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arXiv quant-ph/0008093quant-ph
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带隙材料中的共振荧光:非马尔可夫演化的直接数值模拟

Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolution

M. W. Jack, J. J. Hope

摘要:

发展了一种计算受驱动原子辐射到结构连续介质中的非马尔可夫演化的数值方法。通过引入一组附加的虚拟密度矩阵,将原子约化密度矩阵的形式解写成马尔可夫算法,所述虚拟密度矩阵在算法的近似水平上遵循光子在电磁场中的所有可能轨迹。该技术是微扰的意义上说,更多的虚拟密度矩阵需要的产品的有效存储时间和有效耦合强度变得更大。所需的密度矩阵的数量由$3^{M}$给出,其中$M$是每个存储时间的时间步数。将该方法应用于受驱动二能级原子在光子带隙附近辐射的问题,计算了原子的稳态关联函数。

英文摘要:

A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength become larger. The number of density matrices required is given by $3^{M}$ where $M$ is the number of timesteps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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