Ensembles of atoms or other quantum emitters are envisioned to be an important component of quantum applications, ranging from quantum memories for light to photon-photon gates to metrology. It has historically been an outstanding challenge to exactly solve for the quantum dynamics of an optical field as it propagates through and interacts with an ensemble. The standard axiomatic approach is to use the one-dimensional Maxwell-Bloch equations, which assume that excited atoms emit independently into unwanted directions. This ignores the wave interference of the emitted light, which depends on correlations between the atoms.
Here, we discuss an alternative theoretical approach, which accounts for interference and the precise atomic positions. In this formalism, an interacting quantum spin model describes the dynamics of the atomic internal degrees of freedom under multiple photon scattering, while the field properties can subsequently be re-constructed from the spin correlations. Using this model, we then show how interference can be exploited as an extremely powerful resource to suppress the unwanted emission of light and the subsequent loss of information into undesirable directions. The effects of interference are particularly prominent in ordered arrays of emitters. For example, it can be shown that an array acts as a perfectly lossless waveguide for light, in direct analogy to a conventional photonic crystal waveguide. By exploiting this concept, we derive a novel protocol for a quantum memory for light, whose error probability as a function of optical depth scales exponentially better than previously known bounds.
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