德西特时空中两能级探针的温度编码速率

中文摘要 AI 辅助

我们在开放量子系统框架下研究德西特时空中两能级探针的温度编码过程。从量子计量学视角出发，我们量化了温度编码速率，该速率表征在固定总探针时间下估计温度参数的精度。通过优化每个探针的初始态、演化时间和测量基，我们得到了最大编码速率。对于与自由下落观察者相隔有限距离的静态探针，其探针态中编码了固有吉本斯-霍金温度与位置相关的安鲁温度。我们发现，有效温度的编码速率等于固有温度的编码速率与探针固有加速度对应的安鲁温度的编码速率之和。有趣的是，当固有温度足够小时，固有温度的编码速率会先随安鲁温度升高而增大，达到最大值后再降至零。因此，非零固有加速度并不一定抑制固有温度的编码，反而存在使固有温度编码速率最大化的最优固有加速度。此外，我们研究了安鲁温度的编码速率以及以分离距离为函数、足够精度估计安鲁温度所需的最小总探针时间。我们发现，即使探针位于距离宇宙视界相当远的径向位置（达视界半径的0.1倍），所需的总探针时间及对应的探针数量在实验上仍具有可行性。

英文摘要

We investigate the thermalization process of two-level probes in de Sitter spacetime from a quantum-metrological perspective. For a static probe separated by a finite distance from a freely falling observer, both the intrinsic Gibbons--Hawking temperature and the position-dependent Unruh temperature are encoded in the probe state. The mutual influence between the encoding rate of the Gibbons--Hawking temperature and that of the Unruh temperature is studied. Results show that the thermalization rate is equal to the sum of the encoding rates of the Gibbons--Hawking temperature and that of the Unruh temperature. Interestingly, a nonzero inherent acceleration induced by the separation between the probe and a freely falling observer does not necessarily suppress the encoding of the Gibbons--Hawking temperature. Instead, there exists an optimal inherent acceleration at which the encoding rate of the Gibbons--Hawking temperature is maximized. Furthermore, the required total probe time of estimating the thermal effect with sufficient precision is shown in relation with the thermalization rate. The required total probe time and the corresponding number of probes remain experimentally feasible when the position-dependent inherent acceleration satisfies $\frac{a}{2πω_0}\rightarrow0.1$.

发表机构

• School of Science, Guiyang University（贵阳大学理学院）

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