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

Abstract

Quantum parameter estimation is one of the most important applications in quantum metrology. The basic theory of quantum parameter estimation－quantum Cramer-Rao bound－shows that the precision limit of quantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisher information is extremely important in the quantum parameter estimation. In this paper we use quantum parameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with large detuning. 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 Fisher information of the hybrid system as well as qubit and radiation field for each probing state after the parameter evolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that the quantum Fisher information increases monotonically with the average photon number increasing. The optimal detection state is that when the qubit system is in the equal weight superposition of the ground and the excited state, at this time the quantum Fisher information always reaches a maximum value, When the radiation field of probing state is Fock state or the thermal state, the information about the estimated parameter is included only in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state is higher than that with Fock state.