Atom-Chip Fountain Gravimeter

We demonstrate a quantum gravimeter by combining the advantages of an atom chip for the generation, delta-kick collimation, and coherent manipulation of freely falling Bose-Einstein condensates (BECs) with an innovative launch mechanism based on Bloch oscillations and double Bragg diffraction. Our high-contrast BEC interferometer realizes tens of milliseconds of free fall in a volume as little as a one centimeter cube and paves the way for measurements with sub-$\mu \mathrm{Gal}$ accuracies in miniaturized, robust devices.

Figure 1

Atom-chip based gravimeter setup (a) and space-time trajectories (blue or gray dashed, solid lines) of a BEC without (b) and with (c) relaunch. The chip serves in all steps of state preparation and as retroreflector for light propagating in the $z$ direction (red, blue wavy arrows), thus creating moving lattices, which induce Bragg diffraction or Bloch oscillations for interferometry with BECs (red dots). The number of atoms at the output port is obtained by imaging the spatial absorption (gray dots) of a light pulse traveling along the $x$ direction with a CCD camera. Both space-time diagrams (b) and (c) start with the release of the BEC, and consist of (i) the adiabatic rapid passage to the Zeeman state with the lowest magnetic susceptibility during ${\tau }_{\mathrm{arp}}=10.2\mathrm{ms}$, (ii) the MZI of variable duration $2T$, and (iii) the detection of the wave packets at the output ports, after they have moved apart for ${\tau }_{\text{sep}}=13\mathrm{ms}$ at $\mathrm{ToF}=34$ and 97.6 ms. The MZI is formed by coherently splitting, redirecting, and recombining BECs by Bragg diffraction either in the upward (blue lines) or downward direction (gray lines). Unfortunately, the preparation takes up a considerable fraction of the free-fall time in scenario (b). In contrast, the coherent relaunch of (c) implemented by Bloch oscillations and double Bragg diffraction preceding the MZI allows us to incorporate delta-kick collimation at ${\tau }_{\exp }=6\mathrm{ms}$ after release to reduce the effect of the atomic interaction, as well as Stern-Gerlach-type deflection for ${\tau }_{\mathrm{SG}}=7\mathrm{ms}$, and increases the sensitivity of the interferometer by up to 2 orders of magnitude.

Figure 2

Gravitational acceleration deduced from three signals without relaunch (a) and its Allan deviation (b). Dependence (a) of normalized atom numbers (red diamond, blue squares, black circles) in one output port of the MZI and corresponding sinusoidal fits (red dotted, blue dashed, and black solid lines) for $T=1$, 3, 5 ms on the acceleration $2\pi \alpha /k_{\mathrm{eff}}$ of the Bragg lattice. The interference signals reveal a high contrast of $C=0.75$ thanks to the use of BECs and an increase of noise when $T$ is extended due to higher intrinsic sensitivity. When the lattice acceleration is identical to the local gravitational acceleration, the interference signals assume the same minimum for all $T$ (gray line). Allan deviation (b) of the acceleration (gray circles) and precision of our demonstrator improves with the square root (black line) of the integration time $t$ during 8 h with $T=5\mathrm{ms}$.

Figure 3

Atom-chip fountain gravimeter. Temporal dependence (a) of intensity (top) and velocity (bottom) of the optical lattice employed for relaunch. Absorption images (b) of BECs being accelerated either by Bloch oscillations (left, middle) or launched via a sequence composed of Bloch oscillations and double Bragg diffraction (right). Normalized populations in one output port of the MZI with relaunch and corresponding probability distribution of the signal (c). In both scenarios Bloch oscillations are implemented by adiabatically loading a freely falling BEC into and releasing it from an accelerated lattice by linearly changing the intensity (a). In the first case the lattice is uniformly accelerated from initial to final speed $v_i$ and $v_f$ by Bloch oscillations (red dotted lines), keeping lattice intensity and velocity chirp constant. In contrast, the optimal launch sequence consists of three steps: After deceleration by Bloch oscillations to $-8\hslash k/m$, a Gaussian-shaped light pulse drives double Bragg diffraction such that the BEC obtains $+8\hslash k/m$ followed by a second acceleration with Bloch oscillations (black solid lines). (b) Absorption images depict the corresponding atom distributions approximately 10 ms after the acceleration phases. Atoms can be decelerated almost lossless by Bloch oscillations to $-8\hslash k/m$ (left). However, large losses occur when the speed temporarily vanishes as in the case of an acceleration from $-8$ to $+8\hslash k/m$ (middle). The launch efficiency is enhanced to 75% by our new method (right). (c) With relaunch, the MZI can be extended to larger times leading to an improved sensitivity. The normalized interference signal obtained for $T=25\mathrm{ms}$ with first-order Bragg diffraction, reveals that vibrations induce the phase to scatter over the complete $2\pi$ interval. Nevertheless, the contrast determined by statistical analysis of the signal fluctuations [54] is $C=A/P_0=0.8$, corresponding to a 20-fold increased intrinsic sensitivity of $\mathrm{\Delta }g/g=1.7\times {10}^{-7}$.