Fig. 2.
Interferometric phase and contrast vs. paths’ length. (A) The phase accumulation reveals potential gradients (single diamond geometry). The parabolic behavior indicates a linear potential gradient due to space-time area’s quadratic dependence on the number of shift operations; it is verified to be proportional to the lattice laser power (Inset). The fit to Eq. 2 determines the local force with precision 5 × 10-4 in units of g corresponding to 104 atoms sequentially interrogated in 90 min. A geometric analogue of spin echoes suppresses the accumulated phase (double diamond geometry). The recorded gradient is reduced by a factor of 10, where interferometers with equal maximal separation are compared, e.g., 12 shifts single diamond with 24 shifts double diamond. (B) The double diamond is composed of two single diamonds interspaced with a π pulse; path crossing in the middle yields a geometric cancellation of the phase. (C) The fringe contrast decays exponentially with the number of shifts. The dashed line is the exponential fit to the fringe contrast measured with shift operations replaced by idle blocks; it reflects the spin coherence time. Correcting it for the near-unity shift fidelity yields the dash-dotted line. The increased contrast in the double diamond is likely due to geometric echo refocusing. Error bars show one SEM uncertainty.