Entanglement transfer from a many atom Rydberg W state to a multimode photonic cavity state

A robust quantum protocol is realized that achieves high fidelity transfer from a 3-atom Rydberg system initialized in a W state (|rrg>+|rgr>+|grr>)/√3 to an equivalent photonic W state (|110>+|101>+|011>)/√3 in a multimode cavity. The challenge of achieving transfer is addressed by dynamically adjusting the cavity mode frequencies and modulating the coupling rates to restrict the transfer dynamics to a sequence of avoided crossings. Our two-step protocol effectively reduces the complex problem of multimode transfer with 3 atoms to a sequence of highly efficient two-level avoided crossing problems. The fractional STIRAP method, featuring Gaussian modulation of the coupling rates and linearly chirping of the cavity frequencies, is used to execute partial and complete population transfers at individual stages of the entanglement transfer process. Exact expressions for the non-adiabatic transition probability are derived using the Dykhne formula. Moreover, we propose practical approaches for realizing our protocol in the lab.