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Journal of Modern Optics

Study of Photon Antibunching in the Vacuum Field Two-photon Jaynes-Cummings Model Without the Rotating-wave Approximation

Xie Ruihua, Gong-ou Xu, Liu Dunhuan

Published Oct 1, 1995• 6 citations
Publisher

Abstract

We have numerically investigated photon antibunching in the two-photon Jaynes-Cummings model without the rotating-wave approximation when the system is restricted to the following initial condition: the atom in the excited state and the field in the vacuum state. The influence of the detuning Δ on photon antibunching has also been discussed.

DOI
10.1080/09500349514551841

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We have numerically investigated photon antibunching in the two-photon Jaynes-Cummings model without the rotating-wave approximation when the system is restricted to the following initial condition: the atom in the excited state and the field in the vacuum state. The influence of the detuning Δ on photon antibunching has also been discussed.
Dipole squeezing in the Jaynes-Cummings model with and without the rotating wave approximation (RWA) has been numerically studied when restricted to the following initial conditions: the field in the superposition of the vacuum and one-photon state, and the atom in the ground state. Numerical results show that even if under the condition for which the RWA is considered to be valid, there is a significant effect caused by the virtual-photon field on the dipole squeezing; in the cases of sufficiently strong coupling of the atom-field interaction, the interference between the virtual-photon processes and the real-photon processes quenches the dipole squeezing.
Some nonclassical features, including photon antibunching, atomic squeezing and quantum collapse-revival phenomenon, were numerically studied in the vacuum field Jaynes–Cummings model (JCM). The influence of the initial atomic coherence on these features was discussed. It is shown that the squeezing can appear only if the atom is initially prepared in the coherent state, and photon antibunching can occur if the atom is initially in the excited state or the coherent one. The effect of the virtual-photon field was studied in JCM without the rotating-wave approximation (RWA). We have shown that even under the condition in which RWA is considered to be valid, there are significant effects on the nonc1assical features due to the interference between the virtual-photon processes and the real-photon processes. Quantum dynamics of JCM without RWA was also studied. We showed that regular dynamical behavior is exhibited in the cases rather close to the integrable limits, and irregular dynamical behavior is presented in the cases far from the integrable limits; in addition, all the nonclassical features disappear in the cases far from the integrable limits.
The antibunching effects of the photon in the competing 3-and 1-photon transitions model are studied by means of quantum theory,and the influences of the relative competing strength between the atom and the two-mode field and the initial photon of the field on the second-order correlation function are discussed.It shows that the increase of the relative competing strength and the initial photon can lead to shortening the duration of antibunching effects of the photon.On the other hand,the hoton antibunching effect decreases with the increase of the initial photon of the field.
It is well known that, under the rotating-wave approximation, the Rabi Hamiltonian, which describes the interaction between a two-level atom and a single field mode, reduces to the Jaynes-Cummings model through exclusion of its counter-rotating term. In this work, it is found that, since photons in the mode are indistinguishable, there exist two conditions where the counter-rotating term can never be ignored. These conditions, all subject to the requirements that the atom-mode coupling is weak and the atom is initially in its ground state, are obtained in the stationary perturbation theory and confirmed through an analysis of the atom-mode system's evolution.
We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of the Jaynes–Cummings (J–C) model. The results show that for resonant case, there is no Rabi oscillation for an atom. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequencies and amplitudes from that of the J-C model. It exhibits that the counter-rotating wave interaction could significantly effect the dynamic behaviour of the atom, even under the condition in which the RWA is considered to be justified.