Exponential Improvement in Photon Storage Fidelities Using Subradiance and "Selective Radiance" in Atomic Arrays

A central goal within quantum optics is to realize efficient, controlled interactions between photons and atomic media. A fundamental limit in nearly all applications based on such systems arises from spontaneous emission, in which photons are absorbed by atoms and then rescattered into undesired channels. In typical theoretical treatments of atomic ensembles, it is assumed that this rescattering occurs independently, and at a rate given by a single isolated atom, which in turn gives rise to standard limits of fidelity in applications such as quantum memories for light or photonic quantum gates. However, this assumption can in fact be dramatically violated. In particular, it has long been known that spontaneous emission of a collective atomic excitation can be significantly suppressed through strong interference in emission between atoms. While this concept of "subradiance" is not new, thus far the techniques to exploit the effect have not been well understood. In this work, we provide a comprehensive treatment of this problem. First, we show that in ordered atomic arrays in free space, subradiant states acquire an elegant interpretation in terms of optical modes that are guided by the array, which only emit due to scattering from the ends of the finite system. We also go beyond the typically studied regime of a single atomic excitation and elucidate the properties of subradiant states in the many-excitation limit. Finally, we introduce the new concept of "selective radiance." Whereas subradiant states experience a reduced coupling to all optical modes, selectively radiant states are tailored to simultaneously radiate efficiently into a desired channel while scattering into undesired channels is suppressed, thus enabling an enhanced atom-light interface. We show that these states naturally appear in chains of atoms coupled to nanophotonic structures, and we analyze the performance of photon storage exploiting such states. We find numerically that selectively radiant states allow for a photon storage error that scales exponentially better with the number of atoms than previously known bounds.