In this paper, we experimentally demonstrate a strong correlation
between the frequencies of the Raman pump and the Raman probe inside
an optically pumped Raman laser. We show that the correlation is due
to rapid adjustment of the phase of the dipoles that produce the Raman
gain, following a sudden jump in the phase of the Raman pump. A
detailed numerical model validates this interpretation of the phase
correlation. The width of the spectrum of the beat between the Raman
pump and the Raman laser is significantly narrowed due to this
correlation. As a result, the minimum measurable change in the cavity
length, for a given linewidth of the Raman pump laser, is
substantially reduced. Therefore, this finding is expected to enhance
the sensitivity of such a laser in various metrological applications
(e.g., accelerometry).