Cavity optomechanical quantum memory for twisted photons using a ring Bose-Einstein condensate

We theoretically propose a photonic orbital angular momentum quantum memory, currently of great interest from the perspective of quantum networks, based on a ring-trapped Bose-Einstein condensate interacting with Laguerre-Gaussian beams. The optical states are stored in the large Hilbert space of topologically protected persistent currents of the condensate. In contrast to earlier work, our proposal uses a cavity, which enhances the light-matter interaction by several orders of magnitude, resulting in high fidelity, convenient detection, and no need to repeat read-write cycles degraded by atom loss. Our scheme avoids using multiple internal atomic states as in generic electromagnetically induced transparency-based protocols and thus bypasses problems like off-resonant photoassociation by the control fields and dephasing effects that limit memory storage time. For optimized parameters, our work yields a storage time 3 orders of magnitude better than presently available and opens the way for exploiting existing advantages of cavity-based noise suppression, wavelength transduction, large bandwidth, and nondestructive readout of the memory.