  Stronger constraints on the pseudoscalar coupling constants of an axion and
axion-like particles with a proton and a neutron are obtained from measurements
of the thermal Casimir-Polder force between a Bose-Einstein condensate of
$^{87}$Rb atoms and a SiO$_2$ plate. For this purpose the additional force
acting between a condensate cloud and a plate due to two-axion exchange is
calculated. The obtained constraints refer to the axion masses from 0.1meV to
0.3eV which overlap with the region from 0.01meV to 10meV considered at the
moment as the most prospective.
