Constraints of Average Hamiltonian Theory for Quantum Sensing

Average Hamiltonian theory (AHT) approximates the evolution of a closed quantum system by defining a time-independent effective Hamiltonian, obtained through a series expansion solution of the Schrodinger equation. By generating analytical descriptions that provide insights into complex dynamical systems, AHT has demonstrated broad use in the fields of nuclear magnetic resonance (NMR) and quantum information science (QIS). More recently, application of AHT in quantum sensing has resulted in advanced magnetometry protocols for solid-state spin defects (Choi et al. 2020, Zhou et al. 2020). However, this operating regime does not meet the established criteria for convergence of the Magnus series expansion, which forms the basis of AHT. In this talk, we discuss the accuracy of AHT for (1) predictions of unitary evolution, and (2) determination of the effective gyromagnetic ratio for pulsed magnetometry protocols. These considerations are relevant to a variety of broadband and narrowband sensing sequences, and informs the attainable sensitivity associated with each protocol.