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We develop a scheme to construct the Hamiltonians of the lambda-, vee- and cascade-type three-level conflgurations using the generators of SU(3) group. It turns out that this approach provides a well-deflned selection rule to give difierent Hamiltonians for each conflguration. The lambda- and vee-type conflgurations are exactly solved with difierent initial conditions while taking the two-mode classical and quantized flelds. For the classical fleld, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models by introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two conflgurations for the semiclassical models is completely destroyed on quantization of the fleld modes. The symmetry can be restored within the quantized models when both fleld modes are in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.

Dynamical symmetry breaking of lambda- and vee-type three-level systems on quantization of the field modes