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Quantum system behaviour of Jaynes-Cummings model with Kerr-like medium

Yeen Chia Chan

Published Jan 1, 2016• 0 citations

Abstract

Jaynes-Cummings model is widely used to represent a quantum system as it is able to explain quantum behaviour in a more accurate and simple way. To date, the study of Jaynes-Cummings model does not involve multi-photon transitions and also three-qubit quantum entanglement, both coupled with Kerr-like medium. Thus the main objective of this study is to discover new behaviour for quantum system under these two conditions coupled with Kerr-like medium. In achieving this objective, Jaynes-Cummings model is modified to include multi-photon transition and three-qubit quantum system coupling with Kerr-like medium. Under the multi-photon transition condition, Pegg-Barnett formalism is used to measure the quantum system behaviour in the modified Jaynes-Cummings model. The result shows that as the strength of the coupling increases, the quantum system behaviour becomes more active. However, as the number of photons transition increases, the influence from Kerr-like medium towards quantum system behaviour decreases. Next, under the three-qubit quantum system with one-photon transition condition, the three-qubit state interacts with Markovian and non-Markovian environments, both represented by Lorenztian spectral density. The lower bound concurrence is used to measure quantum entanglement robustness. Result shows that when Kerr-like medium coupling strength is increased for both Markovian and non-Markovian environments, the quantum entanglement are more robust. Concurrently, the influence of quantum entanglement robustness is reduced when dipole-dipole interaction is getting stronger. As a conclusion, this study discovered new quantum system behaviour under the influence of Kerr-like medium with potential application in quantum information processing.

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Jaynes-Cummings model is widely used to represent a quantum system as it is able to explain quantum behaviour in a more accurate and simple way. To date, the study of Jaynes-Cummings model does not involve multi-photon transitions and also three-qubit quantum entanglement, both coupled with Kerr-like medium. Thus the main objective of this study is to discover new behaviour for quantum system under these two conditions coupled with Kerr-like medium. In achieving this objective, Jaynes-Cummings model is modified to include multi-photon transition and three-qubit quantum system coupling with Kerr-like medium. Under the multi-photon transition condition, Pegg-Barnett formalism is used to measure the quantum system behaviour in the modified Jaynes-Cummings model. The result shows that as the strength of the coupling increases, the quantum system behaviour becomes more active. However, as the number of photons transition increases, the influence from Kerr-like medium towards quantum system behaviour decreases. Next, under the three-qubit quantum system with one-photon transition condition, the three-qubit state interacts with Markovian and non-Markovian environments, both represented by Lorenztian spectral density. The lower bound concurrence is used to measure quantum entanglement robustness. Result shows that when Kerr-like medium coupling strength is increased for both Markovian and non-Markovian environments, the quantum entanglement are more robust. Concurrently, the influence of quantum entanglement robustness is reduced when dipole-dipole interaction is getting stronger. As a conclusion, this study discovered new quantum system behaviour under the influence of Kerr-like medium with potential application in quantum information processing.

Phase properties are important in understanding quantum entanglement. Several studies have been carried out on the cases for one and two photon transitions. The effect of multi-photon transition on phase properties in Jaynes-Cummings model coupled with Kerr-medium is studied to further understand phase properties in larger system. This paper develops a model as well as compares the results for different photon transition numbers from one to five photon transition using Pegg-Barnett formalism based m easurement. From the developed model, it has been found that the phase state of the quantum system increases during both collapse and revival of photon transition when the Kerr effect increases. This findi ng shows the behavior of phase properties at higher photon transitions which can benefit further studies in quantum entanglement.

The system under consideration consists of a two-level atom coupled an optical field in k-photon Jaynes-Cummings model with a Kerr medium.The time evolution of field entropy squeezing and population inversion of the atom for three and four-photon transitions was discussed.The influence of Kerr medium on field entropy squeezing and population inversion of the atom was also analyzed.The results show that the field entropy squeezing and population inversion of the atom are sensitive to effect of Kerr medium.

Abstract The influence of the Kerr nonlinearity on the two two-level atoms entanglement is investigated in Jaynes–Cummings model (JCM), so that one of atoms is inside the cavity field and the other atom is outside it. We show that the entanglement of atoms increases with the decrease of the phase decoherence rate or Kerr coefficient, when considering the effect of external environment. Then due to the statistic properties of the anti-bunching effect of photons are related to entanglement, the nonlinear JCM is examined theoretically to analyze the bunching or anti-bunching effect by using the second-order coherence function. We find that the second-order coherence function decreases with the Kerr coefficient. Our results show that the field reflects the stronger bunching effect with the bigger average photon number.

In this paper, we investigated the dynamics of entanglement of pairs of qubits in a system of three identical qubits that interact non-resonantly with the selected mode of a microwave resonator without loss with the Kerr medium by means of single-photon transitions. We have found solutions to the quantum time Schrodinger equation for the total wave function of the system for the initial separable, biseparable and true entangled states of qubits and the Fock initial state of the resonator field. Based on these solutions, the criterion of entanglement of qubit pairs — negativity is calculated. The results of numerical simulation of the negativity of qubit pairs have shown that the presence of disorder and Kerr nonlinearity in the case of an initial non-entangled state of a pair of qubits can lead to a significant increase in the degree of their entanglement. In the case of an initial entangled state of a pair of qubits, the disorder and the Kerr medium can lead to a significant stabilization of the initial entanglement.