  We propose a new mechanism to produce ultracold polar molecules with
microwave fields. The proposed mechanism converts trapped ultracold atoms of
different species into vibrationally excited molecules by a single microwave
transition and entirely depends on the existence of a permanent dipole moment
in the molecules. As opposed to production of molecules by photoassociation or
magnetic-field Feshbach resonances our method does not rely on the structure
and lifetime of excited states or existence of Feshbach resonances. In
addition, we determine conditions for optimal creation of polar molecules in
vibrationally excited states of the ground-state potential by changing
frequency and intensity of the microwave field. We also explore the possibility
to produce vibrationally cold molecules by combining the microwave field with
an optical Raman transition or by applying a microwave field to Feshbach
molecules. The production mechanism is illustrated for two polar molecules: KRb
and RbCs.
