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arXiv 2408.11273quant-ph
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热多光子Jaynes-Cummings模型的Bloch矢量绘制的准周期轨迹

Quasiperiodic trajectories drawn by the Bloch vector of the thermal multiphoton Jaynes-Cummings model

Hiroo Azuma

AI总结:

本研究针对含热涨落的多光子Jaynes-Cummings模型的Bloch矢量准周期演化问题,发现固定时间间隔的离散轨迹存在标度不变性等规律,揭示其源于低温极限下角频率为无理数的有限三角函数描述。

摘要:

我们研究了热多光子Jaynes-Cummings模型(JCM,杰恩斯-卡明斯模型)的Bloch矢量的时间演化。若多光子JCM包含热涨落,其对应的Bloch矢量会以不可预测的方式演化,描绘出无序轨迹并表现出准周期性。然而,若我们以固定时间间隔将轨迹绘制成离散时间序列,会呈现出意料之外的规律性。首先,我们证明该绘图在有限但非零时间间隔的标度变换下具有不变性。其次,我们通过数值计算得到Bloch矢量z分量的绝对值几乎为零的时刻。在这些时刻,二能级系统的密度矩阵近似为基态和激发态的经典系综。我们证明,部分时间值可从无理数的某些近似分数的分母推导得出。这些发现背后的原因是,热多光子JCM的Bloch矢量分量由有限数量的三角函数描述,在低温极限下这些三角函数的无量纲角频率为无理数。

英文摘要:

We study the time evolution of the Bloch vector of the thermal multiphoton Jaynes-Cummings model (JCM). If the multiphoton JCM incorporates thermal fluctuations, its corresponding Bloch vector evolves unpredictably, traces a disordered trajectory, and exhibits quasiperiodicity. However, if we plot the trajectory as a discrete-time sequence with a constant time interval, it reveals unexpected regularities. First, we show that this plot is invariant under a scale transformation of a finite but non-zero time interval. Second, we numerically evaluate the times at which the absolute value of the $z$-component of the Bloch vector is nearly equal to zero. At those times, the density matrix of the two-level system approximates a classical ensemble of the ground and excited states. We demonstrate that some time values can be derived from the denominators of the fractions of certain approximations for irrational numbers. The reason underlying these findings is that the components of the Bloch vector for the thermal multiphoton JCM are described with a finite number of trigonometric functions whose dimensionless angular frequencies are irrational numbers in the low-temperature limit.

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