The Noise Mechanism In Quantum Metrology And Quantum Speed Limit

Quantum metrology is the study on making higher-precision measurement of phys-ical parameters than the classically achievable one by exploiting quantum entanglement or quantum squeezing.It has diverse application prospects in future frequency standard,sensor of tiny magnetic fields,and gravitational wave detection.Quantum speed lim-it describes the most efficient evolution of a quantum system from an initial state to its orthogonal state,which plays a fundamental role in quantum control and adiabatic quantum computation.However,the ubiquitous decoherence in quantum world exert-s unexpected detrimental influences on quantum metrology and quantum speed limit.How to evaluate the influences of decoherence on quantum metrology and quantum speed limit and how to design active ways to beat the detrimental influences of deco-herence have attracted much attention in recent year.The thesis is devoted to explore these issues from the following aspects.First,we evaluate the exact impacts of local dissipative environments of each atom on quantum metrology,based on the Ramsey interferometer.The conventional study on the noise effect of such system focused on the dephasing noise.It was found that the so-called Heisenberg limit,which relates the metrology precision of the atomic frequency to the atom number as n^-1,reduces to the standard quantum limit,which scales to n as n^-1/2and is the same as the short-noise limit in classical metrology,under the Born-Markovian approximation.Further studies demonstrated that the precision raises to the so-called Zeno limit n^-3/4when the non-Markovian effect of the local dephasing noises is considered.Although the result reveals the constructive role of the non-Markovian effect on quantum metrology,it is only present in the short-encoding-time scale and tends to vanish in the long-encoding-time condition.Our exact study on the effect of the local dissipative noises of each atom on the metrology precision indicates that the Heisenberg limit in the ideal case is asymptotically recoverable.Our analysis reveals that this is essentially due to the formation of a bound state between each atom and its environment.This provides an avenue for experimentation to implement quantum metrology under practical conditions via engineering of the formation of the system-environment bound state.Secondly,we propose an active control way,i.e.,the spectrum filtering method,to suppress the effect of noise on actual quantum metrology scheme based on Ramsey interferometer.Although the Heisenberg limit is recovered asymptotically in frequency estimation scheme through reservoir engineering,the system parameters are hard to be adjusted once the system material is fabricated.This restricts the application of reservoir engineering in quantum metrology.To solve this problem,we propose a strategy to beat the dephasing and dissipative noises by periodic driving.It is found that,for both cases,the decoherence factor can be represented by an overlap integral of noise spectral density and the Fourier transform of the periodic control field.Therefore,we can make the overlap integral zero by adjusting the parameter of periodically driven field and thus the decoherence is suppressed completely.This process is what we call spectral filtering.In the context of frequency estimation scheme based on Ramsey interferometer subjected to noise,it is capable of achieving Heisenberg limit once the decoherence is completely suppressed.This investigation supplies a feasible way in achieving Heisenberg limit under realistic condition.At last,we explore the effect of periodically driving field on quantum speed limit time of open system.The quantum speed limit time of closed system characterize the minimum time interval that quantum systems with constant energy and initial energy spread?E needs to evolve between two orthogonal states,which is fundamental to the research of quantum computation.Quantum speed limit time of open system re-flects the minimum time that a quantum system reaches the equilibrium state under the influence of environment.It is a key factor to evaluate the decoherence properties of open quantum system.It has been pointed in previous work that the essence of poten-tial of quantum speed up is the formation of system-reservoir bound state.This result supplies a quantum speed up scheme by using reservoir engineering.In this thesis,we go a step further and propose a quantum speedup protocol,in which a periodic driv-ing field is applied to manipulate the formation of bound state in Floquet quasi-energy spectrum.Our result reveals that,it is possible to make the switch of open quantum system dynamics between with and without the potential of quantum speedup through adjusting parameters of periodic driving.Our further analysis demonstrates the mecha-nism of the switch:If the bound state does not exist in Floquet quasi-energy spectrum,the relative quantum speed limit time would approach a finite value,which implies a limited quantum speedup performance;If the bound state exists in Floquet quasi-energy spectrum,the relative quantum speed limit time would approach zero,which indicates a great potential of quantum speedup.In addition,an experimental scheme is raised to elucidate the mechanism we present above.Our research provides a flexible way to implement quantum speedup in experiment,what's more,it may also inspire the study on nonequilibrium states of matter.Concentrating on the decoherence control problem of quantum engineering schemes,we establish a unified theoretical framework of open and periodically driven quantum systems using bound state theory.The constructive role of the formation of system-reservoir bound state in completely restoring the superiority of quantum metrology un-der realistic condition is revealed.The positive significance of the formation of Floquet bound state in implementing quantum speedup of periodically driven open system is demonstrated.Meanwhile,we propose the spectral filtering method which supplies an experimental feasible scheme to suppress the destructive effect of decoherence on quantum metrology.