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Physics of Wave Processes and Radio Systems

Long-lived entangled states in the double Jaynes–Cummings model taking into account the qubits direct dipole-dipole interaction

Evgeny K. Bashkirov

Published Oct 10, 2025• 0 citations
Publisher

Abstract

Background. The study of entangled states in Jaynes–Cummings models and its multiqubit generalizations and extensions remains an important and relevant topic in modern quantum optics, quantum information science and solid state physics. This is due to the fact that such models naturally describe the dynamics of interaction of logical elements of quantum devices, such as quantum computers or quantum networks (qubits) with microwave fields of resonators used to control the states of qubits. In this regard, it is very important to search for the most efficient schemes of generation, control and monitoring of entangled qubit states within the framework of Jaynes–Cummings type models. Aim. To investigate the entanglement dynamics of a pair of qubits, each of which is locked in a single-mode resonator and interacts non-resonantly with the vacuum field mode, in the presence of detuning between frequencies of transitions in the qubits and frequencies of resonator modes and dipole-dipole interaction of the qubits. Methods. To analyze the dynamics of the considered system, the solution of the time-dependent quantum Schrödinger equation is investigated. The exact solution of the above equation in the case of entangled Bell-type initial qubits states is found. This is used to calculate the criterion of entanglement of a pair of qubits – negativity. Numerical modeling of the time dependence of negativity for different values of the parameters of the considered model has been carried out. Results. It is shown that the presence of detuning, the difference in the qubit-photon couplings and the intensity of the dipole-dipole interaction significantly affect the maximum degree of entanglement of the qubit subsystem during its evolution. It is found that for certain parameters of the model under consideration, the initial Bell entangled states of qubits can be considered as long-lived stable states. Conclusion. The possibility of realization of long-lived and robust two-qubit entangled states in the system under consideration has been established. The obtained results can be used for effective control and manipulation of the degree of entanglement of qubits interacting with microwave fields of resonators.

DOI
10.18469/1810-3189.2025.28.3.7-15

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We have investigated the dynamics of entanglement of two identical qubits non-resonantly interacting with one mode of a thermal electromagnetic field in a lossless cavity in the presence of a direct dipole-dipole interaction. On the basis of the exact solution the evolution equation the negativity for qubits has been found. Numerical simulation of the negativity for various model parameters has been carried out. It has been shown that the interaction of qubits with the cavity thermal field can lead to their entanglement. It has been established that the detuning and dipole-dipole interaction of qubits can be used to manipulate and control the degree of their entanglement.
Background. Interest in the study of entangled states of systems of natural and artificial atoms (qubits) interacting with selected modes of microwave resonators is associated with their use as logic elements of quantum computers. At the same time, the most important task of the physics of quantum computing is the choice of the most effective mechanisms for manipulating and controlling the entangled states of qubits in such devices. Aim. The dynamics of the entanglement of two dipole-coupled superconducting Josephson qubits induced by a thermal noise of a coplanar resonator is studied for various initial states of the qubits. Methods. Based on the exact solution of the quantum Liouville equation for the whole density matrix of the system under consideration, the time behavior of the qubit entanglement parameter (negativity) is found for chaotic thermal, pure separable, and entangled initial states of qubits. Results. It is shown that the entanglement of qubits induced by the thermal noise of the resonator is possible for both the chaotic thermal states and separable states of qubits, except the case when both qubits are excited. It has also been found that, for small values of the dipole–dipole interaction parameter, taking this interaction into account leads to an increase in the degree of entanglement. For values of the dipole-dipole interaction parameter greater than some limit value, the opposite effect takes place. It is found that for entangled initial states of qubits, the inclusion of direct interaction has a small effect on the entanglement dynamics. It is shown that the initial coherence of qubit states can lead to a significant increase in the degree of their entanglement in the presence of a dipole–dipole interaction. Conclusion. The dipole-dipole interaction can be used as an effective mechanism for qubits entanglement manipulation and controlling.
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