= Cold-atom measurement of the gravitational constant
In 2014, <Gabriele Rosi> and colleagues used <atom interferometry>: two <rubidium>-87 clouds prepared by <laser cooling> in <vacuum>, $328\,\mathrm{mm}$ apart, received shared three-pulse <Raman transitions> spaced by $160\,\mathrm{ms}$. <Fluorescence> readout and paired-fringe <ellipse> fitting yielded differential <wave phase>. Twenty-four <tungsten> alloy cylinders, about $516\,\mathrm{kg}$ total, moved between C and F. Cloud subtraction rejected shared vibration; configuration subtraction isolated the source change.<Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms by Gabriele Rosi and others>[Main text pp. 3–5; Methods pp. 13–14; Fig. 1 caption p. 21]{ref}
\Image[/gravitational-constant-atom-interferometer.png]
{title=Cold-atom measurement: two clouds and two source configurations}
{description=Original conceptual scheme; selected cylinders represent surrounding arrays. Geometry is schematic.<Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms by Gabriele Rosi and others>[Main text pp. 3–5 and Fig. 1 caption p. 21]{ref}}
Calibration used timed flight and light-sheet crossings; mirror tilt compensated <Earth> rotation. <Wave vector> reversal rejected unwanted shifts. Modeling included source <Newtonian gravitational potential>, atom <trajectories>, cloud distributions and moving supports. Source positioning, <mass density> variation and cloud geometry limited the reported combined relative <standard uncertainty> to $150$ parts per million.<Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms by Gabriele Rosi and others>[Main text pp. 5–6; Methods pp. 14–18; Table 1, p. 27]{ref}
To understand the subtraction without reproducing that full analysis, consider an ideal <atom interferometer> in uniform vertical <acceleration> during each pulse sequence. Let $k_{\mathrm{eff}}$ be its signed effective vertical <wave vector> component and $T$ the pulse spacing. Its acceleration-dependent <wave phase> is $\phi\simeq k_{\mathrm{eff}}gT^2$; labels U and L denote upper and lower clouds. The double difference is then
$$
S=(\phi_U-\phi_L)_C-(\phi_U-\phi_L)_F\simeq k_{\mathrm{eff}}T^2[(g_U-g_L)_C-(g_U-g_L)_F].
$$
A background field identical in C and F cancels even if it differs between the two clouds. In a fixed-geometry, linear-response model, write $S=G\mathcal K$, where $\mathcal K$ is calculated from the source <mass density>, calibrated pulse sequence and atom <trajectories>. Thus $G_{\mathrm{inferred}}=S/\mathcal K$. Measuring <wave phase> accurately is one part of the task; calculating $\mathcal K$ accurately is another. The real nonuniform field and finite clouds require the trajectory-dependent analysis described above rather than this uniform-field approximation.
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