Book Publisher International (a part of SCIENCEDOMAIN International)

Exploring Rabi Oscillations, Maximally Entangled States and Perfect Teleportation in the Anti-Jaynes-Cummings Interaction: Insights into Quantum Dynamics and Entanglement Applications

Christopher Mayero, Joseph Akeyo Omolo

Published Nov 5, 2024• 0 citations

Abstract

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.

DOI: 10.9734/bpi/crpps/v4/2566

Related papers

Rabi Oscillations, Entanglement and Teleportation in the Anti-Jaynes-Cummings Model

Christopher Mayero, Joseph Akeyo Omolo, Onyango Stephen Okeyo

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 = .

arXiv:2101.07336Journal of Modern PhysicsJan 1, 20216 citations

Atoms and Photons - Their Interaction Dynamics

Max F. Frenzel

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.

arXiv:1212.4339Dec 18, 20120 citations

The anti-Jaynes-Cummings model is solvable : quantum Rabi model in rotating and counter-rotating frames ; following the experiments

Joseph Akeyo Omolo

Abstract This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC)interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specied by a conserved JC excitation number operator which generates the U(1) symmetry of RF and a correlated counter-rotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings (AJC) interaction specied by a conserved AJC excitation number operator which generates the U(1) symmetry of CRF (c) for QRM dynamical evolution in RF, the initial atom-eld state je0i is an eigenstate of the effective AJC Hamiltonian HAJC, while the effective JC Hamiltonian HJC drives this initial state je0i into a time evolving entangled state, and, in a corresponding process for QRM dynamical evolution in CRF, the initial atom-eld state jg0i is an eigenstate of the effective JC Hamiltonian, while the effective AJC Hamiltonian drives this initial state jg0i into a time evolving entangled state, thus addressing one of the long-standing challenges of theoretical and experimental QRM dynamics; consistent generalizations of the initial states je0i , jg0i to corresponding n 0 entangled eigenstates j+en i , j 􀀀g ni of the AJC in RF and JC in CRF, respectively, provides general dynamical evolution of QRM characterized by collapses and revivals in the time evolution of the atomic, eld mode, JC and AJC excitation numbers for large initial photon numbers ; the JC and AJC excitation numbers are conserved in the respective frames RF, CRF, but each evolves with time in the alternate frame.

arXiv:2103.09546Apr 8, 20213 citations

Entanglement teleportation via two-qubit Heisenberg interaction in Jaynes-Cummings model under intrinsic decoherence

Azita Naji, Reza Hamzehofi, Davood Afshar

In this paper, we investigate the entanglement teleportation of a two-qubit state under XYZ Heisenberg interaction in a cavity using the Jaynes-Cummings model. We analyze the channel entanglement, output entanglement and fidelity as a function of decoherence rate and spin coupling constant. We find that the teleportation is more effective if we take the proper initial input state.

Iranian Journal of Physics ResearchOct 1, 20190 citations

Entanglement swapping in the two-photon Jaynes–Cummings model

A.D. dSouza, Wesley Bueno Cardoso, Ardiley Torres Avelar +1 more

In the present work, we study the entanglement swapping via the two-photon process without explicitly using the Bell-state measurement. We employ the appropriate ‘full two-photon Hamiltonian approach’ instead of the ‘effective Hamiltonian approach’ used in recent schemes. We obtain entanglement swapping with 94.7% fidelity for maximally entangled states by conveniently choosing the atom–field interaction time. The success probability is also considered.

Physica ScriptaDec 1, 200916 citations

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

Christopher Mayero, Patrick Owiny

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.

Jul 19, 20210 citations