Quantum Noise for Faraday Light Matter Interfaces

In light matter interfaces based on the Faraday effect quite a number of quantum information protocols have been successfully demonstrated. In order to further increase the performance and fidelities achieved in these protocols a deeper understanding of the relevant noise and decoherence processes needs to be gained. In this article we provide for the first time a complete description of the decoherence from spontaneous emission. We derive from first principles the effects of photons being spontaneously emitted into unobserved modes. Our results relate the resulting decay and noise terms in effective equations of motion for collective atomic spins and the forward propagating light modes to the full atomic level structure. We illustrate and apply our results to the case of a quantum memory protocol. Our results can be applied to any suitable atomic species, and the general approach taken in this article can be applied to light matter interfaces and quantum memories based on different mechanisms.