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Acta Physica Sinica

Evolution of the quantum fidelity in a system of multimode light field interacting resonantly with a two-level atom through degenerate multi-photon process

Wang Ju-xia

Published Jan 1, 2014• 2 citations
Publisher

Abstract

The time evolution properties of the quantum fidelity in a system of multi-mode coherent light field resonantly interacting with a two-level atom via any Nj-degenerate N∑-photon transition process are studied by the fully quantum theory and numerical calculations. The analytical expressions of the quantum fidelity of field and atom, and the numerical calculation results for three-mode field interacting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number, the atomic distribution angle, the phase angle of the atom dipole, the field excitation angle, and the atomic degeneracy on the evolution of the quantum fidelity. The results obtained from the numerical calculation indicate that the above factors lead to the quantum fidelity changing with oscillation behavior. The quantum fidelity of field and atom will drastically decrease as the initial light increases, which is correlated sensitively with the fidelity. The speed change of quantum fidelity is strongly dependent on the atomic degeneracy and the intensity coupling between atoms and fields. The value and frequency of the quantum fidelity change lightly with the atomic distribution angle and the angle of light field excitation as well. The phase angles of the atom dipole almost have no influences on the quantum fidelity of field and atom. According to these properties of the quantum fidelity, we can control the speed and value of quantum fidelity in the system by these constraint conditions.

DOI
10.7498/aps.63.184203

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The time evolution properties of the quantum fidelity in a system of multi-mode coherent light field resonantly interacting with a two-level atom via any Nj-degenerate N∑-photon transition process are studied by the fully quantum theory and numerical calculations. The analytical expressions of the quantum fidelity of field and atom, and the numerical calculation results for three-mode field interacting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number, the atomic distribution angle, the phase angle of the atom dipole, the field excitation angle, and the atomic degeneracy on the evolution of the quantum fidelity. The results obtained from the numerical calculation indicate that the above factors lead to the quantum fidelity changing with oscillation behavior. The quantum fidelity of field and atom will drastically decrease as the initial light increases, which is correlated sensitively with the fidelity. The speed change of quantum fidelity is strongly dependent on the atomic degeneracy and the intensity coupling between atoms and fields. The value and frequency of the quantum fidelity change lightly with the atomic distribution angle and the angle of light field excitation as well. The phase angles of the atom dipole almost have no influences on the quantum fidelity of field and atom. According to these properties of the quantum fidelity, we can control the speed and value of quantum fidelity in the system by these constraint conditions.
Abstract The atom fidelity is investigated in a system consisting of Mtwo-level atoms and M single-mode fields by use of complete quantum theory and numerical evaluation method. The influences of various system parameters on the evolution of atomic fidelity are studied. The results show that the atomic fidelity evolves in a Rabi oscillation manner. The oscillation frequency is mainly modulated by the coupling strength between atoms and light field, the atomic transition probabilities and the average photon numbers. Other factors hardly impact on the atomic fidelity. The present results may provide a useful approach to the maintenance of the atomic fidelity in the atom cavity field systems.
The time evolution of the field quantum entropy in the system of a multi-mode coherent field interacting with a two-level atom through the non-degenerate multi-photon process is investigated using the Von Neumann reduced entropy, the analytical expression of the multimode field entropy including the frequency detuning is obtained. The numerical results for the three-mode field interacting with the atom are presented. The influence of the frequency detuning on the field quantum entropy is discussed. It is found that the frequency detuning has nearly no effect on the entanglement between the three-mode coherent field and the two-level atom when the field and the atom are near resonance, but the time evolution of the field quantum entropy is strongly dependent on the values of the frequency detuning when the field and the atom are far from resonance, especially when the frequency detuning is large enough, the field and the atom are nearly always in entangled states.
In the rotating-wave approximation,the produce and control for periodic quantum echo of atom bit interacting with a two-mode coherent light field is investigated via intensity-dependent coupling multiphoton channel by means of the full quantum theory.The effects on the evolution of the fidelity of atom bit for both the distribution form and distribution range of the average photon number of the two-mode coherent light field,and the photon number k of absorbed(emitted) as the atoms transition are discussed by numerical calculations,respectively.The system parameter of preparation and control for periodic quantum echo of atomic bits are obtained.According to the entanglement theory,the relation of the fidelity of atom bit with atomic reduced entropy is analyzed.The results show that atom bitkeeps good coherence and fidelity,and will produce periodic quantum echo for the two photon process as k=1,by regulation average photon number of the light fields being symmetrical or asymmetrical distribution and its value in a certain range.For k≥2 multiphoton process,the atom bit is always in a maximally entangled with the two-mode coherent light field so that the atom bit is in a state of partial distortion without periodic quantum echo.It is shown that the physical nature of the periodic quantum echo produce is periodic disentangled between the atom bit and the light field.
The evolution process of atomic entangled state is discussed in the interaction of light-field with atoms by use of the complete quantum theory.The influence of multi-parameter on atomic fidelity is studied.Taking advantage of computation,the results show that atoms are always in partly entangled states during the process of interaction atoms with light fields.The evolution properties of fidelity of the atomic quantum state with time appear oscillatory and collapse-revert in a manner similar to Rabi oscillation.Its oscillatory frequency is mainly modulated by the radiation intensity or photon numbers,the coupling intensity between atoms and fight field,the complex probability amplitude of atoms jump,and the complex probability amplitude of annihilate a photon in the light field.And other factors hardly effect on the atomic fidelity.Hence,the entanglement degree and fidelity of atoms could be enhanced or weakened through controlling the three above parameters.
The atom fidelity and degree of entanglement were calculated in the system consisting of M two-level atoms and M multi-mode fields by use of complete quantum theory and number computing method.Through number computing and analyzing,it was found that the atom fidelity and the atom entangled degree present always oscillatory with opposite in phase if initial atoms are in separate state, and both of their frequency gradually increase with the intensity of light field increasing.The atom fidelity tends to 0and degree of entanglement tends to 1under strongly coupling between atoms and light fields.The small fidelity is disadvantage of information transfer but high-fidelity atom information transfer can still obtained by controlling appropriately interaction time.
Using the multiphoton Jaynes-Cummings model,the dynamical properties of the fidelity of quantum states in the system that consists of a two-level atom interacting with a single-mode field via multiphoton transition are studied.The frequency of the field varying with time in the form of sine is considered.The results obtained by numerical calculations show that the time-evolution behavior of the fidelities of field and system is not influenced by the frequency variation of field,but the time-evolution behavior of the fidelity of atom is modulated by the frequency variation of field.The larger the amplitude of the field frequency variance u is,the stronger modulation interaction of the field frequency variance is.When the amplitude u is larger than a fixed value,the time-evolution behavior of the fidelity of atom will display quasiperiodic oscillation behavior.Its oscillation period is in agreement with the period of frequency varying.The initial state of atom influences the time-evolution behavior of the fidelity of atom.