The quantum levels population behavior of the two coupled flux qubits depending on the external driving field characteristics is studied. The explicit expressions for the multiphoton transition probabilities at an arbitrary control field amplitude is obtained for the case of small tunnel splitting energies. We describe the controllable features of their formation and thereby creating or destroying entanglement by system bias tuning on the direct inter-level transition and during the transition through intermediate states. We found a feature of the qubits population inverting that ends in the independence of the resonances positions from the qubits coupling strength. Using Floquet--Markov equation we numerically demonstrate, that the positions of multiphoton resonances are stable to dissipative processes.
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