  The fidelity of gate operations on neutral atom qubits is often limited by
fluctuations of the laser drive. Here, we quantify the sensitivity of quantum
gate fidelities to laser phase and intensity noise. We first develop models to
identify features observed in laser self-heterodyne noise spectra, focusing on
the effects of white noise and servo bumps. In the weak-noise regime,
characteristic of well-stabilized lasers, we show that an analytical theory
based on a perturbative solution of a master equation agrees very well with
numerical simulations that incorporate phase noise. We compute quantum gate
fidelities for one- and two-photon Rabi oscillations and show that they can be
enhanced by an appropriate choice of Rabi frequency relative to spectral noise
peaks. We also analyze the influence of intensity noise with spectral support
smaller than the Rabi frequency. Our results establish requirements on laser
noise levels needed to achieve desired gate fidelities.
