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Equation 86 · Part 5 · The Clock That Comes Back Wrong by Exactly Its Mass

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keff=2(2π/589 nm)=2.1335×107 m−1k_{\rm eff}=2(2\pi/589\,\mathrm{nm})=2.1335\times10^{7}\,\mathrm{m^{-1}}
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What this part means

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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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