Optimizing quantum Fisher information of noisy squeezed spin states

The squeezed spin state (SSS) [1] is a highly nonclassical state which enables us to surpass the standard quantum limit (SQL) in, e.g., the Ramsey interferometry [2]. The sensitivity of the Ramsey interferometry is given by the squeezing parameter. In spin-squeezing experiments in solid-state systems, however, it is difficult to suppress the squeezing parameter below the SQL due mainly to inhomogeneity in energy splittings of spins [3].

The optimal sensitivity of such a quantum-mechanically enhanced measurement is proportional to the inverse of the quantum-Fisher information (QFI). In an ideal SSS, its QFI coincides with the inverse of its squeezing parameter. However, in noisy SSSs however, the relationship between the QFI and the squeezing parameter has yet to be understood.

In this presentation, we consider hybrid quantum systems where inhomogeneous spins interact with each other via a cavity field and noisy SSSs are formed. We numerically optimize the cavity frequency, the driving field, and the evolution time with respect to the QFI on the basis of the Bayesian optimization method [4]. The optimal sensitivity given by QFI will also be discussed.



[1] M. Kitagawa and M. Ueda, Phys. Rev. A47, 5138 (1993).

[2] D. J. Wineland et al., Phys. Rev. A50, 67 (1994).

[3] S. Dooley, EY, et., al., New J. Phys. vol. 18, 053011 (2016).

[4] https://github.com/tsudalab/combo3