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Optics Express

Persistent asymptotic entangled states in an interacting asymmetric Tavis-Cummings model

Omar Qisieh, Wiam Al-Dress, Gehad Sadiek

Published Apr 14, 2026• 0 citations
Publisher

Abstract

The rapid advancement in the field of quantum information processing sparked great interest in developing what are believed to be new promising qubits made of artificial atoms as well as customized natural ones. Those qubits enjoy mutual interaction with other qubits of the same type or different one in what is known as the hybrid quantum systems. In this work, an asymmetrical generalized version of the famous Tavis-Cummings model is used to prototype the behavior of such hybrid systems. The problem is explored in its full generality by analytically solving the model while upholding realistic conditions, namely two mutually interacting non-identical qubits coupled off-resonance to a radiation field, with non-linearity in both the cavity medium and the qubit-field interaction. The work focuses on studying the entanglement dynamics of the system and its asymptotic behavior, with special emphasis on entanglement sudden death (ESD) and birth (ESB). The system is found to exhibit typical death-revival pattern, which asymptotically approaches a pseudo-steady state that is considerably sensitive to the degree of asymmetry between the qubits, the initial state, and other system parameters. We show that for certain initial entangled states, the system parameters can be tuned to provide maximized persistent terminal entanglement values that are steady and free of any collapse-revival patterns or ESD. In contrary, the disentangled initial states asymptotically attain scattered entanglement maxima that lack any systematic behavior. This terminal entanglement behavior can be attained more rapidly by strengthening the mutual interaction between the qubits, a process that is now experimentally accessible with contemporary artificial qubit systems. These results pave the road for preparing strongly entangled qubits in long-life steady states that are crucially needed for performing efficient quantum information algorithms. These systems can be realized using typical qubits such as quantum dots, trapped ions, superconductors, and Rydberg atoms, in either cavity or circuit QED structures.

DOI
10.1364/oe.587079

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The rapid advancement in the field of quantum information processing sparked great interest in developing what are believed to be new promising qubits made of artificial atoms as well as customized natural ones. Those qubits enjoy mutual interaction with other qubits of the same type or different one in what is known as the hybrid quantum systems. In this work, an asymmetrical generalized version of the famous Tavis-Cummings model is used to prototype the behavior of such hybrid systems. The problem is explored in its full generality by analytically solving the model while upholding realistic conditions, namely two mutually interacting non-identical qubits coupled off-resonance to a radiation field, with non-linearity in both the cavity medium and the qubit-field interaction. The work focuses on studying the entanglement dynamics of the system and its asymptotic behavior, with special emphasis on entanglement sudden death (ESD) and birth (ESB). The system is found to exhibit typical death-revival pattern, which asymptotically approaches a pseudo-steady state that is considerably sensitive to the degree of asymmetry between the qubits, the initial state, and other system parameters. We show that for certain initial entangled states, the system parameters can be tuned to provide maximized persistent terminal entanglement values that are steady and free of any collapse-revival patterns or ESD. In contrary, the disentangled initial states asymptotically attain scattered entanglement maxima that lack any systematic behavior. This terminal entanglement behavior can be attained more rapidly by strengthening the mutual interaction between the qubits, a process that is now experimentally accessible with contemporary artificial qubit systems. These results pave the road for preparing strongly entangled qubits in long-life steady states that are crucially needed for performing efficient quantum information algorithms. These systems can be realized using typical qubits such as quantum dots, trapped ions, superconductors, and Rydberg atoms, in either cavity or circuit QED structures.
We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole-dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole-dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.
We study a model of two coupled two-level atoms (qubits) interacting off-resonance (at non-zero detuning) with a single mode radiation field. This system is of special interest in the field of quantum information processing (QIP) and can be realized in electron spin states in quantum dots or Rydberg atoms in optical cavities and superconducting qubits in linear resonators. We present an exact analytical solution for the time evolution of the system starting from any initial state. Utilizing this solution, we show how the entanglement sudden death (ESD), which represents a major threat to QIP, can be efficiently controlled by tuning atom-atom coupling and non-zero detuning. We demonstrate that while one of these two system parameters may not separately affect the ESD, combining the two can be very effective, as in the case of an initial correlated Bell state. However in other cases, such as a W-like initial state, they may have a competing impacts on ESD. Moreover, their combined effect can be used to create ESD in the system, as in the case of an anti-correlated initial Bell state. A clear synchronization between the population inversion collapse-revival pattern and the entanglement dynamics is observed at all system parameter combinations. Nevertheless, only for initial states that may evolve to ESD, the population inversion revival oscillations, where exchange of energy between the atoms and the field takes place, temporally coincide with the entanglement revival peaks, whereas the population collapse periods match the ESD intervals. The variation of the radiation field intensity has a clear impact on the duration of the ESD at any combination of the other system parameters.
In this paper, we investigate the entanglement dynamics of two entangled two-level atoms with initial X state and dipole-dipole coupling intensity in Tavis-Cummings model. The interesting phenomena of entanglement sudden death as well as sudden birth appear during the evolution process. We analyze in detail the effect of purity of initially entangled state of two atoms, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions for the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. The results show that the above system parameters affect the concurrence, entanglement sudden birth and sudden death remarkably, the dipole-dipole coupling intensity affects amplitudes of the concurrence oscillation and leads time interval of the ESD to decrease. With the increasing of the purity, the time of entanglement sudden death and entanglement sudden birth will decrease, it is also notable that invariant and stable entanglement, which can be controlled by different initial states of the atoms, occurs for particular initial X state.
A double Tavis-Cummings model (DTCM) is developed to simulate the entanglement dynamics of realistic quantum information processing where two entangled atom-pairs AB and CD are distributed in such a way that atoms AC are embedded in a cavity a while BD are located in another remote cavity b .T he evolutions of different types of initially shared entanglement of atoms are studied under various initial states of cavity fields. The results obtained in the DTCM are compared with that obtained in the double Jaynes- Cummings model (DJCM) (M. Yonac, T. Yu, J.H. Eberly, J. Phys. B40, S45 (2007)) and an interaction strength theory is proposed to explain the parameter domain in which the so-called entanglement sudden death occurs for both the DTCM and DJCM.
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.
Abstract An exact solution for the evolution operator of the multiphoton three-qubit Tavis–Cummings model was found. On this basis, the entanglement dynamics and the phenomenon of entanglement sudden death for entangled initial W-, GHZ-, and GHZ-like qubit states and the thermal state of the resonator were studied by means of pairwise negativity and fidelity. The results of entanglement parameters calculations showed that in the nonlinear multiphoton processes, the atomic entanglement is stronger than in the linear one-photon process. We also obtained that the so-called sudden death phenomenon occurs only for some kind of initial qubit states and some thermal noise intensities, i.e. the phenomenon is sensitive to the initial conditions. The length of the time interval for the zero entanglement is dependent on not only the initial qubit states but also the photon transition multiple. We also showed that for large values of the multiple, only one W-type initial state and one GHZ-like initial state are the long-lived and maximally persistent and robust states.