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Jaynes-Cummings model complete two photons: study and applications

Alexandre Antoniazzi Franco de Souza

Published Feb 20, 2009• 0 citations
OpenAlex

Abstract

In this work we have studied the two photon Jaynes-Cummings model to describe the interaction of a three-level atom in the configuration with a single-mode of a cativy-field. We have used the effetive and full microscopic Jamiltonian approach to compare the results obtained in these tow descriptions. We employed the two-photon Jaynes-Cummings model int the full microscopic Hamiltonian context to implement schemes to quantuam entanglement swapping, for approximate and conditional quantuam teleportation for an unknown atomic state, for a superposition of zero- and two photon states. Both schemes were implemented using no measurement in the Bell base states.

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In a previous work [Commun. Theor. Phys. 45 (2006) 79] a scheme was presented for approximate and conditional teleportation of an unknown atomic state in a QED-cavity without Bell-state measurement via two-photon Jaynes–Cummings model in the effective Hamiltonian approach. This comment presents an alternative method, based on the so called 'full two-photon Jaynes–Cummings Hamiltonian approach'. Accordingly, it describes the evolution of the two-photon degenerate process for arbitrary average photon number inside the cavity, as the correct way to implement teleportation in this scenario.

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The Scheme of Entanglement Swapping in two-photon Jaynes-Cummings model

Liu Hong

Based on the interaction of atoms and two-photon in cavity QED,the author proposes an entanglement swapping scheme without joint measurement using a two-photon Jaynes-Cummings model.By means of entanglement swapping,we get a nonmaximally entangled pair between an atom and a cavity mode which previously have not any interaction with each other.Through entanglement concentration,we can obtain a maximally entangled state.It can be used in quantum information processing.

Journal of Gansu Lianhe University•Jan 1, 2008•0 citations
In this work we have studied the two photon Jaynes-Cummings model to describe the interaction of a three-level atom in the configuration with a single-mode of a cativy-field. We have used the effetive and full microscopic Jamiltonian approach to compare the results obtained in these tow descriptions. We employed the two-photon Jaynes-Cummings model int the full microscopic Hamiltonian context to implement schemes to quantuam entanglement swapping, for approximate and conditional quantuam teleportation for an unknown atomic state, for a superposition of zero- and two photon states. Both schemes were implemented using no measurement in the Bell base states.
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.
In a previous work [Commun. Theor. Phys. 45 (2006) 79] a scheme was presented for approximate and conditional teleportation of an unknown atomic state in a QED-cavity without Bell-state measurement via two-photon Jaynes–Cummings model in the effective Hamiltonian approach. This comment presents an alternative method, based on the so called 'full two-photon Jaynes–Cummings Hamiltonian approach'. Accordingly, it describes the evolution of the two-photon degenerate process for arbitrary average photon number inside the cavity, as the correct way to implement teleportation in this scenario.
A scheme for approximately and conditionally teleporting an unknown atomic state via two-photon interaction in cavity QED is proposed. It is the extension of the scheme of Ref. [11] [Phys. Rev. A 69 (2004) 064302], which is based on Jaynes–Cummings model in QED and where only a time point of system evolution and the corresponding fidelity implementing the teleportation are given. In our scheme, the two-photon interaction Jaynes–Cummings model is used to realize the approximate and conditional teleportation. Our scheme does not involve the Bell-state measurement and an additional atom, only requiring two atoms and one single-mode cavity. The fidelity of the scheme is higher than that of Ref. [11]. The scheme may be generalized to not only the teleportation of the state of a cavity mode to another mode by means of a single atom but also the teleportation of the state of a trapped ion.