Feasibility of extracting the proton weak charge from quantum-control measurements of atomic parity violation on the $2s-3s$ or $2s-4s$ transition in hydrogen

We explore the feasibility of extracting electroweak observables from a measurement of atomic parity violation in hydrogen. Our proposed quantum-control scheme focuses on the $2s-3s$ or $2s-4s$ transitions in hydrogen. This work is motivated by the recently observed anomaly in the W-boson mass, which may substantially modify the Standard Model value of the proton weak charge. We also study the accuracy of the previously employed approximations in computing parity-violating effects in hydrogen.