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arXiv 1405.0955quant-ph
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量子振荡器非线性的量化

Quantifying the nonlinearity of a quantum oscillator

Matteo G. A. Paris, Marco G. Genoni, Nathan Shammah, Berihu Teklu

备注：
8 pages, 5 figures, published version
发表信息：
Phys. Rev. A 90, 012104 (2014)
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摘要：

我们解决量子振荡器的非线性的量化，并引入两个措施的基础上的基态的性质，而不是潜在的形式本身。第一个测量是基于质量的，并且对应于所考虑的谐振子的基态与参考谐振子的基态之间的重整化Bures距离。然后，为了避免引入这个辅助振子，我们引入了一个不同的措施的基础上的非高斯性（nG）的基态。这两个措施进行评估的样本显着的非线性电位和它们的属性进行了详细的讨论。我们表明，这两个措施是单调函数的对方在大多数情况下，这表明基于nG的措施是一个合适的选择，以捕捉量子振荡器的非谐性质，并量化其非线性独立的具体功能的潜力。我们还提供了潜在的Bures措施无法定义的例子，由于缺乏一个适当的参考谐波电位，而基于nG的措施适当量化其非线性特征。我们的研究结果可能会在实验应用中产生影响，其中有效电位的获得是有限的，例如，在量子控制中，协议依赖于有关基态或热态的信息。

英文摘要：

We address the quantification of nonlinearity for quantum oscillators and introduce two measures based on the properties of the ground state rather than on the form of the potential itself. The first measure is a fidelity-based one, and corresponds to the renormalized Bures distance between the ground state of the considered oscillator and the ground state of a reference harmonic oscillator. Then, in order to avoid the introduction of this auxiliary oscillator, we introduce a different measure based on the non-Gaussianity (nG) of the ground state. The two measures are evaluated for a sample of significant nonlinear potentials and their properties are discussed in some detail. We show that the two measures are monotone functions of each other in most cases, and this suggests that the nG-based measure is a suitable choice to capture the anharmonic nature of a quantum oscillator, and to quantify its nonlinearity independently on the specific features of the potential. We also provide examples of potentials where the Bures measure cannot be defined, due to the lack of a proper reference harmonic potential, while the nG-based measure properly quantify their nonlinear features. Our results may have implications in experimental applications where access to the effective potential is limited, e.g., in quantum control, and protocols rely on information about the ground or thermal state.

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