Chaotic dynamics of coupled two-level atoms in the optical cavity

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 main problems. It is usually considered that in magnetic resonance the so-called resonance condition is sufficient to control the spin system. However, because of the nonlinearity of the system, obstructions to the control of the system's quantum state may emerge. In particular, the quantum dynamics of coupled two-level atoms in the optical cavity are studied in this work. The problem under consideration is a generalization of the paradigmatic model for Cavity Quantum Electrodynamics of the Jaynes-Cummings model in the case of interacting spins. In this work, it is shown that the dynamics are chaotic when taking into account the center-of-mass motion of the system and the recoil effect. Furthermore, even in the case of zero detuning, chaotic dynamics emerge in the system. It is also shown in this work that, because of the chaotic dynamics the system executes an irreversible transition from a pure quantum-mechanical state to a mixed one. Irreversibility, in turn, is an obstacle for controlling the state of the quantum-mechanical system