Quantum Fisher Information And Atomic Entropy Squeezing In Photonic Crystals

Metrology is a discipline that studies measurement and measurement errors.Meanwhile,achieving quantum precision measurement is the main task of quantum metrology combined with metrology and quantum mechanics.Since the measurement accuracy is closely related to the parameter measurement process,the improvement of the measurement accuracy means the improvement of the accuracy of the experiment.From the basic theory of parametric estimation-the Cramér-Rao theorem,we can see that the lowest boundary of the measurement is determined by the quantum Fisher information(QFI)which is the quantum extension of classical Fisher information.In particular,the QFI set the theoretically achievable limit of measurement,and the value of which is bigger,the corresponding measurement precision is higher.So how to increase QFI becomes a key issue to solve.As we all know,Heisenberg uncertainty relation is one of the most basic principles of quantum mechanics,which tells us that it is not possible to simultaneously determine two noncommutative quantum mechanical quantities no matter how the sophisticated equipment is.In spite of this,we can still reduce the fluctuation of one quadrature component by sacrificing the accuracy of another quadrature component without violating this principle,which is the well-known "squeezing" phenomenon.In order to quantify the squeezing,people put forward various definitions,including the concept of information entropy squeezing.Information entropy squeezing is the effective theoretical tool used to measure the squeezing effects produced by the interaction of atoms and fields.It is clear for us that the interaction between quantum system and the surrounding environment usually results in the loss of coherence and squeezing characteristics.Therefore,it is of practical significance to study the dynamics of QFI and entropy squeezing in open systems.Owing to existence of the photonic bandgap in photonic crystals(PCs),the systems present many novel quantum effects,such as the phenomenon of quantum capture.The study on PC environments is another topic of interest for us.Based on the current research background,this dissertation mainly investigates the influence of quantum weak measurements(WM)and quantum measurement reversal(QMR)on the QFI of two-atoms entanglement state in the photonic crystal,and their modulation effect on quantum entropy squeezing and some meaningful conclusions are presented.It is found that the accuracy of parameter measurement can be improved to a certain extent by controlling the detuning when the WM and QMR are not carried out in PCs.When ?(27)0,the QFI will decrease to a steady value larger than zero as time increases in the anisotropic PCs and the QFI oscillates then get a steady value in the isotropic PCs.When ?(29)0,the QFI decays with time to zero in both anisotropic and isotropic PCs.The QFI can be further improved by using the optimal quantum measurement operation,and the greater the WM strength,the greater QFI.So the corresponding parameter measurement accuracy is improved.However,the greater measurement strength,the smaller probability of success.By analyzing the quantum entropy squeezing dynamics in PC environment,we found that better entropy squeezing can be achieved by adjusting the detuning and WM strength.When ?(27)0,the measurement operations are beneficial to entropy squeezing,but as the increase of WM strength,the beneficial effect of entropy squeezing is weakened.In the isotropic PCs,it has a positive effect on entropy squeezing when p is bigger.When ?(27)0,the equal amplitude oscillation behavior occurs and the entropy squeezing is almost unaffected by the WM and QMR in the anisotropic PCs.In the isotropic PCs,there is also periodic oscillation behavior,but the squeezing depth is less than that of anisotropic PCs.