The exchange of off-resonant propagating photons between distant quantum emitters induces coherent interactions among them. The range of such interactions, and whether they are accompanied by dissipation, depends on the photonic energy dispersion, its dimensionality, and/or the light-matter couplings. We characterize the limits of photon-mediated interactions for the case of generic one-dimensional photonic baths under the typical assumptions, i.e., finite range hoppings for the photonic bath plus local and rotating-wave light-matter couplings. In that case, we show how, irrespective of the system's parameter, the coherent photon-mediated interactions can always be written as a finite sum of exponentials and thus cannot display a power-law asymptotic scaling. As an outlook, we show how by relaxing some of these conditions, e.g., going beyond local light-matter couplings (e.g., giant atoms) or with longer-range photon hopping models, power-law interactions can be obtained within certain distance windows or even in the asymptotic regime for the latter case.

中文翻译：

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一维光子浴中光子介导相互作用的极限

遥远的量子发射器之间非共振传播光子的交换引起它们之间的相干相互作用。这种相互作用的范围以及它们是否伴随耗散，取决于光子能量的色散，其尺寸和/或光-质耦合。在典型的假设下，我们描述了一般一维光子浴的光子介导相互作用的极限，即光子浴的有限范围跳变以及局部和旋转波光-质耦合。在那种情况下，我们说明了无论系统参数如何，相干光子介导的相互作用始终可以写成指数的有限总和，从而不能显示幂律渐近标度。展望未来，我们展示了如何通过放松其中的某些条件，例如，