Research On Quantum Fisher Information Based On The Jaynes-Cummings Model

Quantum metrology is the study of the use of quantum mechanical principles to improve the accuracy of measurements beyond the limits of classical measurement accuracy,and quantum parameter estimation is an important theory of quantum metrology.The core problem of quantum parameter estimation is how to use quantum resources to improve the estimation accuracy of the parameter to be estimated,and quantum Fisher information is an important physical quantity used in parameter estimation theory to measure the accuracy limit of parameter estimation.In this paper,the quantum Fisher information of the relevant parameter to be estimated is investigated based on the Jaynes-Cummings model(J-C model).This model describes the interaction between a single two-energy level atom and a single-mode quantum optical field and is the most fundamental and commonly used model in the study of quantum optics and cavity quantum electrodynamics.This article investigates the effect of a range of physical quantities on parameter estimation,such as optical cavity detuning,interaction time,and statistical distribution of photon numbers,using the intensity of light-atom interactions in the model as the parameter to be estimated.The large dimensionality of the Hilbert space of the J-C model,which involves quantum states of both atoms and photons,poses difficulties for theoretical studies.We first investigate the parameter estimation problem in a separate subspace of the complete quantum state space of the J-C model,as well as the maximum quantum Fisher information that can be obtained in this subspace and its optimal initial state.We find that in general the optimal initial state of the system is related to the parameter to be estimated itself,which greatly limits the application of parameter estimation theory to practical measurements.However,when the light-atom interaction time is long,it is possible to find an optimal initial state that does not depend on the parameters to be estimated,which is of interest for practical applications.We then explore the relationship between the subspace quantum Fisher information and the J-C model full quantum state space quantum Fisher information.The results show that,in general,the quantum Fisher information in the full space is not equal to the sum of the quantum Fisher information in each subspace,which is caused by the existence of cross terms between different subspaces in the direct sum space.However,we find that when the quantum states in each subspace take their optimal initial states,the cross terms disappear and the quantum Fisher information in the complete quantum state space is equal to the sum of the quantum Fisher information in each subspace.Thus the parameter estimation in the complete quantum state space for the J-C model can be broken down into two levels of optimization,namely the optimization of the quantum states in the subspace and the optimization of the probability distribution of each subspace in the full space,which is much less complex.In the end,we not only give the maximum quantum Fisher information and the optimal initial state that can be obtained for the parameter estimation of the coupling strength in the J-C model,but also compare the advantages and disadvantages of parameter estimation accuracy for different statistical distributions of photons.This study provides an effective method for quantum parameter estimation of the coupling system between light and atoms,and also provides theoretical basis and guidance for how to design and utilize photon statistical distributions to improve measurement accuracy in experiments.