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arXiv:2009.11328 · Communications in Theoretical Physics

Entanglement of two Jaynes–Cummings atoms in single-excitation space

Ya Yang, Yan Liu, Jing Lu, Lan Zhou

Published Jan 15, 2021• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1572-9494/abd0ea

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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 .
We study the dynamics of entanglement in a one-dimensional coupled-cavity array, with each cavity containing a two-level atom, via the Jaynes-Cummings-Hubbard (JCH) Hamiltonian in the single-excitation sector. The model features a rich variety of dynamical regimes that can be harnessed for entanglement control. The protocol is based on setting an excited atom above the ground state and further letting it evolve following the natural dynamics of the Hamiltonian. Here we focus on the concurrence between pairs of atoms and its relation to atom-field correlations and the involved free-field modes. We show that the extension and distribution pattern of pairwise entanglement can be manipulated through a judicious tuning of the atom-cavity coupling strength. By also including static noise in the cavity frequencies, we explore the onset of Anderson localization and its interplay with the atomic trapping known to take place in the strong-hopping regime. Remarkably, we find that the stronger the disorder is, the higher are the atom-field correlations, whereas the atomic concurrence responds nonmonotonically. Overall, our work offers a comprehensive account of the machinery of the single-excitation JCH Hamiltonian and contributes to the design of hybrid light-matter quantum networks.
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.
How to analytically deal with the general entanglement dynamics of separate Jaynes–Cummings nodes with continuous-variable fields is still an open question, and few analytical approaches can be used to solve their general entanglement dynamics. Entanglement dynamics between two separate Jaynes–Cummings nodes are examined in this article. Both vacuum state and coherent state in the initial fields are considered through the numerical and analytical methods. The gap between two nonidentical qubit-field coupling strengths shifts the revival period and changes the revival amplitude of two-qubit entanglement. For vacuum-state fields, the maximal entanglement is fully revived after a gap-dependence period, within which the entanglement nonsmoothly decreases to zero and partly recovers without exhibiting sudden death phenomenon. For strong coherent-state fields, the two-qubit entanglement decays exponentially as the evolution time increases, exhibiting sudden death phenomenon, and the increasing gap accelerates the revival period and amplitude decay of the entanglement, where the numerical and analytical results have an excellent coincidence.
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 study, we theoretically investigate a system composed of two isolated two-level atoms, each confined within an independent single-mode optical cavity. The cavities are coherently coupled via an optical fiber, enabling photon-mediated interaction between the two subsystems. Each cavity sustains a single-mode quantized electromagnetic field, and each atom couples exclusively to the field within its respective cavity. We analyze the time dependent entanglement dynamics, exploring both atom-atom and cavity-field bipartite entanglement under this hybrid interaction framework. To quantify entanglement, we employ concurrence as the measurement metric. The effects of the atoms' initial states and the optical fiber’s coupling strength on both atom-atom and field-field entanglement are analyzed. Numerical results reveal that when the coupling strength of the optical fiber is close to zero, no entanglement is observed between either the atoms or the fields. However, as the fiber coupling strength increases, entanglement emerges and exhibits collapse and revival behavior over time.