Quantum Entanglement And Quantum Metrology In Photonic Crystals

Metrology is a discipline to study measurement and measurement error.With the development of technology in recent decades,the research about precision of physical quantity has been carried out from macro scale to micro scale.The combination of metrology and quantum mechanics leads to the emergence of quantum precision measurement,which is one of wide attention field of researches.In the quantum metrology field,the quantum Fisher information(QFI)is a key concept which gives a theoretically achievable limit on the precision when estimating an unknown parameter?.As one of the most important resources in quantum information processing,quantum entanglement has been extensively studied in theories and experiments.The present study shows that the quantum entanglement is not only have important applications in quantum communication,but also make important contribute to the development of metrology.Therefore,it is of vital significance to consider the relationship of quantum fisher information and entanglement.In 2010,researchers identified an optimal method for estimating the expectation value from a noisy quantum system.They quantified the information that can be obtained by the measurement in terms of the Fisher information and find its value for the optimal measurement.Recently,people have turned their attention to the problem of parameter estimation in the system of photonic crystal.In photonic crystals,the periodic dielectric structures lead to the formation of a photonic band gap(PBG),which is one of the most promising platforms for hybrid quantum information processing.Motivated by current studies,in this paper,we will investigate the influence of parameters on the measurement precision in N qubits system coupled with isotropic photonic crystal and anisotropic photonic crystal.The analytic expression of the estimation precision with unknown parameters is given by using the time evolution of the Kraus operators.In addition,we have studied the effects of the photonic crystal environment on quantum entanglement by the analytic expression of GM concurrence of N qubits,which depends on detuning 8 and particle number N.The conclusion is:the parameter measurement precision can be greatly improved by controlling the amount of detuning.It is more advantageous for us to improve the parameter precision when the atomic transition frequency lies in photonic crystal's band gap.In addition,we also found that the increase of particle number will lead to a lower precision.Likewise,the similar effect of the detuning and the number of particle on entanglement also can be found.If the detuning of atomic transition frequency and photonic crystal band edge frequency is less than zero,it would be conducive to the preservation of the entanglement measured by the measure of GM concurrence.However,the phenomenon of entanglement sudden death will happen with the increasing of the number of particle.Moreover,we further confirm that entanglement is a necessary but not sufficient condition to enhance the parameter precision.Finally,by comparing the case of isotropic photonic crystal with anisotropic one,ones can known that anisotropic photonic crystal is more beneficial to parameter estimation and the preservation of entanglement.These results provide us a clear train of thought to protect the entanglement and improve the accuracy of measurement.