Optimizing quantum-metrology protocols with Heisenberg limit scaling*

Optical lattice clocks operating near the standard quantum limit (SQL) employ uncorrelated ensembles of cold trapped atoms to reach unprecedented accuracy. Their phase-detection precision is proportional to the square root of the number of atoms. That scaling can be improved when including quantum effects such as entanglement and non-classical correlations. Nonlinear interactions such as the one-axis twisting (OAT) Hamiltonian can generate many-body entangled states such as spin squeezed states (SSSs) that can improve the precision scaling beyond the SQL. Recently, it has been shown that an effective time-reversal protocol consisting of an OAT pulse which is time-reversed after a perturbation can give rise to the more fundamental Heisenberg limit (HL) scaling [1]. In the HL, precision improves proportionally to the number of atoms. This remains true even when considering experimental limitations that further reduce the metrological gain (increasing the distance to the HL but not the 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 work, we generalize the time-reversed OAT approach by considering a short pulse sequence of alternating OAT and rotations instead of a single OAT pulse. By doing so, we can optimize the precision and minimize the contrast loss. While our proposed method can be applied to any existing OAT experiment, we will focus our discussion on the potential implementation in an optical lattice clock atom experiment, where the OAT is created by cavity feedback.

[1] S. Colombo et al, Time-reversal-based quantum metrology with many-body entangled states, arXiv:2106.03754 (2021).