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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Trapping conditions for a pair of two-level atoms interacting with a bimodal cavity field

N. A. Enaki, Viorel Ciornea, Andrei M. Andriesh

Published Feb 21, 2005• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.612313

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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 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.
A new reversible effect of three-level atom in interaction with quantum bimodal cavity field is proposed. The problem consists in the possibility of realization of initial separate state of atom and electromagnetic field after flying time through the cavity field. The discrete values for the flying time interval, which corresponds to the reversibility of the quantum states, were found. The quantum properties of bimodal field, which satisfy the optical trapping conditions for the atom flying through the cavity, were studied. The recursion relation for the amplitude of the electromagnetic field in decompositions on the Fock states was obtained.
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.