  Technical noise present in laser systems can limit their ability to perform
high fidelity quantum control of atomic qubits. The ultimate fidelity floor for
atomic qubits driven with laser radiation is due to spontaneous emission from
excited energy levels. The goal is to suppress the technical noise from the
laser source to below the spontaneous emission floor such that it is no longer
a limiting factor. It has been shown that the spectral structure of control
noise can have a large influence on achievable control fidelities, while prior
studies of laser noise contributions have been restricted to noise magnitudes.
Here, we study the unique spectral structure of laser noise and introduce a new
metric that determines when a stabilised laser source has been optimised for
quantum control of atomic qubits. We find requirements on stabilisation
bandwidths that can be orders of magnitude higher than those required to simply
narrow the linewidth of a laser. We introduce a new metric, the
$\chi$-separation line, that provides a tool for the study and engineering of
laser sources for quantum control of atomic qubits below the spontaneous
emission floor.
