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Physical Review A

Jaynes-Cummings model with atomic position distribution

Alessandro Vaglica

Published Sep 1, 1995• 23 citations
Publisher

Abstract

The position as well as the width of the atomic wave packet passing through an optical cavity may affect the matter-field interaction. As a result, the internal dynamics of a two-level atom, such as the Rabi oscillations or the collapse and revival phenomenon, may be strongly modified with respect to the standard Jaynes-Cummings model. In particular, for a sufficiently large spread of the atomic position, the atomic population inversion displays the characteristic ringing behavior of the Bessel function ${\mathit{J}}_{0}$ differently from the usual full Rabi oscillation.

DOI
10.1103/physreva.52.2319

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The position as well as the width of the atomic wave packet passing through an optical cavity may affect the matter-field interaction. As a result, the internal dynamics of a two-level atom, such as the Rabi oscillations or the collapse and revival phenomenon, may be strongly modified with respect to the standard Jaynes-Cummings model. In particular, for a sufficiently large spread of the atomic position, the atomic population inversion displays the characteristic ringing behavior of the Bessel function J0{\mathit{J}}_{0}J0​ differently from the usual full Rabi oscillation.
The Jaynes-Cummings model provides a useful means of studying several quantum electrodynamic effects in matter-radiation interaction. One such effect is the phenomenon of collapses and revivals of Rabi oscillations. Various aspects of this phenomenon are studied in terms of the dynamical evolution of the atom as well as the statistical properties of the field. In particular, the sensitivity of collapses and revivals on the initial photon statistics, the cavity field damping mechanism is highlighted. For this purpose the basic model of Jaynes and Cummings has been extended and modified. Some multiatom effects are also discussed.
With the help of a two-photon Jaynes-Cummings model, which is an exactly solvable model, we have dealt analytically with the dynamical behavior of the atom and the field for a two-photon process in squeezed and coherent fields under the appropriate approximation. The features of collapses and revivals of Rabi oscillations for the atom and the field in a two-photon process represent strict periodicity. The phase jump and the large and negative frequency for the combination Rabi oscillation are exhibited in the case of a squeezed field. The results show that squeezing in a field strikingly affects the evolution behavior of the atom and the field.
A two-level atom interacting with a cavity field initialized in a coherent state exhibits the collapse and revival features in its population inversion dynamics under the Jaynes–Cummings interaction. When the cavity field is prepared in a number-state filtered coherent state, obtained by filtering the number state | m 〉 from a coherent state | α 〉 , we observe micro-Rabi oscillations in the collapse region instead of a perfect collapse. We find that the Rabi frequency of these micro oscillations depends only on the filtered photo-number m, whereas the amplitude depends on both m and α . This dependence enables one to infer the filtered number state from the coherent-state distribution by analyzing the time evolution of the atomic population inversion. Conversely, the amplitude and frequency of the micro-Rabi oscillations can be tuned by filtering an appropriate number state. Furthermore, we investigate the effect of filtering multiple number states from a coherent state on the atomic population inversion dynamics.
It is shown that the phenomenon of fractional revivals, which was observed in recent laser experiments on atomic wave packets, determines the long-time behavior of the Jaynes-Cummings model for a two-level atom interacting with a quantized cavity field. This provides an alternative mechanism for the generation of coherent superpositions of macroscopically distinguishable states of the field (so-called ``optical Schr\"odinger cats'') via resonant processes. The emergence of these states is associated with the appearance of atomic inversion revivals following each other 2, 3, 4, . . . times faster than the usual ones.
he effect of the counter-rotating terms in the Jaynes-Cummings model is investigated with an extended coherent-state approach. The counter-rotating terms greatly modify the vacuum Rabi splitting. Two peaks with different heights in the weak coupling regime and more than two peaks in the intermediate coupling regime are predicted. The collapses and revivals in the evolution of the atomic population inversion disappear in the intermediate coupling regime, but reappear in the strong coupling regime. This reappearance is similar to that under the rotating-wave approximation, attributed to the summation of periodic cosine functions of the evolution.
A study of multiatom effects, i.e., dipole-dipole interactions and phase-interrupting collisions between atoms in the Jaynes-Cummings model, is presented here. For this purpose we consider two identical two-level atoms interacting with a single-mode field in a lossless cavity and study the effect of the dipole-dipole interaction between these two atoms on the collapse-and-revival phenomenon of Rabi oscillations by calculating the analytical expression of the excitation probability in the coherent field. We also consider another situation in which a single atom interacting with a single-mode field in a damped cavity undergoes phase-interrupting collisions. The effect of phase-interrupting collisions along with the usual cavity damping on the collapse-and-revival phenomenon has been explicitly calculated using the dressed-atom approach under the secular approximation.