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.
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.
The role of retardation in the entanglement dynamics of two distant atoms interacting with a multimode field of a ring cavity is discussed. The retardation is associated with a finite time required for light to travel between the atoms located at a finite distance and between the atoms and the cavity boundaries. We explore features in the concurrence indicative of retardation and show how these features evolve depending on the initial state of the system, distance between the atoms, and the number of modes to which the atoms are coupled. In particular, we consider the short-time and the long-time dynamics for both the multi- and subwavelength distances between the atoms. It is found that the retardation effects can qualitatively modify the entanglement dynamics of the atoms not only at multi- but also at subwavelength distances. We follow the temporal evolution of the concurrence and find that at short times of the evolution the retardation induces periodic sudden changes of entanglement. To analyze where the entanglement lies in the space spanned by the state vectors of the system, we introduce the collective Dicke states of the atomic system that explicitly account for the sudden changes as a periodic excitation of the atomic system to the maximally entangled symmetric state. At long times, the retardation gives rise to periodic beats in the concurrence that resemble the phenomenon of collapses and revivals in the Jaynes-Cummings model. In addition, we identify parameter values and initial conditions at which the atoms remain separable or are entangled without retardation during the entire evolution time, but exhibit the phenomena of sudden birth and sudden death of entanglement when the retardation is included.
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.
Abstract We study the entanglement dynamics of two atoms coupled to their own Jaynes–Cummings cavities in single-excitation space. Here, we use concurrence to measure atomic entanglement, and consider the Bell-like states to be initial states. Our analysis suggests that collapse and revival take place in entanglement dynamics. The physical mechanism behind entanglement dynamics is periodic information and energy exchange between atoms and light fields. For the initial Bell-like states, evolutionary periodicity of the atomic entanglement can only be found if the ratio of the two atom–cavity coupling strengths is a rational number. Also, whether there is a time translation between two kinds of initial Bell-like state depends on odd versus even numbers of the coupling-strength ratio.
Abstract The entanglement between two stationary qubits is a kind of valuable quantum resources in quantum information or quantum network. This paper investigates the time evolution of the entanglement between two atoms, which are initially prepared in the Bell states and each of which interacts with its own cavity field in the identical and non-identical double damping Jaynes-Cummings (J-C) system. It mainly considers the effect of the atomic spontaneous decay Γ and the decay of cavity field κ on the two-qubit entanglement in such system. While causing the decay of entanglement, Γ and κ can also play a positive role in the entanglement evolution, which may imply a way to better control and maintain the entanglement. What is more, the rules governing the transfer of entanglement between two-qubit subsystems in strong coupling regime are finally studied by taking Γ and κ into consideration .
Abstract We consider a generalized double Jaynes–Cummings model consisting of two isolated two-level atoms, each contained in a lossless cavity that interact with each other through a controlled photon-hopping mechanism. We analytically show that at low values of such a mediated cavity–cavity interaction, the temporal evolution of entanglement between the atoms, under the effects of cavity perturbation, exhibits the well-known phenomenon of entanglement sudden death (ESD). Interestingly, for moderately large interaction values, a complete preclusion of ESD is achieved, irrespective of its value in the initial atomic state. Our results provide a model to sustain entanglement between two atomic qubits, under the adverse effect of cavity induced perturbation, by introducing a non-intrusive inter-cavity photon exchange that can be physically realized through cavity-QED setups in contemporary experiments.
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.