Hybrid two-mode squeezing of optical and microwave modes with inbuilt quantum memory

The field of hybrid optical-microwave technology is advancing rapidly, driven by goals such as integrating telecom wavelength optical fiber networks with superconducting circuit-based quantum technology. We present a new protocol for generating entanglement between microwave and optical modes, with an inbuilt quantum memory. The protocol, hybrid Rephased Amplified Spontaneous Emission (RASE), first creates entanglement between a spontaneously emitted photonic mode and an atomic ensemble. The atomic coherence is then mapped to a long-lived nuclear spin transition before being rephased to generate a second photonic mode. We analyse the performance of the protocol for erbium ensembles in crystals, which exhibit narrow transitions at both microwave and optical frequencies. Such materials also possess nuclear-spin coherence times among the longest in the solid state. We describe the theoretical framework to optimize the time-separated, hybrid two-mode squeezed state toward efficient, high bandwidth, and high rate entanglement generation. We will also discuss initial steps toward realizing this protocol experimentally, such as on-chip superconducting resonators for coupling to ensembles of erbium electron spins.