below 4 K 70 mk Need low temperature ylotron motion T << 7. K

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18 Spin Two Cylotron Ladders of Energy Levels n = 4 Cylotron frequeny: ν = 1 eb π m n = 4 n = 3 n = n = 1 n = 0 ν ν ν ν ν ν ν ν n = 3 n = n = 1 n = 0 Spin frequeny: g ν s = ν m s = -1/ m s = 1/

19 Basi Idea of the Fully-Quantum Measurement n = 4 Cylotron frequeny: ν = 1 eb π m n = 4 n = 3 n = n = 1 n = 0 ν ν ν ν ν ν ν ν n = 3 n = n = 1 n = 0 Spin frequeny: g ν s = ν m s = -1/ m s = 1/ Measure a ratio of frequenies: g ν s ν s ν = = 1+ ν ν 10 3 almost nothing an be measured better than a frequeny the magneti field anels out (self-magnetometer) B in free spae

20 Speial Relativity Shift the Energy Levels δ Cylotron frequeny: πν = eb m n = 4 n = 3 n = n = 1 n = 0 ν ν ν ν 7 δ / 5 δ / 3 δ / δ / ν 9 / 7 δ / ν 5 δ / 3 / ν ν δ δ n = 4 n = 3 n = n = 1 n = 0 Spin frequeny: g ν s = ν m s = -1/ m s = 1/ Not a huge relativisti shift, but important at our auray δ ν hν = 10 m 9 Solution: Simply orret for δ if we fully resolve the levels (superposition of ylotron levels would be a big problem)

21 Cylindrial Penning Trap V ~ z x y Eletrostati quadrupole potential good near trap enter Control the radiation field inhibit spontaneous emission by 00x (Invented for this purpose: G.G. and F. C. MaKintosh; Int. J. Mass Spe. Ion Pro. 57, 1 (1984)

22 One Eletron in a Penning Trap very small aelerator designer atom ool 1 khz 00 MHz detet Eletrostati quadrupole potential 153 GHz Magneti field need to measure for g/

23 B in Free Spae ν = ν s = eb m g ν Problem: g ν s = ν Frequenies Shift Perfet Eletrostati Quadrupole Trap ν ' ν ν ν z m s < ν ν = ν ' ν z = ν z g = ν Imperfet Trap tilted B harmoni distortions to V ν m ν s = g ν not a measurable eigenfrequeny in an imperfet Penning trap Solution: Brown- invariane theorem ν = ( ν ) + ( ν ) + ( ν ) z m

24 An Aside Arising from the Last of These Conferenes M More detail: G., Int. J. of Mass Spe. 79, 107 (009) Measured sideband frequeny funtion of B tilt and harmoni distortion ω ( θ, φ, ε ) +ω ( θ, φ, ε ) ω + + only an approx. How bad is this ommon approximation? dimensional analysis : using invariane theorem: (and a bit of symmetry) ω ω θ + ω ε ~1% ω θ ε ω muh, muh smaller

25 Spetrosopy in an Imperfet Trap one eletron in a Penning trap lowest ylotron and spin states g ν s v + ( ν s ν ) v + ν a = = = ν ν ν g 1+ f ( ν z ) ν a ν 3δ ( ν z ) + + ν expansion for v ν z ν m δ To dedue g measure only three eigenfrequenies of the imperfet trap

26 Feedbak Cooling of an Osillator Eletroni Amplifier Feedbak: Strutt and Van der Ziel (194) Basi Ideas of Noiseless Feedbak and Its Limitations: Kittel (1958) Dissipation : Γ = Γ(1 g) Flutuations: T = T (1 g) e Flutuation-Dissipation Invariant: Γ / T = onst Appliations: Milatz, (1953) -- eletrometer Dike, (1964) -- torsion balane Forward, (1979) -- gravity gradiometer Ritter, (1988) -- laboratory rotor Cohadon, (1999) -- vibration mode of a mirror e e e faster damping rate higher temperature Proposal to apply Kittel ideas to ion in an rf trap Dehmelt, Nagourney, (1986) never realized Proposal to stohastially ool antiprotons in trap Beverini, (1988) stohasti ooling never realized Rolston, (1988) same as feedbak ooling (same limitations) Realization of feedbak ooling with a trapped eletron (also inlude noise) D Urso, Odom,, PRL (003) D Urso, Van Handel, Odom, Hanneke,, PRL 94, 1130 (005)

27 one-eletron n self-exited osillator n=1 freq = E ( ) ylotron = hf n + 1 n=0 QND Detetion of One-Quantum Transitions 1 B = B z H = mω z µ B z n=0 ylotron ground state z n=1 ylotron exited state time n=0 ylotron ground state

28 QND Quantum Non-demolition Measurement B H = H ylotron + H axial + H oupling [ H ylotron, H oupling ] = 0 QND ondition QND: Subsequent time evolution of ylotron motion is not altered by additional QND measurements

29 One-Eletron Self-Exited Osillator measure voltage V(t) axial motion 00 MHz of trapped eletron I R damping ruial to limit the os. amplitude feedbak amplitude, φ

30 Observe Tiny Shifts of the Frequeny of a One-Eletron Self-Exited Osillator one quantum ylotron exitation spin flip Unmistakable hanges in the axial frequeny signal one quantum hanges in ylotron exitation and spin B "Single-Partile Self-exited Osillator" B. D'Urso, R. Van Handel, B. Odom and G. Phys. Rev. Lett. 94, (005).

31 Quantum Jump Spetrosopy one eletron in a Penning trap lowest ylotron and spin states In the dark exitation turn off all detetion and ooling drives during exitation

32 Inhibited Spontaneous Emission Appliation of Cavity QED number of n= =1 to n=0 deays τ = 16 s axial frequeny shift (Hz) 15 1 exite, measure time in exited state deay time (s) time (s)

33 Free Spae Cavity-Inhibited Spontaneous Emission B = 5.3 T γ = 1 75 ms Purell Kleppner and Dehmelt Within Trap Cavity B = 5.3 T γ = 1 16 se Inhibited By 10! avity modes ν frequeny Inhibition gives the averaging time needed to resolve a one-quantum transition

34 Big Challenge: Magneti Field Stability n = 3 n = n = 1 n = 0 m s = -1/ m s = 1/ n = n = 1 n = 0 Magneti field anels out g ω ω = s = 1+ a ω ω But: problem when B drifts during the measurement Magneti field take ~ month to stabilize

35 Self-Shielding Solenoid Helps a Lot Flux onservation Field onservation Redues field flutuations by about a fator > 150 Self-shielding Superonduting Solenoid Systems, G. and J. Tan, J. Appl. Phys. 63, 5143 (1988)

36 Eliminate Nulear Paramagnetism Deadly nulear magnetism of opper and other friendly materials Had to build new trap out of silver New vauum enlosure out of titanium ~ 1 year setbak

37 Measurement Cyle g ω ω = s = 1+ a ω ω simplified n = 3 n = n = 1 n = 0 m s = -1/ m s = 1/ n = n = 1 n = 0 3 hours 0.75 hour 1. Prepare n=0, m=1/ measure anomaly transition. Prepare n=0, m=1/ measure ylotron transition 3. Measure relative magneti field Repeat during magnetially quiet times

38 It all omes together: Low temperature, and high frequeny make narrow line shapes A highly stable field allows us to map these lines Measured Line Shapes for g-value Measurement ylotron anomaly n = 3 n = n = 1 n = 0 m s = -1/ n = n = 1 n = 0 m s = 1/ line s: L. Brown Preision: Sub-ppb line splitting (i.e. sub-ppb preision of a g- measurement) is now easy after years of work

39 Cavity Shifts of the Cylotron Frequeny g ω ω = s = 1 a ω ω n = 3 n = n = 1 n = 0 m s = -1/ m s = 1/ n = n = 1 n = 0 B = 5.3 T γ = 1 16 se Within a Trap Cavity spontaneous emission inhibited by 10 avity modes ν frequeny ylotron frequeny is shifted by interation with avity modes

40 Cavity modes and Magneti Moment Error use synhronization of eletrons to get avity modes Operating between modes of ylindrial trap where shift from two avity modes anels approximately first measured avity shift of g

41 008 Measurement redued avity shift orretion unertainty Measuring lifetime and g as a funtion of B Attempting avity sideband ooling

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43 New: Careful Study of the Cavity Shifts

44 Eletron as Magnetometer Lineshapes

45 Shifts and Unertainties g (in ppt = 10-1 ) avity shifts not a problem lineshape broadening

46 New Measurement of Eletron Magneti Moment magneti moment µ = g µ B S ħ g / = spin eħ Bohr magneton m ± D. Hanneke, S. Fogwell and G. First improved measurements (006, 008) sine times smaller unertainty 1.7 standard deviation shift 500 times smaller unertainty than muon g

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48 Dira + QED Relates Measured g and Measured α magneti moment µ = gµ B S ħ fine struture onstant α = 1 4πε 0 e ħ g 3 4 α α α α = 1 + C C C C π + π + π + π +.. δ a Measure Dira point partile QED Calulation Kinoshita, Nio, Remiddi, Laporta, et. hadroni, weak standard model tiny 1. Use measured g and QED to extrat fine struture onstant. Wait for another aurate measurement of α Test QED

49 g Basking in the Refleted Glow of Theorists = C 1 C C C 3 α π 4 α π α π α π α + C5 π +... δ a Remiddi Kinoshita G.G 004

50 Simple Analyti Expressions from QED (where alulations are ompleted) 7 Feynman diagrams 7 Feynman diagrams 871 Feynman diagrams 167 Feynman diagrams polylog:

51 g 3 4 α α α α = 1 + C C C C π + π + π + π +.. δ a experimental unertainty

52 New Determination of the Fine Struture Constant α = 1 4πε 0 e ħ 1 α Strength of the eletromagneti interation Important omponent of our system of fundamental onstants Inreased importane for new mass standard = (1) (37) (33) ± First lower unertainty sine 1987 (006, 008) 0 times more aurate than atom-reoil methods D. Hanneke, S. Fogwell and G.

53 Fine Struture Constant Unertainties

54 Next Most Aurate Way to Determine α (use Cs example) Combination of measured Rydberg, mass ratios, and atom reoil 1 e 1 R 0 h πε 0 Prithard, 4 e me 3 α 4 πε (4 ) h α = Biraben, R h m e R M h M Cs p h f = = M M m M ( f ) reoil Cs p e Cs D1 f M M α = 4R f M m reoil Cs 1C ( D1) 1C e Haensh, Chu, Now this method is >10 times less aurate We hope that will improve in the future test QED Haensh, Tanner, Werthe, Quint, (also Van Dyk) (Rb measurement is similar exept get h/m[rb] a bit differently)

55 Several Measurements Needed for the Atom-Reoil Determinations of the Fine Struture Constant

56 Earlier Measurements (On Muh Larger Unertainty Sale)

57 Test of QED Most stringent test of QED: Comparing the measured eletron g to the g alulated from QED using an independent α δ g = g g ( α) < experiment theory 1 The unertainty does not omes from g and QED, + SM All unertainty omes from α[rb] and α[cs] With a better independent α ould do a ten times better test

58 Dear Jerry, From Freeman Dyson One Inventor of QED... I love your way of doing experiments, and I am happy to ongratulate you for this latest triumph. Thank you for sending the two papers. Your statement, that QED is tested far more stringently than its inventors ould ever have envisioned, is orret. As one of the inventors, I remember that we thought of QED in 1949 as a temporary and jerry-built struture, with mathematial inonsistenies and renormalized infinities swept under the rug. We did not expet it to last more than ten years before some more solidly built theory would replae it. We expeted and hoped that some new experiments would reveal disrepanies that would point the way to a better theory. And now, 57 years have gone by and that ramshakle struture still stands. The theorists have kept pae with your experiments, pushing their alulations to higher auray than we ever imagined. And you still did not find the disrepany that we hoped for. To me it remains perpetually amazing that Nature danes to the tune that we sribbled so arelessly 57 years ago. And it is amazing that you an measure her dane to one part per trillion and find her still following our beat. With ongratulations and good wishes for more suh beautiful experiments, yours ever, Freeman.

59 In Progress Better measurement of the eletron magneti moment and the fine struture onstant Better omparison of the positron and eletron magneti moments Spinoffs Observe a proton spin flip with one-proton self-exited osillator (lose, see new PRL) Attempt to make a one-eletron qubit (see new PRA) Goldman talk this afternoon

60 Close to observing a proton spin flip (we hope). (Mainz talk by Ulmer is oming.)

61 New Dilution Refrigerator and Suspension support plates dilution refrigerator 4. K superonduting solenoid old 100 mk trap new 100 mk trap and suspended eletron moves with the 4. K superonduting solenoid

62 New Superonduting Solenoid

63 Solenoid in Plae Larger to allow positron aess to let eletron move with the solenoid One superonduting lead was broken inside. We had to repair

64 New Silver Trap old new Room for positron entry path Improved avity mode spetrum (to allow avity sideband ooling)

65 Conlusion Took many years to develop the quantum methods to measure the eletron magneti moment Most preise measurement of the eletron magneti moment Most preise determination of the fine struture onstant Most stringent test of QED (higher order and preision) Soon: Most preise test of CPT invariane with leptons More preise eletron magneti moment More preise determination of the fine struture onstant Spinoffs: proton magneti moment one-eletron qubit