Atom-Interferometric Test of the Equivalence Principle at the ${10}^{-12}$ Level

We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ wave packets in the Earth’s gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an Eötvös parameter of $\eta =[1.6\pm 1.8(\mathrm{stat})\pm 3.4(\mathrm{syst})]\times {10}^{-12}$, consistent with zero violation of the equivalence principle. With a resolution of up to $1.4\times {10}^{-11}\mathrm{g}$ per shot, we demonstrate a sensitivity to $\eta$ of $5.4\times {10}^{-11}/\sqrt{\mathrm{Hz}}$.

Figure 1

(a) Schematic of simultaneous ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ interferometer in the initial rest frame of the atoms (not to scale). In pulse zone 1 ($t=0$), each atom cloud is split into two interferometer paths with $\hslash {\mathbf{k}}_1$ momentum difference. In pulse zone 2 ($t=T$), the paths are reflected toward each other with wave vector ${\mathbf{k}}_2$. In pulse zone 3 ($t=2T$), the paths are recombined and interfered with wave vector ${\mathbf{k}}_3$. The effective wave vectors ${\mathbf{k}}_1$, ${\mathbf{k}}_2$, and ${\mathbf{k}}_3$ differ slightly in orientation and magnitude to create a tailored phase response to kinematic initial conditions. The midpoint trajectory of each isotope remains essentially unperturbed throughout the interferometer; the ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ midpoint trajectories are overlapped to within $65\mu \mathrm{m}$. (b) Single fluorescence image ($14.8\mathrm{mm}\times 25.6\mathrm{mm}$) of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ output ports ($0\hslash k$ and $-2\hslash k$) with $8\hslash k$ beam splitters. The detection fringe allows precise single-shot phase extraction.

Figure 2

Compensation method for kinematic d.o.f. Changing the angle (frequency) of pulse zone 1 creates a horizontal (vertical) position-dependent phase. Changing the angle (frequency) of pulse zone 1 by $-\theta$ ($-\mathrm{\Delta }f$) and pulse zone 3 by $\theta$ ($\mathrm{\Delta }f$) creates a horizontal (vertical) velocity-dependent phase. The angle and frequency steps are calibrated to eliminate phase sensitivity to kinematic d.o.f.

Figure 3

EP data (1481 shots). Left: time series of the interferometer phase difference ${\varphi }_{85}-{\varphi }_{87}$, color coded by interferometer order ($4\hslash k$ red, $8\hslash k$ gray, $12\hslash k$ blue). Hollow (solid) points represent measurements with initial beam splitter direction down (up). Right: Histogram of the phase difference as a function of interferometer order, averaged over beam splitter direction, detection fringe direction, and imaging order.