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Equation 83 · Part 2 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol L_rm G

Φ[LG]\Phi[\mathcal L_{\rm G}]
LGL_{\rm G}

What this part means

LrL_rm G is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

LrL_rm G is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

The Galilei loop admits an exact, non-simulated numerical check of the whole chain, because Φ\Phi[LG\mathcal L_{\rm G}] is precisely the recoil phase every stimulated-Raman atom interferometer already uses for its own calibration. Take a sodium atom, m=3.8175×\times10^{-26}\,kg\mathrm{kg} , driven by a two-photon stimulated-Raman transition on the 589\,nm\mathrm{nm} line, effective wavevector keffk_{\rm eff}=2(2π\pi/589\,nm\mathrm{nm})=2.1335×\times10^{7}\,m−1\mathrm{m^{-1}} [ 16 ] . The associated recoil velocity is vrv_r=ℏ\hbar keffk_{\rm eff}/m=5.894\,cm s−1\mathrm{cm\,s^{-1}} . Hold the loop open for T=50\,ms\mathrm{ms} , comparable to the short interrogation times of early stimulated-Raman interferometers, so the…

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