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One-Electron Quantum Cyclotron

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One-Electron Quantum Cyclotron One-Electron Quantum Cyclotron: Gabrielse A New Measurement of the Electron Magnetic Moment and the Fine Structure Constant Gerald Gabrielse Leverett Professor of Physics, Harvard University with Shannon Fogwell and Josh Dorr 2006 DAMOP Thesis Earlier contributions: David Hanneke Prize Winner Brian Odom, 2 Brian D’Urso, ψ Steve Peil, 20 years Dafna Enzer, 7 theses Kamal Abdullah Ching-hua Tseng Joseph Tan N$F 0.1 µm Gabrielse Three Programs to Measure Electron g U. Michigan U. Washington Harvard beam of electrons 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 References 2006: B. Odom, D. Hanneke, B. D’Urso, G. Gabrielse PRL 97 , 030801 (2006). 2008: D. Hanneke, S. Fogwell and G. Gabrielse PRL 100, 120801 (2008). Two recent review chapters in book Lepton Moments , edited by Roberts and Marciano, (World Scientific, Singapore, 2009) G. Gabrielse, “Measuring the Electron Magnetic Moment” G. Gabrielse, “Determining the Fine Structure Constant” Gabrielse New Measurement of Electron Magnetic Moment magnetic S spin µ= g µ B moment ℏ ℏ Bohr magneton e 2m g / 2= 1.001159 652 180 73 ±0.000 000 000 000 28 2.8 × 10 −13 D. Hanneke, S. Fogwell and G. Gabrielse • First improved measurements (2006, 2008) since 1987 • 15 times smaller uncertainty • 1.7 standard deviation shift • 2500 times smaller uncertainty than muon g Gabrielse New Determination of the Fine Structure Constant 1 e2 • Strength of the electromagnetic interaction α = • Important component of our system of ℏ fundamental constants 4πε 0 c • Increased importance for new mass standard α −1 =137.035 999 084 (12) (37) (33) ±0.000000051 3.7 × 10 −10 • First lower uncertainty since 1987 (2006, 2008) • 20 times more accurate than atom-recoil methods D. Hanneke, S. Fogwell and G. Gabrielse Gabrielse Key: Resolving One-Quantum Transitions for One Trapped Electron one-quantum spin flip cyclotron transition electron magnetic moment in Bohr magnetons Gabrielse Twenty Years and 7 PhD Theses? Takes time to develop new ideas and methods needed to determine g/2 to 2.8 parts in 10 13 uncertainty – one PhD at a time • One-electron quantum cyclotron • Resolve lowest cyclotron states as well as spin • Quantum jump spectroscopy of spin and cyclotron motions • Cavity-controlled spontaneous emission • Radiation field controlled by cylindrical trap cavity • Cooling away of blackbody photons • Synchronized electrons identify cavity radiation modes these new new new methods methods thesethese • Trap without nuclear paramagnetism first measurement withwith measurement measurement firstfirst • One-particle self-excited oscillator Gabrielse Orbital Magnetic Moment magnetic L angular momentum µ= g µ moment B ℏ ℏ Bohr magneton e 2m e.g. What is g for identical charge and mass distributions? v e, m e evLρ e eLℏ µ==IA( πρ 2 ) = == L ρ 2πρ 2mvρ 2 m 2 m ℏ v g = 1 µB Gabrielse Spin Magnetic Moment magnetic S angular momentum µ= g µ moment B ℏ ℏ Bohr magneton e 2m g = 1 identical charge and mass distribution g = 2 spin for simplest Dirac point particle g = 2.002 319 304 ... simplest Dirac spin, plus QED (if electron g is different electron has substructure) Gabrielse Why Measure the Electron Magnetic Moment? 1. Electron g - basic property of simplest of elementary particles 2. Determine fine structure constant – from measured g and QED (May be even more important when we change mass standards) 3. Test QED – requires independent ααα 4. Test CPT – compare g for electron and positron best lepton test 5. Look for new physics beyond the standard model • Is g given by Dirac + QED? If not electron substructure (new physics) • Muon g search for new physics needs α and test of QED Gabrielse Gabrielse Trap with One Electron in a Magnetic Field -------charges fc ≈ 150 GHz ψ 2 n = 4 n = 3 n = 2 0.1 n = 1 µm hυc = 7.2 kelvin n = 0 ψ 2 ------- Need low temperature B ≈ 6 Tesla cyclotron motion T << 7.2 K 0.1 µm Gabrielse Electron Cyclotron Motion Comes Into Thermal Equilibrium T = 100 mK << 7.2 K ground state always Prob = 0.99999… n = 4 n = 3 n = 2 spontaneous n = 1 absorb blackbody emission n = 0 photons cold hot electron “temperature” – describes its energy distribution cavity on average Gabrielse Electron in Cyclotron Ground State QND Measurement of Cyclotron Energy vs. Time 0.23 0.11 0.03 9 x 10 -39 average number On a short time scale of blackbody in one Fock state or another photons in the Averaged over hours cavity in a thermal state S. Peil and G. Gabrielse, Phys. Rev. Lett. 83 , 1287 (1999). Gabrielse David Hanneke G.G. Gabrielse First Penning Trap Below 4 K 70 mK Need low temperature cyclotron motion T << 7.2 K Gabrielse Gabrielse Spin Two Cyclotron Ladders of Energy Levels n = 4 ν c n = 3 n = 4 ν ν c Cyclotron c n = 2 Spin n = 3 ν c frequency: ν c n = 1 frequency: n = 2 ν c 1 eB ν c n = 0 g ν = n = 1 c ν ν s = ν c 2π m c 2 n = 0 ms = -1/2 ms = 1/2 Gabrielse Basic Idea of the Fully-Quantum Measurement n = 4 ν c n = 3 n = 4 ν ν c Cyclotron c n = 2 Spin n = 3 ν c frequency: ν c n = 1 frequency: n = 2 ν c ν c n = 0 g 1 eB n = 1 ν = ν ν c = ν s c 2π m c 2 n = 0 ms = -1/2 ms = 1/2 g ν ν −ν Measure a ratio of frequencies: =s =1 + s c B in free 2 ν c ν c space ≈10 −3 • almost nothing can be measured better than a frequency • the magnetic field cancels out (self-magnetometer) Gabrielse Special Relativity Shift the Energy Levels δδδ n = 4 ν− 9 δ / 2 c n = 3 n = 4 νc − 7 δ / 2 Cyclotron νc − 7 δ / 2 n = 2 Spin n = 3 νc − 5 δ / 2 frequency: νc − 5 δ / 2 n = 1 frequency: n = 2 νc − 3 δ / 2 eB νc − 3 δ / 2 n = 0 g 2πν = c n = 1 ν− δ / 2 ν s = ν c m c 2 n = 0 ms = -1/2 ms = 1/2 Not a huge relativistic shift, δ hν c −9 =2 ≈ 10 but important at our accuracy ν c mc Solution: Simply correct for δ if we fully resolve the levels (superposition of cyclotron levels would be a big problem) Gabrielse Cylindrical Penning Trap V~ 2 z2− x 2 − y 2 • Electrostatic quadrupole potential good near trap center • Control the radiation field inhibit spontaneous emission by 200x (Invented for this purpose: G.G. and F. C. MacKintosh; Int. J. Mass Spec. Ion Proc. 57 , 1 (1984) Gabrielse One Electron in a Penning Trap • very small accelerator • designer atom cool 12 kHz 200 MHz detect need to Electrostatic 153 GHz measure for g/2 quadrupole Magnetic field potential Gabrielse Frequencies Shift Imperfect Trap • tilted B Perfect Electrostatic • harmonic B in Free Space Quadrupole Trap distortions to V eB ν = ν' < ν ν c m c c c ν νz= ν c ' z νm= ν z ν m g g g ν= ν νs= ν c ν= ν s2 c 2 s2 c g ν Problem: = s not a measurable eigenfrequency in an 2 ν c imperfect Penning trap Solution: Brown-Gabrielse invariance theorem 2 2 2 νc=() ν c + () ν z + () ν m An Aside Arising from the Last of These Conferences Gabrielse M More detail: G. Gabrielse, Int. J. of Mass Spec. 279 , 107 (2009) Measured sideband frequency – function of B tilt and harmonic distortion ωθφε+(,,)+ω − (,,) θ φ ε ≈ ωc only an approx. How bad is this common approximation? ∼ dimensional analysis : ∆ωc ωθ c+ ωε c ~1% 92 1 2 using invariance theorem: ∆ωc ≈ θ − εω − (and a bit of symmetry) 4 2 much, much smaller Gabrielse Spectroscopy in an Imperfect Trap • one electron in a Penning trap • lowest cyclotron and spin states g νv+( νν − ) v + ν =s = c sc = ca 2 νc ν c ν c 2 (ν z ) ν a − g 2ν c ≈1 + 2 2 3δ (ν z ) fc + + 2 2 ν c ≫ ≫ ≫ expansion for vcν z ν m δ To deduce g measure only three eigenfrequencies of the imperfect trap Feedback Cooling of an Oscillator Gabrielse Electronic Amplifier Feedback: Strutt and Van der Ziel (1942) Basic Ideas of Noiseless Feedback and Its Limitations: Kittel (1958) Dissipation :Γ=Γ−e (1g ) Fluctuations: TTge =− (1 ) faster damping rate Fluctuation-Dissipation Invariant: Γe / Te = const higher temperature Applications: Milatz, … (1953) -- electrometer Dicke, … (1964) -- torsion balance Forward, … (1979) -- gravity gradiometer Ritter, … (1988) -- laboratory rotor Cohadon, … (1999) -- vibration mode of a mirror Proposal to apply Kittel ideas to ion in an rf trap Dehmelt, Nagourney, … (1986) never realized Proposal to “stochastically” cool antiprotons in trap Beverini, … (1988) – stochastic cooling never realized Rolston, Gabrielse (1988) – same as feedback cooling (same limitations) Realization of feedback cooling with a trapped electron (also include noise) D’Urso, Odom, Gabrielse, PRL (2003) D’Urso, Van Handel, Odom, Hanneke, Gabrielse, PRL 94, 11302 (2005) Gabrielse QND Detection of One-Quantum Transitions 1 ∆BBz =2 →H = mω 2 z 2 − µ Bz 2 2 2 z 2 -excited oscillator -excited n=0 n=1 n=0 cyclotron cyclotron cyclotron ground excited ground state state state electron self self electronelectron one- n=1 1 freq= Ecyclotron = hf c ( n + 2 ) n=0 time QND Gabrielse Quantum Non-demolition Measurement B H = Hcyclotron + Haxial + Hcoupling [ Hcyclotron , Hcoupling ] = 0 QND condition QND: Subsequent time evolution of cyclotron motion is not altered by additional QND measurements Gabrielse One-Electron Self-Excited Oscillator measure voltage V(t) I2R damping axial motion 200 MHz of trapped electron crucial to limit the osc.
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