The time evolution of the field quantum entropy and entanglement in a system of multi-mode coherent light field resonantly interacting with a two-level atom by de-generating the multi-photon process is studied by util...The time evolution of the field quantum entropy and entanglement in a system of multi-mode coherent light field resonantly interacting with a two-level atom by de-generating the multi-photon process is studied by utilizing the Von Neumann re-duced entropy theory,and the analytical expressions of the quantum entropy of the multimode field and the numerical calculation results for three-mode field inter-acting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number,the atomic distribution angle and the phase angle of the atom dipole on the evolution of the quantum field entropy and entanglement. The results obtained from the numerical calculation indicate that: the stronger the quantum field is,the weaker the entanglement between the quan-tum field and the atom will be,and when the field is strong enough,the two sub-systems may be in a disentangled state all the time; the quantum field entropy is strongly dependent on the atomic distribution angle,namely,the quantum field and the two-level atom are always in the entangled state,and are nearly stable at maximum entanglement after a short time of vibration; the larger the atomic dis-tribution angle is,the shorter the time for the field quantum entropy to evolve its maximum value is; the phase angles of the atom dipole almost have no influences on the entanglement between the quantum field and the two-level atom. Entangled states or pure states based on these properties of the field quantum entropy can be prepared.展开更多
The Cheeger’s inequalities and some existence criteria for spectral gap and for general symmetric forms are established. The criteria are also extended to general reversible Markov processes but not reported here. Ev...The Cheeger’s inequalities and some existence criteria for spectral gap and for general symmetric forms are established. The criteria are also extended to general reversible Markov processes but not reported here. Even though in the past several decades, the topics have been widely studied, as far as we know the first problem in the unbounded case and the second one in the general case remain open.展开更多
基金the Natural Science Foundation of Shaanxi Province of China (Grant No 2001SL04)the Science and Technology Key Task Foundation Item of Shaanxi Province (Grant No 2002K05-G9)
文摘The time evolution of the field quantum entropy and entanglement in a system of multi-mode coherent light field resonantly interacting with a two-level atom by de-generating the multi-photon process is studied by utilizing the Von Neumann re-duced entropy theory,and the analytical expressions of the quantum entropy of the multimode field and the numerical calculation results for three-mode field inter-acting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number,the atomic distribution angle and the phase angle of the atom dipole on the evolution of the quantum field entropy and entanglement. The results obtained from the numerical calculation indicate that: the stronger the quantum field is,the weaker the entanglement between the quan-tum field and the atom will be,and when the field is strong enough,the two sub-systems may be in a disentangled state all the time; the quantum field entropy is strongly dependent on the atomic distribution angle,namely,the quantum field and the two-level atom are always in the entangled state,and are nearly stable at maximum entanglement after a short time of vibration; the larger the atomic dis-tribution angle is,the shorter the time for the field quantum entropy to evolve its maximum value is; the phase angles of the atom dipole almost have no influences on the entanglement between the quantum field and the two-level atom. Entangled states or pure states based on these properties of the field quantum entropy can be prepared.
文摘The Cheeger’s inequalities and some existence criteria for spectral gap and for general symmetric forms are established. The criteria are also extended to general reversible Markov processes but not reported here. Even though in the past several decades, the topics have been widely studied, as far as we know the first problem in the unbounded case and the second one in the general case remain open.
