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本文研究了基于连续空结果测量方案来提高一个二能级原子在遭受一个零温度玻色热库环境影响下其相位估计精度问题.首先通过解析的方法,得到了在热库环境中执行了n次空结果的测量以后原子系统最终态的表达式.为了更加突出连续测量在二能级原子动力学中的重要作用,将最终态中核心的振幅系数改成一种特殊的形式,获得了振幅系数一个非常简洁的数学表示式.有趣的是,我们发现：基于连续测量的二能级原子动力学由环境的谱宽度和测量的时间间隔乘积的标度参数密切相关,且在一些特殊情况下可以退化成已经存在的量子芝诺效应和马尔科夫近似的结果.进一步,我们也发现：不管是马尔科夫和非马尔科夫条件下,通过调节这个标度参数,二能级原子的相位估计的量子Fisher信息都能得到显著的提高.总之,本文中对环境后选择的空结果频繁测量方案可以有效降低退相干对量子Fisher信息的破坏作用,这一结果为开放量子系统中实现高精度测量提供了新的理论方案.
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关键词:
- 开放量子系统 /
- 量子Fisher信息 /
- 连续空结果测量
Quantum Fisher Information plays a central role in the fields of quantum metrology and quantum precision measurement. However, quantum systems are susceptible to the influence of noisy environments, which reduces the precision of parameter estimation (as measured by quantum Fisher information). Therefore, overcoming the impact of environmental noise on quantum systems to enhance the quantum Fisher information of parameters has become an important scientific issue in quantum precision measurement. In this paper, we investigate the enhancement of phase estimation precision for a two-level atom subjected to a zero-temperature bosonic environment, based on a continuous null-result measurement scheme. First, an analytical expression for the final state of the atomic system after n null-result measurements is derived. To highlight the crucial role of continuous measurement in the dynamics of the two-level atom, the core amplitude coefficient in the final state is reformulated into a specific form, yielding a concise mathematical expression. Interestingly, we find that the dynamics of the two-level atom under continuous measurements are closely related to a scaling parameter—the product of the environmental spectral width and the measurement time interval. In certain special cases, this formulation reduces to known results such as the quantum Zeno effect and Markovian approximations. Furthermore, we demonstrate that, under both Markovian and non-Markovian conditions, the quantum Fisher information for the atomic phase estimation can be significantly enhanced by tuning this scaling parameter. Using an exactly solvable model, we also provide an explanation for the quantum Zeno effect without explicit use of the projection postulate, and find that in certain limits, a concise formula for $\tilde{h}(t) = h^n(\tau)$ accurately captures the numerical results across a broad range of parameters. In summary, the proposed scheme of frequent null-result measurements with post-selection on the environment effectively mitigates the detrimental effects of decoherence on the quantum Fisher information, offering a novel theoretical approach for achieving high-precision measurements in open quantum systems. -
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