  Spin systems are one of the most promising candidates for quantum
computation. At the same time control of a system's quantum state during time
evolution is one of the actual problems. It is usually considered that to hold
well-known resonance condition in magnetic resonance is sufficient to control
spin system. But because of nonlinearity of the system, obstructions of control
of system's quantum state may emerge.
  In particular quantum dynamics of two 1/2 spin-qubit system in the optical
cavity is studied in this work. The problem under study is a generalization of
paradigmatic model for Cavity Quantum Electrodynamics of James-Cummings model
in case of interacting spins. In this work it is shown that dynamics is chaotic
when taking into account center-of-mass motion of the qubit and recoil effect.
And besides even in case of zero detuning chaotic dynamics emerges in the
system. It is also shown in this work that because of the chaotic dynamics the
system execute irreversible transition from pure quantum-mechanical state to
mixed one. Irreversibility in its turn is an obstacle for controlling state of
quantum-mechanical system.
