Phase matching refers to a process in which atom-field interactions lead to the creation of an output field that propagates coherently through the interaction volume. By studying light scattering from arrays of cold atoms, we show that conditions for phase matching change as the dimensionality of the system decreases. In particular, for a single atomic chain, there is phase-matched reflective scattering in a cone about the symmetry axis of the array that scales as the square of the number of atoms in the chain. For two chains of atoms, the phase-matched reflective scattering can be enhanced or diminished as a result of Bragg scattering. Such scattering can be used for mapping collective states within an array of neutral atoms onto propagating light fields and for establishing quantum links between separated arrays.

中文翻译：

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较小尺寸的相位匹配

相位匹配是指原子-场相互作用导致创建通过相互作用体积相干传播的输出场的过程。通过研究冷原子阵列的光散射，我们显示出相位匹配的条件随着系统维数的减小而改变。特别是，对于单个原子链，在圆锥体中围绕阵列的对称轴存在相位匹配的反射散射，该散射与链中原子数的平方成比例。对于两个原子链，由于布拉格散射，可以增强或减小相位匹配的反射散射。这种散射可用于将中性原子阵列中的集体状态映射到传播的光场上，并用于在分离的阵列之间建立量子链接。