  We show that it is possible to realize simultaneous Raman lasing at two
different frequencies using a double-$\Lambda$ system pumped by a bi-frequency
field. The Raman lasers are phase-locked to one another, and the beat-frequency
matches the energy difference between the two meta-stable ground states. Akin
to a conventional Raman laser, the phase-locked Raman laser pair is expected to
be subluminal. As such, it is expected to be highly stable against
perturbations in cavity length, and have a quantum noise limited linewidth that
is far below that of a conventional laser. Because of these properties, the
phase-locked Raman laser pair may find important applications in precision
metrology, including atomic interferometry and magnetometry. To elucidate the
behavior of this laser pair, we develop an analytical model that describes the
stimulated Raman interaction in a double-$\Lambda$ system using an effective
2-level transition. The approximation is valid as long as the excited states
adiabatically follow the ground states, as verified by numerical simulations.
The effective model is used to identify the optimal operating conditions for
the bi-frequency Raman lasing process. This model may also prove useful in
other potential applications of the double-$\Lambda$ system, including
generation of squeezed light and spatial solitons.
