Nearly-Heisenberg precision scaling in spatiotemporally correlated noise environments by optimized sensor geometry*

 We study the influence of non-collective couplings on frequency

  estimation by Ramsey interferometry in the presence of spatiotemporally

  correlated Gaussian quantum noise. For the relevant case of a bosonic

  environment, we previously found [1] that randomizing the probe positions

  makes their spatial correlations vanish on average, leading to

  super-classical, Zeno-like precision scaling in a suitable parameter

  regime and a metrological gain over the sub-SQL scaling reported in the

  collective noise limit [2]. Building up on these results, we consider a

  setup where the qubit sensors are placed in a one-dimensional regular

  lattice with noise-optimized separation. This allows us to improve the

  performance by creating negative spatial correlations between the qubits,

  and to beat the Zeno limit with both the paradigmatic GHZ state and the

  experimentally relevant one-axis-twisted state, reaching near-Heisenberg N^-35/36

  scaling with the former, and N^-7/9  scaling with the latter.