Estimation of light-matter coupling constant under dispersive interaction based on quantum Fisher information

Quantum parameter estimation is one of the most important applications in quantum metrology. The basictheory of quantum parameter estimation???quantum Cramer-Rao bound???shows that the precision limit ofquantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisherinformation is extremely important in the quantum parameter estimation. In this paper we use quantumparameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with largedetuning. The initial probing state is the direct product state of qubit and radiation field in which Fock state,thermal state and coherent state are taken into account respectively. We calculate the quantum Fisherinformation of the hybrid system as well as qubit and radiation field for each probing state after the parameterevolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that thequantum Fisher information increases monotonically with the average photon number increasing. The optimaldetection state is that when the qubit system is in the equal weight superposition of the ground and the excitedstate, at this time the quantum Fisher information always reaches a maximum value, When the radiation fieldof probing state is Fock state or the thermal state, the information about the estimated parameter is includedonly in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state ishigher than that with Fock state