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Optics Communications

Trapping conditions for a three-level atom interacting with cavity fields

N. A. Enaki, Viorel Ciornea, D. L. Lin

Published Sep 12, 2003• 5 citations
Publisher

Abstract

The interaction between a single-mode cavity field and a string of three-level atoms of cascade type with equally spaced energy levels is investigated. The matrix elements of dipole transitions between adjacent levels are different. Trapping conditions for the flying time in the cavity as well as the explicit state of the field are found. The results are shown to be qualitatively different from the case of two-level systems. The properties of cavity fields are examined. In various limits, the state exhibits vacuum nutation as well as sub-Poissonian statistics and squeezing properties.

DOI
10.1016/j.optcom.2003.06.003

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The interaction between a single-mode cavity field and a string of three-level atoms of cascade type with equally spaced energy levels is investigated. The matrix elements of dipole transitions between adjacent levels are different. Trapping conditions for the flying time in the cavity as well as the explicit state of the field are found. The results are shown to be qualitatively different from the case of two-level systems. The properties of cavity fields are examined. In various limits, the state exhibits vacuum nutation as well as sub-Poissonian statistics and squeezing properties.
The bi-quanta interaction between the bi-modal cavity electromagnetic field and atomic string consisting of undistinguishable pair of two-level atoms relatively dipole forbidden transition, is studied. The trapping conditions for the flying time of the atoms in cavity are obtained. Moreover, we received the so called cotangent state for the proposed system. The properties of the electromagnetic field for such state are examined. Analyzing the obtained numerical results we concluded that this state exhibits non-classical properties: such as sub-Poissonian statistics, squeezing, or more interestingly, vacuum nutation.
We studied the interaction between the single-mode cavity and an atomic string consisting of equidistant three-level atoms (or pairs of indistinguishable two-level atoms) that is injected at such a low flux that at most one atom at a time is present inside the cavity. We investigated the trapping effect in such systems, and we obtained the trapping conditions for the flying time inside the cavity. We derived the so-called cotangent state for the proposed systems, and we examined the properties of the electromagnetic field for such state.
The interaction between the laser cooled and trapped equidistant three-level atom (ion) and the quantized cavity field is investigated. The dipole moment matrix transition elements between the adjacent atomic energy levels d12 and d23 are assumed to be different. This model generalizes the problem of the pair of indistinguishable two-level atoms interacting with the squeezed vacuum which is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements. The exact analytical solution for the atom-field state-vector is found in the case in which at the initial moment t = 0, the single-mode cavity field is supposed to be in the squeezed vacuum state. With the help of this solution, the quantum-statistical and squeezing properties of the radiation field are studied. The obtained results are compared with those for the single two-level atom model. It should be noted that in the proposed model, the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one. The two limiting cases are analyzed. In the first limiting case in which d12 → d23 the quantum-statistical properties of the single-mode cavity field resemble those for the pair of indistinguishable two-level atoms. In the second one d12 → 0 the quantum-statistical and squeezing features of the proposed model are similar with those for the single two-level atom model.
The behavior of the dipole moment of a three-level atom interacting with cavity fields of arbitrary detunings is investigated. The time evolution and squeezing conditions of the components and correlation function of the dipole moment are calculated for three cases: one-mode field and a \ensuremath{\Xi}-type atom initially in the upper state, two-mode field and a \ensuremath{\Lambda}-type atom initially in the upper state, and two-mode field and a \ensuremath{\Lambda}-type atom initially in one of the lower states. A number of interesting features are found and discussed.
The cavity field spectrum of a cascade three-level atom interacting with single-mode field with Kerr-like medium in the cavity is investigated. The numerical results for the initial field in pure number state, coherent state and squeezed vacuum state are calculated, respectively. It is found that the Kerr-like medium affects the spectral structure even though the initial field is in vacuum when the atom is in upper level. In the case of strong input field, the number state spectrum shows two peaks with different heights; and the superposition state spectrum shows a multi-peak structure with an equal distance of two neighboring peaks. The spectral ``central frequency" shifts away from the resonant frequency with the increasing of average photon number.