Many precision laser applications require active frequency stabilization.
However, such stabilization loops operate by pushing noise to frequencies
outside their bandwidth, leading to large "servo bumps" that can have
deleterious effects for certain applications. The prevailing approach to
filtering this noise is to pass the laser through a high finesse optical
cavity, which places constraints on the system design. Here, we propose and
demonstrate a different approach where a frequency error signal is derived from
a beat note between the laser and the light that passes through the reference
cavity. The phase noise derived from this beat note is fed forward to an
electro-optic modulator after the laser, carefully accounting for relative
delay, for real-time frequency correction. With a Hz-linewidth laser, we show
≳20 dB noise suppression at the peak of the servo bump (≈250
kHz), and a noise suppression bandwidth of ≈5 MHz -- well beyond the
servo bump. By simulating the Rabi dynamics of a two-level atom with our
measured data, we demonstrate substantial improvements to the pulse fidelity
over a wide range of Rabi frequencies. Our approach offers a simple and
versatile method for obtaining a clean spectrum of a narrow linewidth laser, as
required in many emerging applications of cold atoms, and is readily compatible
with commercial systems that may even include wavelength conversion