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Quantum interference and local field effects in a medium of V-type three-level atoms

We study the intrinsic optical bistability displayed by a small sample of $V$-type three-level atoms induced by the near dipole-dipole interaction. The use of the coherent state properties in the limit of the generalized second-order Born approximation for BBGKY-hierarchy of equations for the reduced density operators allows one to derive the operator describing the near dipole-dipole interaction (local field correction) with interference terms involving no additional assumptions. The dynamics of populations of the excited states and the total spontaneous intensity are analysed as functions of the external laser field strength allowing for the off-diagonal structure of the local field and relaxation operators.