Abstract
Nonlinear effects related to the resonant interaction of electromagnetic fields that act on four transitions of a five-level M scheme of atomic levels in the stationary limit are studied. Eight stationary solutions that depend on the state of circular polarizations of three operating classical modes of the field are found for the atomic density matrix. To decrease the absorption of the fields on the atomic transitions, the regime of electromagnetically induced transparency is used. The conditions under which the M scheme is close in its optical properties to two- or three-level schemes are found. Based on the obtained eight solutions, the total accumulated phase shifts of the working waves are calculated. It is shown that the M scheme can perform the operation of double controlled phase shift. Alternatively to the method proposed, this operation also can be carried out using five two-qubit operations, which reduces its noise immunity.
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