A theoretical analysis of extending frequency-bin entanglement from photon-photon to atom-photon hybrid systems

Inspired by the recent developments in the research of atom-photon quantum interface and energy-time entanglement between single photon pulses, we propose to establish the concept of a special energy-time entanglement between a single photon pulse and internal states of a single atom, which is analogous to the frequency-bin entanglement between single photon pulses. We show that this type of entanglement arises naturally in the interaction between frequency-bin entangled single photon pulse pair and a single atom, via straightforward atom-photon phase gate operations. We also discuss the properties of this type of entanglement and show a preliminary example of its potential application in quantum networking. Moreover, a quantum entanglement witness is constructed to detect such entanglement from a reasonably large set of separable states.