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.
Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics
本文用不变混沌鞍的性质描述了介质腔中的混沌射线动力学。我表明，在特定方向上的远场发射的本地化有关的鞍形的不稳定的流形，沿腔体内的能量分布的非线性模式。对于具有混合相空间的腔，混沌鞍分为双曲和非双曲分量，分别与腔内能量的中间指数（t<tc）和渐近幂律（t> tc）衰减有关。鞍形腔的两个分量的流形的对齐解释了为什么即使腔内的能量集中从t <t_c to t>t_c急剧变化，远场发射也只会发生轻微的变化。环形台球的模拟证实和说明的预测。
