Atom-photon entanglement transfer using a 3-D multimode cavity with a single uniformly moving mirror

A scheme is developed to generate efficient coherent transfer from the Rydberg atomic W state to the photonic W state, 1 /√3 (|rrg〉+|rgr〉+|grr〉)⊗|000〉→1 /√3(|ggg〉⊗(|110〉+|101〉+|011〉), using a single multimode cavity. Each mode is selected to be initially resonant with a Rydberg to ground state transition for a single 3 atom configuration and is linear chirped to gradually transfer population from the Rydberg to ground states over a 1 ns interval. A theoretical model of the 3-dimensional cubical cavity with a single slow uniformly moving mirror is used as a template to derive the spatial modes and interaction Hamiltonian for the chirped cavity modes. The problem of realizing the |ggg〉⊗|011〉 component has been solved by chirping each of the 3 cavity modes such that mode 2 will be resonant with the lowest energy transition at a time T₁ when half of the |rrg〉,|grr〉 initial populations are depleted through interaction with mode 3. High fidelity atom-photon transfers require optimal selection of cavity parameters involving the mode numbers, chirp rates, time delays, and mode coupling rates in order to control inter-mode coupling processes and suppress repopulation of the Rydberg state. The determination of these parameters is a quantum control problem; we solved it using parametric optimization for the total state by means of the Laplace transformed integro-differential equation for the wavefunction.