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Physica Scripta

Delaying disappearance of entanglement by the linear modulation of atom-field coupling

Yao-Hua Hu, Yong-Gang Tan

Published Jun 6, 2014• 6 citations
Publisher

Abstract

By considering a double Jaynes–Cummings (JC) model with linear modulation of the atom-field coupling coefficients, we investigate the entanglement evolution between two atoms, and focuss on the effect of the linear sweep on the entanglement. The results show that the entanglement is very sensitive to the linear modulation of the atom-field coupling coefficients. Both for one-photon processes and for two-photon processes, the disappearance of the initial entanglement is delayed due to the linear modulation as compared to the double standard JC model, and the delayed time is long or short depending on the value of the parameters in the modulation function. Moreover, the entanglement of the two atoms in the double standard JC model disappears periodically. However, this periodicity is completely lost in the linear modulation case. In addition, the larger the photon numbers in the cavities, the shorter the delayed time of the disappearance of the initial entanglement.

DOI
10.1088/0031-8949/89/7/075103

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By considering a double Jaynes–Cummings (JC) model with linear modulation of the atom-field coupling coefficients, we investigate the entanglement evolution between two atoms, and focuss on the effect of the linear sweep on the entanglement. The results show that the entanglement is very sensitive to the linear modulation of the atom-field coupling coefficients. Both for one-photon processes and for two-photon processes, the disappearance of the initial entanglement is delayed due to the linear modulation as compared to the double standard JC model, and the delayed time is long or short depending on the value of the parameters in the modulation function. Moreover, the entanglement of the two atoms in the double standard JC model disappears periodically. However, this periodicity is completely lost in the linear modulation case. In addition, the larger the photon numbers in the cavities, the shorter the delayed time of the disappearance of the initial entanglement.
A model containing two two-level atoms and a single-mode cavity is considered, and the effect of the time-dependent atom-field couplings on entanglement between the two atoms is studied. The results indicate that both for one-photon processes and for two-photon processes, the disappearance of the initial entanglement is delayed due to the linear modulation of the atom-field coupling coefficients as compared to the constant coupling model. The delayed time of the disappearance of the initial entanglement for the two-photon processes is much longer than that for the one-photon processes in the case of adiabatic variation.
Extending the double Jaynes–Cummings model to a more complicated case where the mode–mode competition is considered, we investigate the entanglement character of two isolated atoms by means of concurrence, and discuss the dependence of atom–atom entanglement on the different initial state and the relative coupling strength between the atom and the corresponding cavity field. The results show that the amplitude and the period of the atom–atom entanglement evolution can be controlled by the choice of initial state and relative coupling strength, respectively. We find that the phenomenon of entanglement sudden death (ESD) is sensitive to the initial conditions. The length of the time interval for zero entanglement depends not only on the initial degree of entanglement between two atoms but also on the relative coupling strength of atom–field interaction. The ESD effect can be weakened by enhancing the mode–mode competition between the three- and single-photon processes.
Considering a double two-photon JC model, we investigate the entanglement between the two two-level atoms and that between the two cavity fields, and study the effect of the Stark shift on entanglement. The results show that, on the one hand the atom–atom and cavity–cavity concurrences evolve periodically with time and the periods are affected by the Stark shift; on the other hand, the two atoms are not disentangled at any time when the Stark shift is considered, and for large values of the Stark shift parameter, the two atoms can remain in a stationary entangled state. In addition, we find that the so-called entanglement sudden death can occur under appropriate conditions on the dynamic Stark shift for a certain initial state of the system.
The effect of retardation in the atom-field interaction on the dynamics of entanglement in a double Jaynes-Cummings system is investigated. We consider large cavities in which a finite time necessary for light to travel between the atoms and the cavity mirrors may result in retardation effects. Our results demonstrate the qualitatively new behaviour observable in the time evolution of entanglement when the retardation effects are included. Solutions for single and double excitation in the system are presented. We follow the temporal evolution of an initial entanglement and find that the evolution is affected drastically by the retardation effects. In particular, the harmonic oscillations of the atomic populations and the concurrence, characteristic of single-mode Jaynes-Cummings systems, are suppressed when the retardation effects are included. The process of revival of the entanglement degrades with an increasing number of the cavity modes to which the atoms are coupled. It is also found that the effect of the retardation on the doubly excited states is more drastic than on the single excitation states that at relatively short times, the retardation leads to a complete distortion of entanglement carried by a doubly excited state.
In this research, we investigate the entanglement between two cavities, each consisting of a two-level atom and a deformed multi-photon field. The model used in this study is the deformed Jaynes-Cummings (DJC) model. A physical interpretation of the introduced model is that there are two separate cavities with Kerr-like environments, each containing a two-level atom and a non-deformed multi-photon field, where each atom interacts locally with its corresponding field. Generally, we assume that the coupling constants between the atoms and fields are unequal, and we also consider non-zero detuning. We prove that the simple rules applicable to symmetric cavities without detuning do not hold for asymmetric cavities. We will show that the presence of asymmetric cavities and detuning are factors that can be used to control entanglement. Additionally, we examine the effects of deformed fields (Kerr-like environments) on the temporal evolution of entanglement and demonstrate that they cause the entanglement to become more oscillatory. We will show that when the sign of entanglement changes, the temporal evolution of entanglement will be completely different. We consider two different initial states of the system and show that the temporal evolution of entanglement will differ for these two states. In fact, the temporal evolution of entanglement depends on the initial state of the system. To measure the entanglement, we use the concurrence parameter, where a value of one indicates maximum entanglement and a value of zero indicates no entanglement. We will also show that an initial maximum atomic entanglement can be transferred to another pair of qubits, and the type of this qubit pair depends on whether the ratios of the coupling constants are even or odd. We demonstrate that for odd ratios of coupling constants, the initial maximum atomic entanglement can be completely transferred to the fields at a specific time.