Space-time description of photon emission from an atom
Space-time description of photon emission from an atom
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原子光子发射的时空描述
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发表时间：
2000
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通讯作者：
O. Keller
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文献类型：
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作者：
O. Keller
从假设出现在横向组的微观麦克斯韦-洛伦兹方程的场-物质相互作用，适当归一化，电磁场可以看作是描述单光子发射和吸收过程中的空间和时间，第一个量子化的启动光子发射由一个单一的原子。新兴的光子的波函数被引入作为一个六矢量对象构造从复杂的分析信号的黎曼-西尔伯斯坦矢量属于相反的光子螺旋。当原子不再具有电动力学活性时，发射的光子在第一量子化中由自由空间中光子所熟知的所谓能量波函数来描述。从新兴的光子波函数的动量表示的条件上的分析部分的横向原子电流密度的建立，确保准确地发射一个光子。在坐标表象中，建立了一个光子动力学的传播子描述。光子传播子被引入作为一个两个组件的旋量，其中上，下张量分量的构造，分别从描述横向电场和磁场的时空演化的传播子的正和负螺旋度组合。结果表明，光子的发射区域与空间中横向原子流密度不为零的区域相一致。对于在电偶极跃迁中发射的光子，发射区域基本上是原子的近场区，并且该区域因此确定光子的初始（和最佳）空间约束。从一个在有限时间内处于活动状态的原子中射出的光子必然是多色的，与之相关的波包基本上被限制在以真空光速向外运动的球壳之间。为了以启发式的方式说明基本理论的主要原理，我们将其应用于研究点状原子的单光子正弦波列的发射。发现产生一个光子所需的原子电流密度与波列中的振荡周期无关，因此只取决于波列中的周期数。导出了单光子能量的显式表达式，并证明了只有在极短的脉冲序列中，才会出现与教科书结果的明显偏差，即$E=ensuremath{Elzxh}{ensuremath{omega}}_{0}，$。研究了原子-光子耦合系统中原子近场区的径向能量流，确定了出射光子在离原子一定距离处的周期平均向外能量输运.
Starting from the postulate that the electromagnetic field appearing in the transverse set of microscopic Maxwell-Lorentz equations governing field-matter interactions, properly normalized, can be looked upon as describing one-photon-emission and -absorption processes in space and time, a first-quantized initiation of photon emission by a single atom is presented. The wave function for the emerging photon is introduced as a six-vector object constructed from the complex analytical signals of the Riemann-Silberstein vectors belonging to opposite photon helicities. When the atom is no longer electrodynamically active, the emitted photon is described in first quantization by the so-called energy wave function well known for photons in free space. From the momentum representation of the emerging photon wave function a condition on the analytical part of the transverse atomic current density is established which ensures that precisely one photon is emitted. A propagator description of the emerged photon dynamics in the coordinate representation is established. The photon propagator is introduced as a two-component spinor, where upper and lower tensor components are constructed, respectively, from positive and negative helicity combinations of the propagators describing the time-space evolution of the transverse electric and magnetic fields. It is shown that the emission region for the photon coincides with the region in space where the transverse atomic current density is nonvanishing. For a photon emitted in an electric dipole transition the emission region essentially is the near-field zone of the atom, and this zone therefore determines the initial (and best) spatial confinement of the photon. The photon emerging from an atom active for a finite time necessarily is of the polychromatic sort and the associated wave packet essentially is confined between spherical shells moving outwards with the vacuum speed of light. To illustrate the main principles of the fundamental theory in a heuristic fashion we apply it to a study of the emission of a one-photon sinusoidal wavetrain from a pointlike atom. It is found that the atomic current density needed to create just one photon is independent of the oscillation period in the train and thus depends only on the number of periods in the wave train. An explicit expression for the one-photon energy is derived, and it is shown that only for extremely short pulse trains pronounced deviations from the textbook result, $E=ensuremath{Elzxh}{ensuremath{omega}}_{0},$ occur. The radial energy flow in the coupled atom-photon system in the near-field zone of the atom is investigated, and the cycle-averaged outwards energy transport carried by the emerging photon in a given distance from the atom is determined.