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ACTA PHOTONICA SINICA

Relevance Between Fidelity and Degree of Entanglement in the System of Two-level Atoms Interacting with Multi-mode Fields

Wang Ju-xi

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

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.

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Chinese Physics•Aug 22, 2006•13 citations
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.
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.
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.
Using the complete quantum theory，the process of M two-level atoms interacting with M multi-mode light fields with intensity-dependent coupling is studied. It is found that quantum entanglement information can be transferred back and forth or be preserved between the cavity fields and atoms under certain time conditions. The entanglement states of the atoms or the cavities can be transferred when t=π/(2λ). The results are verified by numerically computing the entanglement degree. And it was shown that the entanglement states of the atoms or the cavities can be preserved when t=π/λ.
The evolution of quantum information of light field fidelity in the percedure interaction between two atoms and light field under considering atom-atom coupling and intensity-dependent coupling are investigated by mean of full quantum theory and numerical computation method.The results show that the light field fidelity relates closely with intensity of initial light field,coefficient of field-atom coupling,and coefficient of atom-atom coupling.The influence of these factors leads to fidelity oscillation.It is advantageous of improving the light field fidelity if controlling and making intensity of light weak and atom-atom coupling strong.The more stronger initial light intensity or atom-field coupling,the faster the frequency of light field fidelity and the more obvious varying regularity.The fidelity present also collapse-revert when initial light intensity or atom-atom coupling is strong.The light field could keep steady state during strongly coupling between atom and light field.
Interaction between two atoms is considered.The fidelities of quantum states in the system of the two-mode entangled coherent field interacting with atoms in Bell states are derived.The results indicate that for ideal cavity,the fidelity of the system always equals to one for the coherent maintenance state at original time.The fidelities of the system surge periodically from 0 to 1 for the etceteras Bell state at original time when average photon number of two-mode entangled coherent states cavity fields are very small.When average photon number of two-mode entangled coherent states cavity fields increase,oscillatory frequency of the fidelities of the system augments and swing decrease.For fine cavity,the fidelity of the system is humdrum exponent attenuation for the coherent maintenance state at original time.The fidelities of the system are oscillatory exponent attenuation for the etceteras Bell state at original time,and when average photon number of two-mode entangled coherent states cavity fields increase,oscillatory frequency of the fidelities of the system augments and swing decrease.
We investigate the entanglement in a system of two coupling atoms interacting with a single-mode field by means of quantum information entropy theory. The quantum entanglement between the two atoms and the coherent field is discussed by using the quantum reduced entropy, and the entanglement between the two coupling atoms is also investigated by using the quantum relative entropy. In addition, the influences of the atomic dipole–dipole interaction intensity and the average photon number of the coherent field on the degree of the entanglement is examined. The results show that the evolution of the degree of entanglement between the two atoms and the field is just opposite to that of the degree of entanglement between the two atoms. And the properties of the quantum entanglement in the system rely on the atomic dipole–dipole interaction and the average photon number of the coherent field.