Phase-accumulating hyperfine strain sensing with rare-earth-ion phase memories

Abstract

Long-lived hyperfine coherences in rare-earth-ion crystals provide controlled phase evolution windows for metrology. We use this resource to propose an experimental protocol for accessing strain shifts of ground state hyperfine transitions in non-Kramers rare-earth-ion doped (REID) materials, a quantity that is difficult to access directly with conventional spectroscopic methods. Starting from the crystal field Hamiltonian, we relate the response to strain-dependent effective quadrupole and Zeeman tensors, including changes in electronic wave functions, virtual electronic admixtures, and the bare nuclear quadrupole interaction. The protocol optically prepares a selected hyperfine class, uses a phase-controlled rf $π/2$ pulse to create the sensing coherence, and applies synchronized dynamical decoupling pulses during the phase evolution interval so that a coherent ac strain drive accumulates phase rather than averaging away. The accumulated phase is then retrieved by Raman heterodyne readout. The resulting framework provides a route to understanding strain-induced hyperfine couplings in non-Kramers REID systems.