Fine structure constant determinations

Transcription

1 Fine structure constant determinations F. Nez Laboratoire Kastler Brossel, UPMC,ENS,CNRS Metrology of simple systems and fundamental tests Quantum metrology and fundamental constants S. Galtier, F. Nez, L. Julien, P. Cladé, S. Guellati-Khélifa, F. Biraben, R. Bouchendira

2 Determinations of the fine structure constant Lecture I e α 4 0 c p,h-90 hfs muonium He fine structure h / m quantum L Hall effect g of the electron (UW) g of the electron (Harvard) h/m (neutron) h/m (Cs) h/m (Rb) Solid state physics mv=h/λ DB v r =ћk/m QED

3 General outline Lecture I : less accurate determinations of Quantum Hall effect Hydrogen fine and hyperfine structure Helium fine structure Exotic hydrogen-like atoms Lecture II : most accurate determinations of g- (lepton) h/m contribution of in new SI

4 Magnetic moment of free leptonic particles Discussed here : electron, positron, muon is the most stringent test of QED (*) The g-value is a dimensionless measurement of the magnetic moment Its experimental determination is the most stringent test of CPT invariance with leptons (comparison electron - positron) g q m J and, if one is confident in QED calculations, is a test for physics beyond the Standard Model (e.g. electron substructure) (*) gives the most precise determination of α if there is no physics beyond the Standard Model (*) if α is known

5 The electron magnetic moment The magnetic moment of a particle with charge q and mass m is related to its angular momentum by the g factor : For an electron, one introduces the Bohr magneton e g q m J B and then J me Dirac s theory predicted g= for a free electron (pure spin momentum) g B In a magnetic field, the coupling energy of a given magnetic moment with the field is given by B. so that : -the magnetic moment precesses around the field at the Larmor frequency L g qb m B e - magnetic moment -energy levels in an atomic bound system are shifted (Zeeman effect) by a quantity which is simply related to the g factor and to the various quantum numbers of the level E S 1/ P 1/ 540 G H(S 1/ -P 1/ ) B

6 Measurements of the electron g-factor g For a free electron the g-factor is simply deduced from = B e - magnetic moment and the cyclotron frequency (Lorentz) and its anomaly is defined as Larmor frequency (spin) ae c g e eb m e L a e >0 g B L C eb m e e - µ e- QED : m e m e +m µ e- g <! h/mc Radiative reaction : in the cyclotron motion, the electron is slow down by the radiative reaction C decreases more than L : g>

7 Measurements of the electron g-factor In Nov. 1947, the first determination of a e was performed by Kusch and Foley by Zeeman splitting in an atomic beam magnetic resonance experiment with Ga and then in Na and In (Apr. 1948) Their result was a e = (5) in agreement with the prediction of Schwinger (1948) a e = = Beginning of comparison theory-experiment of the g- For a review of early measurements, see : A. Rich and J.C. Wesley, Rev. Mod. Phys. 44, 50 (197)

8 Measurements of the electron g-factor First experimental method : Direct observation of the electron spin precession in a given magnetic field (Michigan) 100 kev electrons (100 ns pulses) are polarized and trapped in a 1 kg magnetic field during a predetermined time T The spin rotation during this time is recorded versus T accuracy on a e J.C. Wesley and A. Rich, Phys. Rev. A 4, 1341 (1971) The same method is easily extended to the g-factor of positron J. Gilleland and A. Rich, Phys. Rev. Lett. 3, 1130 (1969)

9 Measurements of the electron g-factor Second experimental method : Study of transitions induced by a RF field in a Penning trap in a given magnetic field (Washington, Mainz, Stanford, Harvard) The energy levels of one electron in a magnetic field are given by : E 1 n, ms n c ms L where and a L c g a 1 is the anomaly frequency c a L c n n Rabi-Landau levels 1 Ñω C n 0 n n 1 0 Ñω L m s Ñω a 1 directly related to a e a e a c m s B 1 µ e- B µ e-

10 Measurements of the electron g-factor : in a Penning trap A quadrupolar electric potential is applied which confine the electron along the z axis V 1 x y x, y, z m z e z + e - + B - The transverse confinement is obtained by the application of the magnetic field The electron movement is the sum of : - a cyclotron rotation at a slightly modified frequency - an oscillation along the z axis - a slow rotation at the magnetron frequency - An electron suspended in a Penning trap is a homemade atom called geonium P. Ekstrom and D. Wineland, Scientific American 43, 91 (1980) L.S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 33 (1986)

11 Measurements of the electron g-factor : Pioneer work in Washington - Penning trap at 4K - single electron stored Measurement of the cyclotron frequency and of the anomaly frequency Results : g / (40) 4 x e Detection of spin-flip through the induced shift of the axial frequency z z0 n m 1 depend on the trap (here 1.3Hz) and g e / g e 1 (0.5.1) 10 1 R.S. Van Dyck Jr, P.B. Schwinger and H.G. Dehmelt, Phys. Rev. D 34, 7 (1986) and Phys. Rev. Lett. 59, 6 (1987)

12 Measurements of the electron g-factor : the Harvard experiment the most precise determination of the electron g-factor - + e - + B - Cylindrical Penning trap invented to form a microwave cavity that could inhibit spontaneous emission (by a factor of up to 50) narrowed line width Trap cavity cooled to 100 mk the electron cyclotron motion is its ground state Calculable trap careful control and probe of radiation field and magnetic field in the trap cavity The one quantum change in cyclotron motion is resolved

13 Measurements of the electron g-factor : the Harvard experiment the most precise determination of the electron g-factor Electron s lowest cyclotron and spin levels Special relativity makes the transition cyclotron frequency decrease by a very small shift n 1 m s where c 10 / mc c 9 not negligible at this level of accuracy! 5.4 T stabilized magnetic field very stable trapping potential provided by a charged capacitor Numerical values : c z m / / 150 GHz 00 MHz / 133 khz a / 174 MHz (measured)

14 Measurements of the electron g-factor : the Harvard experiment the most precise determination of the electron g-factor Quantum non demolition (QND) detection The one-quantum sensitivity is obtained through the coupling of the cyclotron motion to the thermally driven axial motion at 00 MHz frequency where electronic detection is efficient This coupling is obtained with a magnetic bottle gradient of B (Ni rings) The shift is z B n m s here 4 Hz in 00 MHz sin(ω a t) + e - + B - F - Micro wave inlet (ω c ) spin flip anomaly transition induced by applying an oscillating potential to the electrodes one-quantum cyclotron excitation induced by microwaves injected into the cavity

15 Measurements of the electron g-factor : the Harvard experiment the most precise determination of the electron g-factor Quantum-jump spectroscopy : measuring the quantum jumps per attempt to drive them as a function of drive frequency (different modes of the trap cavity) Result : in 006 g / (76) 7.6 x in 008 g / (8).8 x cyclotron transitions anomaly transitions B. Odom et al., Phys. Rev. Lett. 97, (006) D. Hanneke et al, Phys. Rev. Lett. 100, (008) and Phys. Rev. A 83, 051 (011)

16 electron anomaly : discussion The last result obtained in Harvard is : Taking into account the presence of the muon and tau particles, the QED contribution to the electron g - can be written : a e 1 ae (0.8) 10.4 x A where Ai Ai Ai Ai. Ai.. and A Since the experimental uncertainty is less than 1% of the coefficient is needed to match the precision of theory with experiment A 1 m m A m m A m m, m m 1 A e e In addition, the total non QED (hadronic) contribution to a e is 1.7() x e 4 e see :T. Kinoshita in Lepton dipole moments, Ed. World Scientific (010) But the comparison of theory with measured electron anomaly needs also a value of α obtained by an independent measurement

17 electron anomaly : discussion Complexity of QED calculations where a e A i A m m A m m A m m, m m 1 A e e A i A i A i 3. A 3 i e 4.. e A 1 1 A ( 35 ) 891 Feynman diagrams! (mostly numerical calculations) 373 calculated by independent methods 518 vertex diagrams amalgamated in 47 diagrams see :T. Kinoshita in Lepton dipole moments, Ed. World Scientific (010) and ref. therein

18 electron anomaly and fine structure constant On another hand, the last measurement of the electron g-factor, combined with recent calculations of A 1 (8) and A 1 (10) coefficients gives the most precise determination of the fine structure constant ( 85 )( 331).5 x B. Odom et al., Phys. Rev. Lett. 97, (006) and 99, (007) D. Hanneke, S. Fogwell and G. Gabrielse, Phys. Rev. Lett. 100, (008) A 1 (10) : T. Aoyama, M.Hayakawa, T. Kinoshita and M. Nio, arxiv v1 (4 May 01) 167 diagrams! A 1 (10) = 9.16(58)

19 Measurements of the muon g-factor First experiment at the Columbia-Nevis Cyclotron : the direct observation of the muon magnetic moment precession in a magnetic field provided the indication that the muon behave like a heavy electron with a g-factor given by g (8) in agreement with predictions of QED R.L. Garwin et al., Phys. Rev. 118, 71 (1960) Columbia During the following years, experiments were performed at CERN, either at the synchrocyclotron or at the proton synchrotron : G. Charpak et al., Phys. Lett. 1, 16 (196) J. Bayley et al., Nucl. Phys. B150, 1 (1979) leading to increasing accuracy

20 Measurements of the muon g-factor Experiment in Brookhaven by V. Hughes and collaborators study of the spin precession relative to the momentum in a given magnetic field In both CERN and Brookhaven experiments, relativistic muons are stored in circular orbits in a uniform magnetic field and are detected through their decay electrons µ e - e Correlation spin e - direction (P.V.) The anomaly frequency is observed as an oscillation of the detected electrons The magnetic field is deduced from proton NMR Columbia Result : a (63) 10 3 G. Bennet et al., Phys. Rev. D 73, (006) E81 collaboration

21 muon anomaly : discussion The average current experimental result is : 11 a (63) μ10-6 Due to the mass dependence, the muon g - is 4 x 10 4 times more sensitive to hadronic and electroweak effects than the electron g - The hadronic contribution to a µ is 60 μ10-6 This result allows to check the contribution of virtual hadrons to the muon anomaly Including all contributions, the theoretical value of a µ in the Standard Model is : a (6) which differs from the experimental value by 89 (86) x σ Both theory and experiment must be improved to know if it is or not an indicator of physics beyond the standard model see :T. Kinoshita in Lepton dipole moments, Ed. World Scientific (010)

22 General outline Lecture I : less accurate determinations of Quantum Hall effect Hydrogen fine and hyperfine structure Helium fine structure Exotic hydrogen-like atoms Lecture II : most accurate determinations of g- (lepton) h/m contribution of in new SI

23 Determination of the fine structure constant α from h/m Rydberg constant in terms of energy : hc R 1 m e c α α R c 87 m Rb M P M m P e m h 87 Rb Bound systems (with hydrogen) back in the competition - Rydberg constant : 5 x 10-1 (hydrogen spectroscopy) (CODATA 010) - atom-to-proton mass ratio :1.4 x (ion trap) - electron-to-proton mass ratio : 4. x (ion trap) α R c Ar A r Rb h e m87 Rb 87 Ar( 87 Rb) is the mass of 87 Rb in atomic mass unit (ref 1 C) Ar(e) is the electron mass in atomic mass unit (ref 1 C)

24 h/m neutron neutron : de Broglie p m v h v velocity measured with time of flight Bragg diffraction d 0 m n d h 0 W04. R c A A r r e nd W04 0 Kruger et al, Metrologia (1999) 36() p.147 fix HeNe d0 m optic n rayons X HeNe Deslattes et al, (1973) PRL 31, p.97 Mana G. 001 Proc. E. Fermi Course CXLVI displac t : 85 µm d 0 0,19 nm HeNe 633 nm X 0,07 nm

25 Recoil effect h/m Determination of the fine structure constant α from h/m The recoil velocity is directly related to the h/m ratio J.L. Hall et al, : PRL 37,1339 (1976) b k and can be measured very E=h m v r precisely in terms of frequency p=ћk m (Doppler effect) a Spontaneous emission Raman two photon transition a b 4E r c a b c m ħk v r =μ---- m Same internal state Two different internal states Momentum transfer almost perfectly defined photon transition light shift 87 Rb v r K v~300m/s need to cool atom sample

26 Principle of our experiment selection (Raman transition or Ramsey fringes) MOT + molasses N ħk coherent acceleration measurement (Raman transition or Ramsey fringes) 87 Rb selection of an initial sub-recoil velocity class 5P 3/ coherent acceleration : N Bloch oscillations, momentum transfer Nħk measurement of the final velocity class 5S 1/ F= F=1 vr = v / (N)

27 Coherent acceleration of atoms : simple approach Succession of stimulated Raman transitions (same hyperfine level) m Energy v r F=1 k per cycle 1 t h h Addiabatic passage : acceleration of the atoms k v r 10 k v r 6 k v r Momentum The atom is placed in an accelerated standing wave: in its frame, the atom is submitted to an inertial force k 0 k 4 k 6 k Bloch oscillations in a periodic potential LKB (1996)

28 Atom in an accelerated lattice m 1 1 & Velocity of the lattice v=( 1 - )/k Light shifts : Periodic potential U U(x, t) 0 cos(k vt) U 0 v Wannier function (center at v=0) Velocity distribution Wannier function (center at Nv r ) v r Acceleration v

29 Rabi oscillations δ b 1 max P a b Ω a max/ 0 p p Ωt Probability : P( a b Ω ) Ω δ sin 1 δ Ω Ωt Atom interferometer 1 δ=0 P a b for Ωt p p-raman pulse a xxxxxxxxxxxxx b and b a p/ -Raman pulse a xxxxxxxxxxxxxx 1 a - i b and

30 Atom interferometry Light interferometer Photon, light-wave mirror Atom interferometer Atom, wave-function p-raman pulse a xxxxxxxxxxxxx b and b a beam splitter Output : fringe: nb of photons (Out 1) = f( ΔΦ) p/ -Raman pulse a xxxxxxxxxxxxxx 1 a - i b and Output : fringe : nb of atom in quantum state a = f( ΔΦ) Out space Space y x ΔΦ Out 1 p/ pulse b a p pulse p/ pulse time a.u. Light detected 0 ΔΦ=f(n, ΔL) Probability to be in a a.u. state at the end of the time sequence ΔΦ=f(g,Φ pulses(lasers) )

31 87 Rb Velocity measurement : p pulses 5P 3/ F=1 F= 5S 1/ Selection: F= F=1 sel MOT + optical molasses Raman transition Doppler sensitive In our earlier experiment ( configuration), two Raman pulses were used - to select a subrecoil velocity distribution - and to measure the final velocity distribution Blow away beam Tuned Frequency Measurement: F=1 F= meas Detection pop. in atomic state (F=1 and F=) : fluorescence resonance in a laser beam F= -pulse -pulse g F=1-5v r 0 +5 v r -5v r 0 +5 v r -5v r 0 +5 v r

32 Improvement of the velocity selection Selection: F= F=1 sel MOT + T R optical molasses Blow away beam Tuned Frequency Measurement: F=1 F= meas Detection (idem) /-pulses /-pulses In our present experiment ({ { configuration), - the first pair of pulses (frequency δ 1 ) selects a velocity pattern 1/T R Ramsey pattern velocity - the second pair of pulses (frequency δ ) selects another velocity pattern When the detection frequency δ is swept, the signal obtained is the convolution of two Ramsey patterns Interferometric method Frequency = - 1 Fit of the central part precise determination of the velocity

33 Bloch oscillations and atomic interferometry high sensitivity of atomic interferometry + high efficiency of Bloch oscillations v+nv 0 r v 0 / / space / / T R time T R N Bloch oscillations v-nv 0 r acceleration deceleration T R T R detection selection F= F=1 blow away beam measurement F=1 F=

34 Measurement of the recoil velocity mes k 1 k upwards acceleration + spectra g sel k k 1 downwards acceleration sel mes k 1 + k spectra δsel δ We measure (Doppler effect) : ΔV meas k1 k up Acceleration in both opposite directions : V vr up v r k m B m (N k k 1 V N down down up sel meas sel meas up down (N N ) k k k 1 with V Avg( V ) B down, V 1,,1 (no contribution of g) )

35 «Atom elevator» mes Bloch oscillations = high efficiency (99.95% per recoil) increase the size of the vacuum chamber more recoils transferred to the atoms higher accuracy on recoil determination acc dec acc sel dec acc dec acceleration deceleration T R T R detection selection ±300 ± blow away 500 F= F=1 beam measurement F=1 F=

36 Results with new vacuum chamber 170 measurements (14 hours) Each measurement : 6μ10-9 (h/m) and 3 μ10-9 () (~5 min) Relative uncertainty on h/m : 4.4μ10-10 and.μ10-10 on

37 Results : correlation? Testing for correlations in measurements : T.Witt BIPM : no correlations Metrologia (007)

38 Error budget Source (1/α) ( ) ( ) Laser frequencies Beams alignment Wave front curvature and Gouy phase nd order Zeeman effect Gravity gradient Light shift (one photon) Light shift (two photon) Light shift (Bloch oscillations) Index of refraction (cold atomic cloud and backgrd vapor).0 Global systematic effects Statistical uncertainty.0 Rydberg constant and mass ratio. TOTAL UNCERTAINTY 6.6

39 Systematics : beams alignment k1k k cosθ k(1 θ /) Maximum angle estimated 40 µrad from coupling between optical fibers 3.3μ10-10

40 Wavefront curvature and Gouy phase shift Momentum of the photon? p where Φ is the phase of the laser beam z p= ћk holds only for a perfect plane wave For a Gaussian beam : Φ z k 1 k 4 w 4r w 4 r k R where w is the waist of the beam, R the wave front curvature and r the distance from the propagation axis of the beam. Beam diagnostics with a Shack-Hartmann analyzer w=3.6 mm R > 30 m Largest systematic effect 5μ10-10 larger beam size more light power

41 10 0 a e C 1 α C π α π Test of QED: electron anomaly C 3 α π 3 C δ 4 α π 4 a m /m,m /m,weak,hadron... e μ e τ 14 a a meas a theo ( ) e e e α π First test of the QED at the 10-9 level α π α π 3 α π 4 α π 5 m m e μ m m e τ a(weak) a(hadron) First test of the muonic and hadronic corrections h/m(rb) 008 h/m(rb) 010 UW 1987 Harvard 008 Rb 010 Rb 010 only electronic QED contributions (a e )/10-1

42 CODATA deduced from all experiments deduced from experiments except g -

43 deduced from experiments except g - CODATA deduced from all experiments Improved QED (10th order calculation : ArXiv: May 01)

44 Determination of the fine structure constant LKB-10 (Paris) : α -1 = (91) [6.6μ10-10 ] PRL 106, (011) a e = (84) a e = (84) new QED due to h/m Harvard Uni-08 : a e = (8) PRL 100,10801 (008) α -1 = (51) [3.7μ10-10 ] α -1 = (34) [.5μ10-10 ] new QED mainly due to exp. a e (UW) QED 007 h/m(cs) 00 a e (Harvard, 006) +QED 007 a e (Harvard, 008) h/m(rb) 010 h/m(rb) 006 h/m(rb) a e (Harvard, QED 01)

45 General outline Lecture I : less accurate determinations of Quantum Hall effect Hydrogen fine and hyperfine structure Helium fine structure Exotic hydrogen-like atoms Lecture II : most accurate determinations of g- (lepton) h/m contribution of in new SI

46 The fine structure constant in the proposed new SI constant curr. SI u R μ10 8 new SI constant curr. SI u R μ10 8 u R μ10 8 new SI u R μ10 8 m(k) m( 1 C) h M( 1 C) e k 91 0 K J. 0 N A R K R 91 0 μ F. 0 ε σ Z m e N A h h m h m m hn M h e h m m m e 1 1 C R m C e u A c R c R ca r( e )M R 1 1 C N m C 0c A e u c u m u I. Mills et al, Phil. Trans. R. Soc A (011), 369,

47 The fine structure constant in the proposed new SI Current SI: the fine structure constant contribute to the test of the validity of the expression of R K (~absolute determination), K J (~gyromagnetic factor of the proton) (see Codata 00, 006, 010) the comparison of the Avogadro experiment with Watt balance experiments New SI: The fine structure constant will play a central role and especially the determination of h/m ratios (cf previous slide) Experimentally, the association of a Watt balance with h/m(atom) experiment allows: to link a macroscopic mass to an atomic mass Cladé et al Europhys. Lett 71 (5) pp. 730 (005) to realize new experimental schemes to determine the Avogadro constant Biraben et al, Metrologia 43 (006) L47-L50

48 Conclusion The fine structure constant in 01 is mainly determined with electron anomaly and QED Independent determination is essential to test QED, currently h/m with cold atom is the only competitive method Hydrogen is the Rosetta stone of modern physics (T.W. Hänsch 1976) also for the 1th century? Many thanks to all my colleagues for their help, slides (*), comments and suggestions and thank you for your attention! (* L. Julien QED 01, Cargèse)

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50 Discussion : most precise determinations of the fine structure constant Comparison July 01 LKB-10 (Paris) : α -1 = (91) [6.6μ10-10 ] PRL 106, (011) a e = (84) a e = (84) new QED due to h/m Harvard Uni-08 : a e = (8) PRL 100,10801 (008) α -1 = (51) [3.7μ10-10 ] α -1 = (34) [.5μ10-10 ] new QED mainly due to exp. The present value of the fine structure constant is still determined with QED Independent determination is essential to test QED, actually h/m method with cold atom is the only competitive method