  It is suggested that direct evidence of Bose-Einstein condensation of alpha
particles is obtained by observing a phase mode (Nambu-Goldstone boson) with
long wavelength even when characteristic features such as superfluidity is
diffucult to observe. For the 7.65 MeV $0_2^+$ Hoyle state in $^{12}$C and 15.1
MeV $0^+$ state in $^{16}$O, which are candidates for an alpha particle
condensate, it is suggested that the emergent band head $0^+$ state of the
$K=0_2^+$ rotational band with a very large moment of inertia is considered to
be a Nambu-Goldstone boson.
