Atomic Coherence Time and Measurement Precision Limits in a Wannier-Stark Lattice Clock

Optical clocks are the most accurate and precise measurement devices created, with applications ranging from tests of fundamental physics to redefinition of the SI second. Measurement precision in atomic clocks is limited by quantum projection noise (QPN), which depends on the number of uncorrelated atoms interrogated and atomic coherence time. To maximize coherence time in our system, we operate with a dilute, 1 mm long cloud of fermionic Sr⁸⁷ atoms trapped in a Wannier-Stark lattice. In this regime, we systematically map out the lattice-depth and density dependence of our atomic coherence times. Dephasing is minimized at a lattice depth of about 10 photon recoils, where the contribution of on-site p-wave interactions balances with off-site s-wave interactions. Even at this optimum, coherence times remain limited by atomic interactions and depend on the local density within our gaussian cloud. Atom-atom coherence times reach 60 seconds between two 250 𝜇m regions with an average of ~12 atoms per lattice site and 90 seconds between two 250 𝜇m regions with an average of ~3 atoms per lattice site. For a given dead time between succesive measurements, there is a balance between atom number and the resulting coherence time which optimizes measurement stability. We leverage this understanding of coherence times in our system to achieve record level self-synchronous stability of 1.5 x 10^-18 / √τ, with τ the averaging time. The challenges we present will inspire new system designs and the future use of entanglement.