基于量子Fisher信息的耗散相互作用光-物质耦合常数的估计

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

量子参数估计在量子度量学中有着重要的应用,量子Cramer-Rao下界表明量子参数估计精度极限与量子Fisher信息是直接相关的.本文利用量子参数估计理论对光场与原子失谐很大(大失谐)的Jaynes-Cummings模型耦合常数进行估计.制备探测初态为Qubit系统与光场的直积态,光场分别为Fock态、热态和相干态,分别计算了这三种探测态经大失谐Jaynes-Cummings模型哈密顿量演化后复合系统以及Qubit和光场系统的量子Fisher信息.通过分析发现,复合系统的量子Fisher信息随平均光子数单调递增,Qubit基态与激发态的等权叠加态为最优探测态,此时量子Fisher信息达到最大值;当探测态的光场为Fock态和热态时,关于被估计参数的信息都包含于Qubit系统;对于大失谐Jaynes-Cummings模型耦合常数的估计,光场为热态或相干态时耦合常数的估计精度高于光场为Fock态时的精度.

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.