Optimal initial states for quantum parameter estimation based on Jaynes–Cummings model [Invited]

Quantum parameter estimation is a crucial tool for inferring unknown parameters in physical models from experimental data. The Jaynes–Cummings model is a widely used model in quantum optics that describes the interaction between an atom and a single-mode quantum optical field. In this Letter, we systematically investigate the problem of estimating the atom-light coupling strength in this model and optimize the initial state in the full Hilbert space. We compare the precision limits achievable for different optical field quantum states, including coherent states, amplitude- and phase-squeezed states, and provide experimental suggestions with an easily prepared substitute for the optimal state. Our results provide valuable insights into optimizing quantum parameter estimation in the Jaynes–Cummings model and can have practical implications for quantum metrology with hybrid quantum systems.