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Effects of frequency detuning and excitation quantum number on the dynamics of entanglement in the Jaynes-Cummings polariton model

Christopher Mayero, Patrick Owiny

Published Jul 19, 2021• 0 citations
Publisher

Abstract

Abstract We present a scheme for generating polaritons which are maximally entangled qubit states in the Jaynes-Cummings interaction mechanism. Considering a specific case of an atom initially in an excited state entering a cavity mode initially in vacuum state and in a non-resonant atom-field Jaynes-Cummings interaction, we demonstrate using graphical representation on the Bloch sphere that an increase in frequency detuning leads to an increase in Rabi oscillations. Analysis of the dynamical behaviour of quantum entanglement in the general Jaynes-Cummings atom-field interactions measured by concurrence show that frequency detuning and photon number parameters are vital in enhancing entanglement.

DOI
10.21203/rs.3.rs-727169/v1

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Physics of Wave Processes and Radio Systems•Oct 10, 2025•0 citations
Abstract We present a scheme for generating polaritons which are maximally entangled qubit states in the Jaynes-Cummings interaction mechanism. Considering a specific case of an atom initially in an excited state entering a cavity mode initially in vacuum state and in a non-resonant atom-field Jaynes-Cummings interaction, we demonstrate using graphical representation on the Bloch sphere that an increase in frequency detuning leads to an increase in Rabi oscillations. Analysis of the dynamical behaviour of quantum entanglement in the general Jaynes-Cummings atom-field interactions measured by concurrence show that frequency detuning and photon number parameters are vital in enhancing entanglement.
This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states.We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process.With the generated anti-polariton qubit state as one of the initial qubits, we present quantum teleportation of an atomic quantum state by applying entanglement swapping protocol achieving an impressive maximal teleportation fidelity 1 F ρ = .
In this work, the authors investigated the dynamics of entanglement of two identical two-level atoms (qubits) in the framework of the two-photon double Jaynes–Cummings model, taking into account the detuning between atoms and the double frequency of the field modes of the resonators, as well as the Kerr medium in both resonators. The authors derived the time dependence of the negativity parameter for the Bell initial states of the atoms and the vacuum states of the resonator fields. The results showed that detuning and Kerr nonlinearity leads to stabilization of the entanglement for all initial Bell-type atomic states. For some initial atomic entanglement states, the detuning and Kerr environment in the resonators can prevent the effect of sudden death of the atom-atom entanglement.
This study presents a method for producing maximally entangled qubit states, also known as entangled anti-polariton qubit states, in the anti-Jaynes-Cummings interaction mechanism. We show that, in an initial vacuum-field, the time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process, and that Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process occur in the reverse sense relative to the Jaynes-Cummings interaction process. We demonstrate quantum teleportation of an atomic quantum state using the created anti-polariton qubit state as one of the initial qubits. We accomplish a perfect maximal teleportation fidelity of unity by employing an entanglement swapping procedure.
In this paper, we investigated the entanglement dynamics between two superconducting qubits in the framework of not-resonant double Jaynes-Cummings model taking into account the direct dipole-dipole interaction. We explored the dependence of the atom-atom entanglement on the strength of the dipole-dipole interaction and detuning. The results show these parameters affect the period of negativity oscillations but not the maximum value of entanglement in contrast to two-atom Jaynes-Cummings model with common cavity mode.
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.
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.