Optimally entangled atomic states for quantum metrology*

Optical lattice clocks operating near the standard quantum limit (SQL) employ uncorrelated ensembles of cold trapped atoms to reach unprecedented accuracy. Their precision is proportional to the square root of the number of atoms. Going beyond the SQL requires correlations between the atoms. That is, nonlinear interactions such as the one-axis twisting Hamiltonian may be used to generate many-body entangled states such as spin squeezed states (SSS). For a SSS, noise is reduced for one quadrature and enhanced for the orthogonal quadrature. Although SSS improve the precision scaling beyond the SQL, they are limited due to the curvature of the Bloch sphere and cannot reach the fundamental Heisenberg limit (HL) of quantum metrology where the precision scales linearly with the number of atoms. Moreover, experimental limitations further reduce the metrological gain and scaling. For example, photon scattering into free space when using light-mediated interactions to implement one-axis twisting induces contrast loss in the measured signal.

In our presentation, we introduce a family of entangled states that leads to an improvement in the precision scaling proportional to the Heisenberg limit. We show how to create these entangled states using a combination of standard controls and the one-axis twisting Hamiltonian. The required types of controls have already been used previously to achieve the best sensitivity improvement beyond the SQL to date. Thus, we expect the proposed family of quantum states to be achievable with only small modifications to existing experimental setups, improving metrological scaling beyond the current state of the art. We discuss general considerations for the experimental implementation and their impact on the final metrological gain and precision scaling.