Parameter Estimation In Optical Fields Environment With Quantum Fisher Information

In this thesis,we mainly consider two-level systems which interact with different kinds of Boson structured optical-field environments and study how the parameters of the environments and quantum entanglement of the systems have effects on the phase estimation precision in quantum decoherence process.We expect to provide some theoretical basis for high-precision measurement in open systems.Our main research work may be divided into three parts as follows:Firstly,we derive a geometric representation of quantum Fisher information of a twolevel system.This formula can be generalized to any mixed state.The quantum Fisher information about phase parameter could be expressed as the square of a module of its Bloch vector.By means of time-dependent quantum master equation,we furtherly investigate the dynamics of quantum Fisher information in Jaynes-Cummings model.In the case of amplitude-damping channel with Lorentzian spectrum density function,we find that the detune between the frequency of atom and central frequency of the field can impact the decay of quantum Fisher information.Under the condition of the strong system-reservoir couplings,the detune could suppress the decay of quantum Fisher information obviously.In the weakcoupling case,the detune will still suppress the decay of quantum Fisher information,but the effect is not magnificent.In the case of the phase damping channel with ohm-like spectrum density function,the parameter s will affect the dynamics of quantum Fisher information.For the sub-ohmic reservoir,the increase of s can slow down the decay of the quantum Fisher information.The values of quantum Fisher information always decrease monotonicly.For the super-ohmic reservoir,the oscillation phenomena of the quantum Fisher information may happen.Secondly,we investigate the dynamics of the precision of the parameter estimation in many driven entangled atoms,each of which interacts with a local structured Bosonic reservoir respectively.The dynamics of the quantum Fisher information for many entangled atoms is obtained by the method of the super-operator mapping.The estimation limit is superior to the standard quantum limit during a characteristic intervals.At a given time,the precision of parameter estimation can be improved to a maximal value if the number of entangled atoms is chosen to be an optimal value.However,the decay of quantum Fisher information is accelerated with the increase of the number of entangled atoms.When the coupling between atoms and Bose-field is described by ohm-like frequency spectrum function,the increase of exponent s will suppress the attenuation of quantum Fisher information to some extent.When the type of the environment is Lorentz spectrum,both the strength of couplings and detune have effects on quantum Fisher information.At last,the influence of generalized partial measurement on parameter estimation precision is also studied under the quantum noise channels.Through applying generalized local measurement on the quantum state,the influence of the polarization angle parameter of initial states can be totally eliminated in phase-damping channel.And the influence of the environment parameter can be totally eliminated in amplitude-damping channel,the influence of the polarization angle parameter can be partially eliminated in depolarizing channel.Therefore,the generalized partial measurement can protect the parameter estimation precision under the noise channels.