Quantum Metrology To Spectral Density

Metrology is devoted to develop method to measure physical parameters in high sensitivity.The precision of any metrology scheme subjected to classical physics is constrained by the shot-noise limit.How to break through this limit is an urgent need for the development of modern precision science and technology.Quantum metrology is a discipline that studies how to use quantum resources,quantum encoding and quantum measurement to improve measurement precision.It has been found that by using quantum entanglement as resources and unitary evolution as parameter encoding of quantum probes,Heisenberg's limit measurement precision far beyond the shot-noise limit can be obtained.After rapid development in recent years,quantum metrology has demonstrated its great potential in the next generation of technological innovations.On the other hand,decoherence is a physical process of attenuation of quantum coherence caused by the coupling of microscopic systems to quantum reservoir with infinite degrees of freedom.It is the main obstacle to the realization of all quantum engineering tasks with quantum coherence as resources.How to recognize decoherence and how to control decoherence is the most important issue in realizing quantum engineering tasks.Since decoherence depends sensitively on the spectral density of the quantum reservoir,precise measurement to spectral density is the main core of studying decoherence.In this thesis,we propose a quantum metrology scheme to measure the spectral density of a quantum reservoir by using two-level systems as quantum probe and the non-unitary evolution of the probe caused by its coupling to the quantum reservoir as parameter encoding.The quantum reservoir is not only a physical object that we want to measure using quantum resources,but also a source to cause decoherence of our quantum resources.Therefore,how to effectively avoid the consumption of quantum resources by decoherence and obtain a high-precision measurement to the quantum reservoir is our main motivation.By the exact non-Markovian dynamics of the probe coupled to the quantum reservoir,we found that,with the formation of a bound state in the energy spectrum of the whole system composed by the quantum probe and the reservoir,the metrology error to the parameters in the spectral density behaves as a decreasing function with the increase of the encoding time.In sharp contrast to the Markovian result,where the metrology error tends to divergent with time,the result reveals that the encoding time also can act as a resource in quantum metrology even in the non-unitary parameter encoding case.Further study demonstrates that by using the multipartite entanglement of quantum probe,the scaling relation of the metrology error to the number of probes not only can exceed the classical shot-noise limit,but also gradually approach the Heisenberg limit.We analytically derive the specific physical conditions for achieving this high-precision quantum metrology.The results provide the physical basis for highly precise quantum metrology to the spectral density of the quantum reservoir by the use of non-unitary evolution of quantum probes,which greatly enriches the traditional encoding method that only uses unitary evolution of quantum probes.Furthermore,our bound-state mechanism reveals the constructive effect of the long-time steady-state behavior of quantum probes on quantum metrology,which is not obtainable by the traditional decoherence dynamic description based on Bonn-Markov approximation.Its beneficial value lies in introducing time as a measurement resource into the scheme,which provides a new control dimension for improving the accuracy of quantum measurement.The high-precision measurement of the spectral density we obtained has positive practical significance for decoherence control in quantum engineering.