A measurement using a one-electron quantum cyclotron gives the electron magnetic moment in Bohr magnetons, g=2 1:001 159 652 180 73 28 [0.28 ppt], with an uncertainty 2.7 and 15 times smaller than for previous measurements in 2006 and 1987. The electron is used as a magnetometer to allow line shape statistics to accumulate, and its spontaneous emission rate determines the correction for its interaction with a cylindrical trap cavity. The new measurement and QED theory determine the fine

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... e constant, with ÿ1 137:035 999 084 51 [0.37 ppb], and an uncertainty 20 times smaller than for any independent determination of . The electron magnetic moment is one of the few measurable properties of one of the simplest of elementary particles -revealing its interaction with the fluctuating QED vacuum, and probing for size or composite structure not yet detected. What can be accurately measured is g=2, the magnitude of scaled by the Bohr magneton, B e@=2m. For an eigenstate of spin S, with g=2 1 for a point electron in a renormalizable Dirac description. QED predicts that vacuum fluctuations and polarization slightly increase this value. Physics beyond the standard model of particle physics could make g=2 deviate from the Dirac/QED prediction (as internal quarkgluon substructure does for a proton). The 1987 measurement that provided the accepted g=2 for nearly 20 years [1] was superceded in 2006 by a measurement that used a one-electron quantum cyclotron [2] . Key elements were quantum-jump spectroscopy and quantum nondemolition (QND) measurements of the lowest cyclotron and spin levels [3], a cylindrical Penning trap cavity [4] (Fig. 2) , inhibited spontaneous emission [5] , and a one-particle self-excited oscillator (SEO) [6] . This Letter reports an improved measurement that has a 2.7 and 15 times lower uncertainty than the 2006 and 1987 measurements, respectively, and confirms a 1.8 standard deviation shift of the 1987 value [ Fig. 1(a) ]. The interaction of the electron and its surrounding trap cavity is probed by measuring g=2 and the electron's spontaneous emission rate as a function of magnetic field, thereby determining the corrections needed for good agreement between measurements at different fields. The electron is also used as its own magnetometer to accumulate quantum-jump line shape statistics over days, making it possible to compare methods for extracting the resonance frequencies. The new measurement and recently updated QED theory [7] determine with an uncertainty 20 times smaller than does any independent method [ Fig. 1(b) ]. The uncertainty in is now limited a bit more by the need for a higher-order QED calculation (underway [7]) than by the measurement uncertainty in g=2. The accuracy of the new g sets the stage for an improved CPT test with leptons. It also will allow an improved test of QED, and will be part of the discovery of low-mass dark-matter particles or the elimination of this possibility [8], when a better independent measurement of becomes available. Figure 3 represents the lowest cyclotron and spin energy levels for an electron weakly confined in a vertical magnetic field Bẑ and an electrostatic quadrupole potential. The latter is produced by biasing the trap electrodes of Fig. 2. The measured cyclotron frequency f c 149 GHz (blue in Fig. 3 ) and the measured anomaly frequency a 173 MHz (red in Fig. 3 (2) with only small adjustments for the measured axial frequency z 200 MHz, the relativistic shift = c h c =mc 2 10 ÿ9 , and the cavity shift g cav =2. The latter is the fractional shift of the cyclotron frequency caused by the interaction with radiation modes of the trap cavity. The Brown-Gabrielse invariance theorem [9] has been used to eliminate the effect of both quadratic distortions to the electrostatic potential, and misalignments of the trap electrode axis with B. Small terms of higher order in z = f c are neglected. FIG. 1. Most accurate measurements of the electron g=2 (a), and most accurate determinations of (b).