Single-bounce quantum gravimeter to measure the free-fall of anti-hydrogen

Abstract

We propose an innovative concept for a quantum gravimeter, where atoms prepared in a Heisenberg-limited state perform a single bounce on a mirror followed by a free fall. This quantum gravimeter produces a simple and robust interference pattern which should allow to measure the free-fall acceleration of atoms. We estimate the expected accuracy of the measurement in the GBAR experiment, which aims at testing the equivalence principle on anti-hydrogen at CERN antimatter facilities. Using simulations and estimation techniques based on Cramer-Rao law and Fisher information, we show that the new quantum sensor improves the expected accuracy of the measurement. The proposal opens the door to free fall measurements on rare or exotic atomic species, especially in situations where experimental time or detection events are limited by intrinsic physical reasons.

Figures (4)

• Figure 1: Schematic representation of the experimental setup. A Gaussian wave-packet prepared in a trap falls down onto a mirror where it experiences a single bounce. Subsequent free fall reveals interferences which are recorded as positions of atoms on a detection plate.
• Figure 2: Representation of the evolution of the wave-function from the source to the detection. The square modulus $\vert\psi(z)\vert^2$ of the wave-function is represented as a function of $x=Vt$ (for a velocity $V_0=1m\per s$). The main plot shows the mean motion from the source to the detection plate. Details are shown in the zooms devoted to zones of particular interest: a) evolution of the wave-function over the mirror (described by eq.\ref{['eq:discrete_decomposition']}); b) transition to the second phase corresponding to free fall (described by eq.\ref{['eq:propagator']}); c) fully revealed interference fringes after a long phase of free fall after the mirror.
• Figure 3: Three curves for the probability of detection at altitude $z$ calculated for slightly different values of ${g\xspace}$. The solid (blue) curve corresponds to the standard gravity acceleration, while the dashed (red, shifted towards the right) and dotted (green, shifted towards the left) curves correspond respectively to values decreased and increased by a relative variations of $10^{-4}$. The zoom shows that fringes are visible on a large range of values of $z$. (colors online)
• Figure 4: Top plot : Histograms of the estimators $\hat{g}$ for a large number of simulations performed each with $N$ randomly drawn detection events. The broader blue histogram corresponds to $N=100$ and the narrower green one to $N=1000$. Bottom plot : Expected relative accuracy $\sigma_{{g\xspace}}/g_0$ for the measurement of ${g\xspace}$ calculated from the dispersion on histograms, and represented as blue dots depending on the number $N$. For large enough values of $N$, the dots are aligned on the dashed red line showing the Cramer-Rao law. (colors online)