  The pursuit of compact lasers with low-thresholds has imposed strict
requirements on tight light confinements with minimized radiation losses. Bound
states in the continuum (BICs) have been recently demonstrated as an effective
mechanism to trap light along the out-of-plane direction, paving the way to
low-threshold lasers. To date, most reported BIC lasers are still bulky due to
the absence of in-plane light confinement. In this work, we combine BICs and
photonic band gaps to realize three-dimensional (3D) light confinements, as
referred to miniaturized (mini-) BICs. Together with 3D carrier confinements
provided by quantum dots (QDs) as optical gain materials, we have realized
highly-compact active BIC resonators with a record-high quality ($Q$) factor up
to 32500, which enables single-mode continuous wave (CW) lasing with the lowest
threshold of 80 W/cm$^{2}$ among the reported BIC lasers. In addidtion, our
photon statistics measurements under both CW and pulsed excitations confirm the
occurence of the phase transition from spontaneous emission to stimulated
emission, further suggesting that conventional criteria of input-output and
linewidth are not sufficient for claiming nanoscale lasing. Our work reveal a
via path towards compact BIC lasers with ultra-low power consumption and
potentially boost the applications in cavity quantum electrodynamics (QEDs),
nonlinear optics and integrated photonics.
