Dephasing channel for predictive modeling of spin-motion entanglement in blockaded Rydberg atom quantum simulation

In Rydberg atom arrays, Hamiltonians engineered in the perturbative regime of strong Rydberg interactions can develop entanglement with motional degrees of freedom. The entanglement between spin and motion leads to effective dephasing of the internal spin dynamics, even when atoms are initially prepared in their motional ground states. Moreover, due to the inherent complexity of the motional Hilbert space, numerical modeling of this dephasing effect poses significant challenges. In this talk, we propose an effective quantum channel designed to accurately and efficiently model dephasing effects in internal dynamics under Rydberg blockade. First, to describe the details of the model, we present the theoretical foundations of the channel and show how they generate a closed analytical operator acting upon the Liouville space of reduced spin density states, without reference to the enormous motional Hilbert space of the problem. Then, we compare the channel accuracy and speed against exact numerical simulation of small systems. Finally, we use the channel to quantify the performance of a prototypical entanglement distribution experiment in a Rydberg chain. Through this analysis, we demonstrate the advantages of our channel in optimizing control parameters, ultimately facilitating the modeling of motional dephasing effects in Rydberg chains and the synthesis of robust optimal control pulses.