Table 2 Requirements on the pointing of the relaunch, starting parameters, variation of gravitational acceleration, and its gradient.

	\(\alpha _{\delta \tau } (rad)\)	\(\alpha _{\Gamma }\)	\(\beta \)	\(v_{x0}\) (\(\upmu \)m/s)	\(v_{y0}\)	\(v_{z0}\)	\(y_0\) (\(\upmu \)m)	\(z_0\)	\({\delta }g\) (m/s\(^2\))	\({\delta }\Gamma \) (1/s\(^2\))
Compact	\(1.3\,\times 10^{-4}\)	\(<0.1\)	\(9.4\,\times 10^{-5}\)	200 \(^{*}\)	250 \(^{\dagger }\)	250 \(^{\dagger }\)	100 \(^{\ddagger }\)	100 \(^{\ddagger }\)	\(5.6\,\times 10^{-4}\)	\(7.2\times 10^{-2}\)
High sensitivity	\(6\,\times 10^{-6}\)	\(2.5\,\times 10^{-6}\)	\(6.6\,\times 10^{-9}\)	26 \(^{\star }\)	10 \(^{\dagger }\)	10 \(^{\dagger }\)	100 \(^{\ddagger }\)	100 \(^{\ddagger }\)	\(5.4\,\times 10^{-8}\)	\(1.1\times 10^{-8}\)

The parameters are calculated to induce contributions (see Eqs. 5 to 14) by a factor of \(10\cdot {n}\) below the shot-noise limit (\(1/\sqrt{N}\)) for the scenarios in the lower rows of Table 1. We assume \(\delta \tau =10\,\mathrm {ns}\) for a typical experiment control system³¹, Earth’s gravity gradient \(\Gamma _{x}=\Gamma _{y}=-0.5\Gamma _{z}=1.5\times 10^{-6}\,\mathrm {s}^{-2}\), and \(\Omega _{x}=\Omega _{y}=\Omega _{z}=7.27\times 10^{-5}\) rad/s using Earth’s rotation rate as an upper limit^50,51.
\(^*\)Limited by the velocity acceptance of the beam splitter^41,43.
\(^\star \)Assuming a gravity gradient compensation^21,66,67,68 to \(0.1\cdot \Gamma _{x}\), neglecting the impact on other terms as the small change in the enclosed area⁶⁶.
\(^\dagger \)Requirement set to limit the change in position w.r.t. the beam splitter between first and last pulse to \(100\,\upmu \mathrm {m}\).
\(^\ddagger \)Constraint to have the atoms within \(100\,\upmu \mathrm {m}\) of the center of the beam splitter at the first pulse.

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