Quantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics of the probe analytically, whereas numerical simulations are employed in the strong coupling and long-time regime. We then evaluate the quantum Fisher information for the estimation of the cutoff frequency and the temperature of the environment. Our results provide clear evidence that pure dephasing is not optimal, unless we focus attention to short times. In particular, we found several working regimes where the presence of a transverse interaction improves the maximum attainable precision, i.e. it increases the quantum Fisher information. We also explore the role of the initial state of the probe and of the probe characteristic frequency in determining the estimation precision, thus providing quantitative guidelines to design optimized detection to characterize bosonic environments at the quantum level.

中文翻译：

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超越纯移相的量子探测

量子探测是利用与复杂环境相互作用的简单量子系统来提取有关某些环境参数（例如环境温度或其光谱密度）的精确信息的艺术。在这里，我们分析了单量子位探针在表征热平衡下的欧姆玻色子环境方面的性能。特别是，我们分析了调整探头与环境之间相互作用的哈密顿量的影响，超越了传统的纯移相范式。在弱耦合和短时状态下，我们分析地解决了探针的动力学问题，而在强耦合和长时间状态下采用了数值模拟。然后，我们评估量子 Fisher 信息以估计截止频率和环境温度。我们的结果提供了明确的证据，表明纯移相不是最佳的，除非我们将注意力集中在短时间内。特别是，我们发现了几种工作机制，其中横向相互作用的存在提高了最大可达到的精度，即它增加了量子 Fisher 信息。我们还探索了探针的初始状态和探针特征频率在确定估计精度中的作用，从而为设计优化检测以在量子级别表征玻色子环境提供定量指导。