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Journal of Qufu Normal University

SPONTANEOUS EMISSION OF ATOM AND QUANTUM ENTANGLED STATE IN J-C MODEL

Zuo Zhan

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

Through studying the interaction between a two_level atom and a single mode emission field in rotating_wave approximations of Jaynes_Cummings Model, the atom and the field are in a coupled superposition state_entangled state is obtained. The expectation value of atom dipole moment is always zero, but the fluctuation of dipole moment is a constant, but not zero. Therefore it is concluded that the spontaneous emission of atoms is caused by the fluctuation of dipole moment, not by the dipole moment oscillation of the atomic system. The property of the entanglement is also studied and it is obtained that information entropy and the amount of entanglement are oscillating with time_evolution periodically and are related with the coupling coefficient and detuning. The quantum state changes between disentangled state and entangled state. The quantum state will be entangled state for a long time when the detuning is small.

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Through studying the interaction between a two_level atom and a single mode emission field in rotating_wave approximations of Jaynes_Cummings Model, the atom and the field are in a coupled superposition state_entangled state is obtained. The expectation value of atom dipole moment is always zero, but the fluctuation of dipole moment is a constant, but not zero. Therefore it is concluded that the spontaneous emission of atoms is caused by the fluctuation of dipole moment, not by the dipole moment oscillation of the atomic system. The property of the entanglement is also studied and it is obtained that information entropy and the amount of entanglement are oscillating with time_evolution periodically and are related with the coupling coefficient and detuning. The quantum state changes between disentangled state and entangled state. The quantum state will be entangled state for a long time when the detuning is small.
Abstract. We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r12 and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small inter-atomic separations, in contrast to the small sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulae for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r 12 and interact with each other via the dipole–dipole interaction, and the antisymmetric state of the system is included throughout, even for small interatomic separations, in contrast to the small-sample model. It is shown that for sufficiently large values of the dipole–dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
The entangled properties of motorial atom and field in the two-photon Jaynes-Cummings model with atomic motion are studied by using the quantum information theory.It is shown that:(1) When the parameter p of the field model structure with atomic motion is smaller,the entanglement of system is not provided with the characteristic of periodic oscillations,when the value of p is greater,the entanglement of system is obviously provided with the characteristic of periodic oscillations,the oscillation period is as much again as atom is resting.When motorial atom is prepared in ground state or excited state,the system is in the disentangled state;when motorial atom is prepared in coherent superpositions states,the entanglement occurs between motorial atom and field.
We investigate the time evolution of the entanglement in the interacting system of a single two-level atom and a single mode coherence field with phase decoherence and discuss the influences of the coupling constant of light and atoms,mean photon number of light and detuning.The results show that the oscillating frequency of the entanglement of the system will increase with the increasing of the coupling constant of light and atoms and the mean photon number of light.The influence of the detuning on time evolution of the entanglement is obvious without phase decoherence and the quantum state of the field and atom will stay in a most entangled state for a long time when the detuning is proper.The phase decoherence causes the fading of entanglement when the system is resonant and it will fade to zero at last.The entanglement of the system is a fading oscillation at first with phase decoherence.The detuning restrains the phase decoherence with the time evolution.In this case the entanglement of the system will not fade to zero at last.The oscillating amplitude of the entanglement is lessening at first and the entanglement will quickly become a constant value with the increasing of detuning.The system will stay in an entangled state with phase decoherence if the detuning is proper.
According to the complete quantum theory,the quantum field-entropy evolution properties in a system of the two coupled two-level atoms interacting with a single-mode odd-coherent state light field are studied.Through numerical calculation the influence of the initial mean photon number n_0,the coupled intensity g of interaction between the single-mode field and atoms,and the coupled intensity g_a of dipole-dipole interaction between the two coupled atoms on the quantum field-entropy evolving while the initial state of the light field is a single-mode odd-coherent and the two coupled two-level atoms lay in different Einstein Poclolsky Rosen(EPR) entangled state respectively.The results indicate that the time evolving of quantum field-entropy is closely related to the initial atoms state.The quantum field-entropy evolution can display the phenomena of entanglement and disentanglement while they are periodically under the condition of intensity field(n_01). Meanwhile the phenomena of quantum interference is also discovered.The periodicity of the quantum field-entropy anomalous oscillation decreases gradually with the increasing of g values.When g_a is an especial constant,it is shown that the phenomena of period collapse-reversion can present.