Quantum Interference Effect And The Theory Of Quantum State Measurement

Three quantum interferences based on different physical mechanism,which derives from a weak field probing on the quantum states prepared by a Gaussian pulse,were demonstrated in this paper.Two projects about quantum state measurement were also presented.One is to measure the geometric phase of quantum state prepared by Gaussian pulse with interference fringes in the spectral domain,and the other is to measure the energy spacing of A-T splitting with incoherent light.The paper is divided into four parts:Part one:The quantum system prepared by Gaussian pulse was investigated firstly.It was found that the quantum phase cumulated during the weak nonadiabatic evolution cannot be neglected when the system stays in a non-eigenstate.In a resonant system,the constant phase difference between two eigenstates was cumulated because the degeneration of two quantum states at the start of the Gaussian pulse.In a nonresonant system,the subtle nonadiabatic evolution can also cumulate the phase difference.The cyclic point can be found in a quantum system driven by a Gaussian pulse and the geometric phase can be observed in this system.Secondly,By simulating numerically with density matrix motion equation and discerning the physical process with analytical expression,we found that the quantum phases are sensitive to the different quantum interference effects and the geometric phase plays an important role in the type-Ⅱquantum interference.In particular, the period of the signal for the different type quantum interferences is predicted correctly by our explicit formulation of various interference.Finally,based on the quantum interferences,a novel project to measure the geometric phase with fringes in spectral domain was present in this paper.To avoiding the tailor effect of the probe field,the probe pulse should be longer than the pump pulse.The nonadiabatic phase can be picked up by the typeⅠinterference and measured in spectral domain.The Geometric phase can be picked up by the typeⅡinterference and measured in spectral domain.The geometric phase in a nonresonant system can also be measured by this method.The typeⅠquantum interference will be depressed in a system driven by a linear chirp Gaussian pulse because of the selective population.Part two:Firstly,we study the oscillating of the transition in the two-state system driven by a linearly weak chirped pulse.The analytical expression of the wave function of the excited state is similar to the Fresnel diffraction by an edge.We show that the population oscillation results from the quantum diffraction of the wave function in time domain.Then in a system driven by the strong pulse,it was also obtained that the behavior of population on the final state is similar to the Fresnel diffraction by an edge.Moreover,the typeⅠquantum interference will change the phase of the probability function,and lead to a higher numbers of oscillation.The typeⅡquantum interference will affect the population prominently and lead to the population be modulated by the pulse area.Part three:A novel and high resolution method for measuring quantum states with incoherent light in the time-domain is presented.Taking Autler-Townes as an example,the physics process and the evolutive rule during measuring are discussed by an explicit and analytical formulation in detail;and the influence of measuring process on the quantum state is disclosed.With this method,the very small splitting of the energy-level and large energy-level space can be measured availably at the same time,while the transverse relaxation rate of the system can be obtained directly by testing the decay time of the signal.Comparing with the characteristics of the measuring methods between the time-domain and frequency-domain,we found that the measuring quantum states with incoherent light in the times-domain is robust and valid for disclosing information of the quantum stare entirely.Part four:A degenerate two-level atomic system was considered where a strong pulse prepared the quantum state,and a weak pulse with perpendicular polarization probed the quantum system.The strong pulse drives the parallel transition and the weak pulse connects the cross transition.It was found that in the system S_1/2→P_1/2,the quantum interference affects the propagation of the weak pulse prominently.The probe field will be amplified where Cos[2θ(t′)]＜0 and absorbed where Cos[2θ(t′)]＞0.But in the system S_1/2→P_3/2,the probe field will always be amplified.