  Spectral hole burning reduces sodium laser guide star efficiency. Due to
photon recoil, atoms that are initially resonant with the single-frequency
laser get Doppler shifted out of resonance, which reduces the return flux.
Frequency-chirped (also known as frequency-swept) continuous-wave lasers have
the potential to mitigate the effect of spectral hole burning and even increase
the laser guide star efficiency beyond the theoretical limit of a
single-frequency laser. On-sky measurements of a frequency-chirped,
single-frequency laser guide star are performed at the Roque de los Muchachos
Observatory on La Palma. In the experiment, a 35-cm telescope and a fast photon
counting receiver system are employed to resolve the return flux response
during laser frequency sweeps gaining insights into the population dynamics of
the sodium layer. At a launched laser power of 16.5 W, we find a maximum gain
in return flux of 22\% compared to a fixed-frequency laser. Our results suggest
a strong dependence of chirping gain on power density at the mesosphere, i.e.
laser power and seeing. Maximum gains are recorded at a chirping amplitude on
the order of 150 MHz and a chirping rate of 0.8 MHz $\mu$s$^{-1}$, as predicted
by theory. Time-resolved measurements during the chirping period confirm our
understanding of the population dynamics in the sodium layer. To our knowledge
these are the first measurements of return flux enhancement for laser guide
stars excited by a single frequency-chirped continuous-wave laser. For higher
laser powers, the effectiveness of chirping is expected to increase, which
could be highly beneficial for telescopes equipped with high-power laser guide
star adaptive optics systems, also for emerging space awareness applications
using laser guide stars such as satellite imaging and ground-to-space optical
communications.
