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Modern Physics Letters A

The quantum communication efficiency of the fractional anti-Jaynes–Cummings model

Eman G. El-Hadidy, K. El Anouz, NASSER METWALLY

Published Sep 7, 2023• 7 citations
Publisher

Abstract

The efficiency of the fractional state that is generated between a single atom and field by using anti-Jaynes–Cummings model (AJCM) is discussed. The fractional degree and the interaction parameters may be used as controllers to increase the efficiency of the fractional state in the context of quantum communication. It has been shown that, the quantum correlation, capacity, and the ability of the fractional state, increase suddenly/gradually at small/large fractional degree, respectively. At small fractional orders, the constant behavior for all these phenomena is displayed at a short interaction time. The fractional quantum state that is generated by the anti-Jaynes–Cummings model is more efficient than that generated by the well-known Jaynes–Cummings model (JCM), where it can be used to teleport an unknown two-qubit state with larger fidelity.

DOI
10.1142/s0217732323501262

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The efficiency of the fractional state that is generated between a single atom and field by using anti-Jaynes–Cummings model (AJCM) is discussed. The fractional degree and the interaction parameters may be used as controllers to increase the efficiency of the fractional state in the context of quantum communication. It has been shown that, the quantum correlation, capacity, and the ability of the fractional state, increase suddenly/gradually at small/large fractional degree, respectively. At small fractional orders, the constant behavior for all these phenomena is displayed at a short interaction time. The fractional quantum state that is generated by the anti-Jaynes–Cummings model is more efficient than that generated by the well-known Jaynes–Cummings model (JCM), where it can be used to teleport an unknown two-qubit state with larger fidelity.
A fractional quantum state has created between two-qubit system by a Heisenberg XYZ model in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The impact of the initial state settings and the interaction parameters on the amount of the quantum correlation is discussed. We used the concurrence and local quantum uncertainty to quantify these correlations. It is shown that, both quantifiers increase suddenly/gradually depending on the order of the fractional state, and whether the system is ferromagnetic or anti-ferromagnetic. The fractional parameter may increase/ stabilized the memory of the generated fractional state. Small values of the DM interaction can maximize the initial quantum correlation of a partial entangled state. The possibility of using these fractional time-dependent states as quantum channels to perform quantum teleportation has examined. It is shown that, preparing the system in anti-ferromagnetic regime improves the fidelity of the teleported state. The strength of the DM interaction and the fractional’s order has a clear effect on the fidelity’s behavior, where they may be used as control parameters to increase the efficiency of the fractional quantum channel in the context of quantum communication.
In this paper we investigate the fractional quantum correlations via squashed entanglement and negativity, where an analytical solution of a fractional Schrödinger equation under an XXX model of a spin-spin Hamiltonian has been introduced. It has shown that, by starting with an initially large entangled state, both quantifiers decrease during the interaction. This decay increases as one increases the degree of the fractional order and the coupling constant between the two spins. However, the squashed entanglement and the negativity increase gradually if the initial state contains a small amount of quantum correlations. The sudden/gradual changes of these phenomena have been observed at small/large values of the fractional order, respectively. The constant behavior of these measures is observed at small values of fractional orders. Our results show that the fractional state can be used as a quantum channel with high efficiency to perform quantum teleportation. The long-lived constant behavior of the teleportation inequality indicates that the efficiency of this channel will be constant during the teleportation process.
We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon statistics evolved to super-Poissonian from sub-Poissonian during the respective AJC, JC interactions. Further, for high values of r, the form of the time evolution of atomic population inversion depicted enhanced ringing revivals at the collapse region in comparison to the case of an initial coherent state. What is more, at higher values of r the time evolution of DEM showed more rapid oscillations and recorded higher values, concurrently, an increase in the degree of mixedness.
The Jaynes-Cummings model (JCM) describes the interaction of a two-level atom with a single quantised field mode in an optical cavity. In this BSc project we derive the basic Rabi model Hamiltonian and show how it leads to the JCM Hamiltonian. The results are then used to analyse the general time evolution of a bipartite atom-field system and its properties, such as entanglement. We extend a scheme developed by Browne and Plenio [D. Browne and M. B. Plenio, Physical Review A, vol. 67, no. 1, Jan. 2003.] to entangle two cavities that interact with an atom. Our scheme allows to produce states that are arbitrarily close to a Bell state with a success probability greater than 0.75, whereas the success rate of the original method tends to 0 for perfect fidelity. Further, we extend both schemes by allowing the atom or the cavity to be in a thermal state and find that the fidelity of the produced states is reduced with increasing temperature. Finally, we apply our scheme to quantum teleportation, where we find that the fidelity of the teleported state compared to the original state also decreases as the temperature is increased.
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 = .
Abstract In this work, we investigate the possibility of predicting the phenomena of the quantum Mpemba fractionally, where it is assumed that a single qubit, which is initially prepared in three different cases, hottest, hotter and colder states, interacting with its surroundings made up of two qubits via XYZ chain model in the presence of Dzyaloshinskii–Moriya interaction ( DM ). The trace distance between the equilibrium and time fractional evolution of the system is used to predict the Mpemba phenomena. The impact of the interaction parameters and the fractional orders on the stabilization behavior of the qubit is discussed. It is shown that thermalization case is reached at small fraction order during a short interaction time. However, as one increases the fractional orders, the thermalization is observed at large interaction time. For ferromagnetic case and large strength of DM interaction, the stabilization behavior is predicted at small interaction time, while for anti-ferromagnetic and small values of DM , the stabilization is reached at large interaction time.