New determination of the fine structure constant and test of the quantum electrodynamics

Abstract

We report a new measurement of the ratio $h/m_{\mathrm{Rb}}$ between the Planck constant and the mass of $^{87}\mathrm{Rb}$ atom. A new value of the fine structure constant is deduced, $α^{-1}=137.035\,999\,037\,(91)$ with a relative uncertainty of $6.6\times 10^{-10}$. Using this determination, we obtain a theoretical value of the electron anomaly $a_\mathrm{e}=0.001~159~652~181~13(84)$ which is in agreement with the experimental measurement of Gabrielse ($a_\mathrm{e}=0.001~159~652~180~73(28)$). The comparison of these values provides the most stringent test of the QED. Moreover, the precision is large enough to verify for the first time the muonic and hadronic contributions to this anomaly.

Figures (5)

• Figure 1: Determinations of $\alpha$ with a relative uncertainty smaller than $10^{-8}$; $a_\mathrm{e}$(UW): measurement by Dehmelt at the University of Washington VanDick; $h/m_{\mathrm{Cs}}$: measurement of the Cesium recoil velocity at Stanford Wicht; $h/m_{\mathrm{Rb}}$: measurement of the Rubidium recoil velocity at Paris in 2006 Clade2 and 2008 Cadoret; $a_\mathrm{e}$(Harvard): measurement of $g-2$ at Harvard University in 2006 Gabrielse2006 and 2008 Gabrielse2008; CODATA 2006: best adjustment by the Committee on Data for Science and Technology codata06; the arrow corresponds to the shift of the values of $\alpha$ due to the reevaluation of the QED calculation of $a_\mathrm{e}$ in 2007 Gabrielse2007Kinoshita.
• Figure 2: Example of the four spectra needed to deduce $h/m_{\mathrm{Rb}}$ (see the text). Each spectrum represents the quantity $N_2/(N_1+N_2)$ where $N_1$ and $N_2$ are the population of the $F$ = 1 and 2 levels in function of the frequency difference between the two pairs of $\pi/2$ pulses. The measured position of the central fringe is indicated above the spectra.
• Figure 3: Measurements of the ratio $h/m_{\mathrm{Rb}}$ during about 15 hours. The standard deviation of the mean is $4.4\times 10^{-10}$ with $\chi^2/(n-1)$ = 1.05. The inset shows the autocorrelation function of these 170 measurements. The solid and dashed lines represent the 1 $\sigma$ and 2 $\sigma$ standard deviation of the autocorrelation function.
• Figure 4: (Color online). Sensitivity of the $h/m_{\mathrm{Rb}}$ measurements to the alignment: results of the measurements when the angle between the two Bloch beams is modified. The most precise point corresponds to the measurements in Fig. \ref{['pointshsurm']}. The difference between this value and the summit of the parabola which is fitted to the data is 0.35 ppb.
• Figure 5: (Color online). Upper figure: in blue, relative contributions to the electron anomaly of the different terms of equation (\ref{['eqAnomalie']}), in red their uncertainties. The dashed line corresponds to the relative uncertainty of the new $\alpha$ value. Lower figure: comparison of the measurements of the electron anomaly (UW 1987 VanDick and Harvard 2008 Gabrielse2008) with the theoretical value obtained by using the new value of $\alpha$ (label Rb 2010). The point "Rb 2010 - only QED" is obtained without the last term of equation (\ref{['eqAnomalie']}).