Recapture Probability for anti-trapped Rydberg states in optical tweezers

In a neutral atom quantum computer, the qubits are individual neutral atoms trapped in optical tweezers. Excitations to Rydberg states form the basis for the entanglement procedure that is at the basis of multi-qubit quantum gates. However, these Rydberg atoms are often anti-trapped, leading to decoherence and atom loss. In this work, we give a quantum mechanical description of the anti-trapping loss rates and determine the recapture probability after Rydberg excitation, distinguishing between having the laser traps turned on and off. We find that there is ample time ($\approx$ 30 $\mu$s, in a Strontium-88 system) needed for the wave functions to expand out off the trap. Therefore, even with traps on, $\approx$ 100% recapture probabilities can be expected for times in which significant entanglement operations between atoms can be performed. We find that for 2D radial traps with bosonic Strontium-88 atoms, the time in which perfect recapture can be achieved, is of the same order of magnitude for traps on, and off.