Relaxation of a two-level system (TLS) into a resonant infinite-temperature reservoir with a Lorentzian spectrum is studied. The reservoir is described by a complex Gaussian-Markovian field coupled to the nondiagonal elements of the TLS Hamiltonian. The theory can be relevant for electromagnetic interactions in microwave high-$Q$ cavities and muon spin depolarization. Analytical results are obtained for the strong-coupling regime, $\Omega_0\gg\nu$, where $\Omega_0$ is the rms coupling amplitude (Rabi frequency) and $\nu$ is the width of the reservoir spectrum. In this regime, the population difference and half of the initial coherence decay with two characteristic rates: the most part of the decay occurs at $t\sim\Omega_0^{-1}$, the relaxation being reversible for $t\ll(\Omega_0^2\nu)^{-1/3}$, whereas for $t\gg(\Omega_0^2\nu)^{-1/3}$ the relaxation becomes irreversible and is practically over. The other half of the coherence decays with the rate on the order of $\nu$, which may be slower by orders of magnitude than the time scale of the population relaxation. The above features are explained by the fact that at $t\ll\nu^{-1}$ the reservoir temporal fluctuations are effectively one-dimensional (adiabatic). Moreover, we identify the pointer basis, in which the reduction of the state vector occurs. The pointer states are correlated with the reservoir, being dependent on the reservoir phase.
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机译：研究了将两级系统（TLS）松弛到具有Lorentz谱的共振无限温度储层中的过程。用与TLS哈密顿量的非对角线元素耦合的复杂高斯-马尔可夫场描述储层。该理论可能与微波高QQ腔中的电磁相互作用和μ子自旋去极化有关。获得了强耦合体制$ \ Omega_0 \ gg \ nu $的分析结果，其中$ \ Omega_0 $是均方根耦合幅度（拉比频率），$ \ nu $是储层谱的宽度。在这种情况下，种群差异和初始相干衰减的一半具有两个特征速率：衰减的大部分发生在$ t \ sim \ Omega_0 ^ {-1} $，弛豫在$ t \ ll（是可逆的） \ Omega_0 ^ 2 \ nu）^ {-1/3} $，而对于$ t \ gg（\ Omega_0 ^ 2 \ nu）^ {-1/3} $，松弛变得不可逆且实际上结束了。相干性的另一半随速率的变化而降低，可能比总体弛豫的时间尺度慢几个数量级。以上特征可以通过以下事实来解释：在t \ ll \ nu ^ {-1} $处，储层的时间波动实际上是一维的（绝热的）。此外，我们确定了指针基础，状态矢量在其中发生了减少。指针状态与容器相关，取决于容器相位。
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